比特派app官方下载网站安卓|interference

作者：比特派app官方下载网站安卓

2024-03-13 01:19:31

Interference | Definition, Examples, & Facts | Britannica

Search Britannica

Click here to search

Search Britannica

Click here to search

Home

Games & Quizzes

History & Society

Science & Tech

Biographies

Animals & Nature

Geography & Travel

Arts & Culture

Money

Videos

On This Day

One Good Fact

Dictionary

New Articles

History & Society

Lifestyles & Social Issues

Philosophy & Religion

Politics, Law & Government

World History

Science & Tech

Health & Medicine

Science

Technology

Biographies

Browse Biographies

Animals & Nature

Birds, Reptiles & Other Vertebrates

Bugs, Mollusks & Other Invertebrates

Environment

Fossils & Geologic Time

Mammals

Plants

Geography & Travel

Arts & Culture

Entertainment & Pop Culture

Literature

Sports & Recreation

Visual Arts

Companions

Demystified

Image Galleries

Infographics

Lists

Podcasts

Spotlights

Summaries

The Forum

Interference Definition & Meaning - Merriam-Webster

Menu Toggle

Merriam-Webster Logo

Games & Quizzes

Word of the Day

Grammar

Wordplay

Word Finder

Thesaurus

Join MWU

Shop

Books

Merch

Settings

My Words

Recents

Account

Log Out

Thesaurus

Join MWU

Shop

Books

Merch

Username

My Words

Recents

Account

Log Out

Est. 1828

Dictionary

Definition

Synonyms

Example Sentences

Word History

Phrases Containing

Entries Near

Cite this EntryCitation

Kids DefinitionKids

Medical DefinitionMedical

Legal DefinitionLegal

Interference of Waves - Interference Definition, Derivation, Review Question, Video and FAQs

Login Study MaterialsNCERT SolutionsNCERT Solutions For Class 12 NCERT Solutions For Class 12 PhysicsNCERT Solutions For Class 12 ChemistryNCERT Solutions For Class 12 BiologyNCERT Solutions For Class 12 MathsNCERT Solutions Class 12 AccountancyNCERT Solutions Class 12 Business StudiesNCERT Solutions Class 12 EconomicsNCERT Solutions Class 12 Accountancy Part 1NCERT Solutions Class 12 Accountancy Part 2NCERT Solutions Class 12 Micro-EconomicsNCERT Solutions Class 12 CommerceNCERT Solutions Class 12 Macro-EconomicsNCERT Solutions For Class 11 NCERT Solutions For Class 11 PhysicsNCERT Solutions For Class 11 ChemistryNCERT Solutions For Class 11 BiologyNCERT Solutions For Class 11 MathsNCERT Solutions Class 11 AccountancyNCERT Solutions Class 11 Business StudiesNCERT Solutions Class 11 EconomicsNCERT Solutions Class 11 StatisticsNCERT Solutions Class 11 CommerceNCERT Solutions For Class 10 NCERT Solutions for Class 10 Social ScienceNCERT Solutions for Class 10 Maths NCERT Solutions for Class 10 Maths Chapter 1NCERT Solutions for Class 10 Maths Chapter 2NCERT Solutions for Class 10 Maths Chapter 3NCERT Solutions for Class 10 Maths Chapter 4NCERT Solutions for Class 10 Maths Chapter 5NCERT Solutions for Class 10 Maths Chapter 6NCERT Solutions for Class 10 Maths Chapter 7NCERT Solutions for Class 10 Maths Chapter 8NCERT Solutions for Class 10 Maths Chapter 9NCERT Solutions for Class 10 Maths Chapter 10NCERT Solutions for Class 10 Maths Chapter 11NCERT Solutions for Class 10 Maths Chapter 12NCERT Solutions for Class 10 Maths Chapter 13NCERT Solutions for Class 10 Maths Chapter 14NCERT Solutions for Class 10 Maths Chapter 15MoreNCERT Solutions for Class 10 Science NCERT Solutions for Class 10 Science Chapter 1NCERT Solutions for Class 10 Science Chapter 2NCERT Solutions for Class 10 Science Chapter 3NCERT Solutions for Class 10 Science Chapter 4NCERT Solutions for Class 10 Science Chapter 5NCERT Solutions for Class 10 Science Chapter 6NCERT Solutions for Class 10 Science Chapter 7NCERT Solutions for Class 10 Science Chapter 8NCERT Solutions for Class 10 Science Chapter 9NCERT Solutions for Class 10 Science Chapter 10NCERT Solutions for Class 10 Science Chapter 11NCERT Solutions for Class 10 Science Chapter 12NCERT Solutions for Class 10 Science Chapter 13NCERT Solutions for Class 10 Science Chapter 14NCERT Solutions for Class 10 Science Chapter 15NCERT Solutions for Class 10 Science Chapter 16MoreNCERT Solutions For Class 9 NCERT Solutions For Class 9 Social ScienceNCERT Solutions For Class 9 Maths NCERT Solutions For Class 9 Maths Chapter 1NCERT Solutions For Class 9 Maths Chapter 2NCERT Solutions For Class 9 Maths Chapter 3NCERT Solutions For Class 9 Maths Chapter 4NCERT Solutions For Class 9 Maths Chapter 5NCERT Solutions For Class 9 Maths Chapter 6NCERT Solutions For Class 9 Maths Chapter 7NCERT Solutions For Class 9 Maths Chapter 8NCERT Solutions For Class 9 Maths Chapter 9NCERT Solutions For Class 9 Maths Chapter 10NCERT Solutions For Class 9 Maths Chapter 11NCERT Solutions For Class 9 Maths Chapter 12NCERT Solutions For Class 9 Maths Chapter 13NCERT Solutions For Class 9 Maths Chapter 14NCERT Solutions For Class 9 Maths Chapter 15MoreNCERT Solutions For Class 9 Science NCERT Solutions for Class 9 Science Chapter 1NCERT Solutions for Class 9 Science Chapter 2NCERT Solutions for Class 9 Science Chapter 3NCERT Solutions for Class 9 Science Chapter 4NCERT Solutions for Class 9 Science Chapter 5NCERT Solutions for Class 9 Science Chapter 6NCERT Solutions for Class 9 Science Chapter 7NCERT Solutions for Class 9 Science Chapter 8NCERT Solutions for Class 9 Science Chapter 9NCERT Solutions for Class 9 Science Chapter 10NCERT Solutions for Class 9 Science Chapter 11NCERT Solutions for Class 9 Science Chapter 12NCERT Solutions for Class 9 Science Chapter 13NCERT Solutions for Class 9 Science Chapter 14NCERT Solutions for Class 9 Science Chapter 15MoreNCERT Solutions For Class 8 NCERT Solutions For Class 8 MathsNCERT Solutions For Class 8 ScienceNCERT Solutions for Class 8 Social ScienceNCERT Solutions for Class 8 EnglishNCERT Solutions For Class 7 NCERT Solutions For Class 7 MathsNCERT Solutions For Class 7 ScienceNCERT Solutions for Class 7 Social ScienceNCERT Solutions for Class 7 EnglishNCERT Solutions For Class 6 NCERT Solutions For Class 6 MathsNCERT Solutions For Class 6 ScienceNCERT Solutions For Class 6 Social ScienceNCERT Solutions for Class 6 EnglishNCERT Solutions For Class 5 NCERT Solutions For Class 5 MathsNCERT Solutions For Class 5 EVSNCERT Solutions For Class 4 NCERT Solutions For Class 4 MathsNCERT Solutions For Class 4 EVSNCERT Solutions For Class 3 NCERT Solutions For Class 3 MathsNCERT Solutions For Class 3 EVSNCERT Solutions For Class 3 EnglishNCERT Solutions For Class 2 NCERT Solutions For Class 2 MathsNCERT Solutions For Class 2 EnglishNCERT Solutions For Class 1 NCERT Solutions For Class 1 MathsNCERT Solutions For Class 1 EnglishNCERTNCERT SyllabusClassesClass 1 - 3Class 4 - 5Class 6 - 10CBSENCERT Books NCERT Books for Class 5NCERT Books Class 6NCERT Books for Class 7NCERT Books for Class 8NCERT Books for Class 9NCERT Books for Class 10NCERT Books for Class 11NCERT Books for Class 12NCERT Exemplar NCERT Exemplar Class 8NCERT Exemplar Class 9NCERT Exemplar Class 10NCERT Exemplar Class 11NCERT Exemplar Class 12RD Sharma RD Sharma Class 6 SolutionsRD Sharma Class 7 SolutionsRD Sharma Class 8 SolutionsRD Sharma Class 9 SolutionsRD Sharma Class 10 SolutionsRD Sharma Class 11 SolutionsRD Sharma Class 12 SolutionsPHYSICS MechanicsOpticsThermodynamicsElectromagnetismFamous PhysicistsUnit ConversionKirchhoff's LawsFaraday's LawLaws of MotionRefraction of LightMaxwell's EquationElectrostaticsBernoulli's PrincipleProjectile MotionElectric ChargePhysics SymbolsMoreCHEMISTRY Periodic TableStereochemistryOrganic CompoundsInorganic ChemistryQuantum NumbersAtomic Mass of ElementsPeriodic Properties of Elements118 Elements and Their SymbolsBalancing Chemical EquationsSalt AnalysisAcids, Bases, and SaltsBenzeneOrganometallic CompoundsAtomic Number and Mass NumberMoreMATHS Pythagoras TheoremPrime NumbersProbability and StatisticsFractionsSetsTrigonometric FunctionsRelations and FunctionsSequence and SeriesMultiplication TablesDeterminants and MatricesProfit And LossPolynomial EquationsDividing FractionsSocial Science Manufacturing IndustriesSahara DesertAmazon RiverIndian TribesMughal DynastyMonuments of India ListJudiciaryAutocratic MeaningFundamental Rights of IndiaUnion Territories of IndiaCapitals of Seven Sisters of IndiaMost Populated States In IndiaBIOLOGY MicrobiologyEcologyZoologyPhotosynthesisFORMULAS Maths FormulasAlgebra FormulasTrigonometry FormulasGeometry FormulasCBSE Sample Papers CBSE Sample Papers for Class 6CBSE Sample Papers for Class 7CBSE Sample Papers for Class 8CBSE Sample Papers for Class 9CBSE Sample Papers for Class 10CBSE Sample Papers for Class 11CBSE Sample Papers for Class 12CBSE Previous Year Question Paper CBSE Previous Year Question Papers Class 10CBSE Previous Year Question Papers Class 12Lakhmir Singh Solutions Lakhmir Singh Class 9 SolutionsLakhmir Singh Class 10 SolutionsLakhmir Singh Class 8 SolutionsCBSE Notes Class 6 CBSE NotesClass 7 CBSE NotesClass 8 CBSE NotesClass 9 CBSE NotesClass 10 CBSE NotesClass 11 CBSE NotesClass 12 CBSE NotesCBSE Revision Notes CBSE Class 9 Revision NotesCBSE Class 10 Revision NotesCBSE Class 11 Revision NotesCBSE Class 12 Revision NotesCBSE Extra Questions CBSE Class 8 Maths Extra QuestionsCBSE Class 8 Science Extra QuestionsCBSE Class 9 Maths Extra QuestionsCBSE Class 9 Science Extra QuestionsCBSE Class 10 Maths Extra QuestionsCBSE Class 10 Science Extra QuestionsCBSE Class Class 3Class 4Class 5Class 6Class 7Class 8Class 9Class 10Class 11Class 12Textbook SolutionsCalculatorsBasic Calculators Percentage CalculatorLoan CalculatorEmi CalculatorFraction CalculatorAlgebra CalculatorFactoring CalculatorDistance CalculatorPercentage Increase CalculatorSquare Footage CalculatorSquare Root CalculatorPercentage Change CalculatorRatio CalculatorTriangle CalculatorFractions CalculatorArea CalculatorPercentage Difference CalculatorPercentage Off CalculatorScientific Notation CalculatorSimple Interest CalculatorEquation CalculatorLcm CalculatorRounding CalculatorLong Division CalculatorMixed Fraction CalculatorMoreMaths Calculators Compound Interest CalculatorIntegral CalculatorDerivative CalculatorGraphing CalculatorStandard Deviation CalculatorLimit CalculatorBinary CalculatorMatrix CalculatorCp CalculatorDiscount CalculatorAntiderivative CalculatorExponents CalculatorProbability CalculatorSample Size CalculatorSlope CalculatorArea Of A Circle CalculatorCircumference CalculatorCombination CalculatorInverse Matrix CalculatorMod CalculatorPythagorean Theorem CalculatorConfidence Interval CalculatorDouble Integral CalculatorMatrix Multiplication CalculatorInverse Function CalculatorVolume CalculatorVolume Of A Cylinder CalculatorZ Score CalculatorVariance CalculatorMorePhysics Calculators Power CalculatorVoltage Drop CalculatorChemistry Calculators Molarity CalculatorCommerceClass 11 Commerce Syllabus Class 11 Accountancy SyllabusClass 11 Business Studies SyllabusClass 11 Economics SyllabusClass 12 Commerce Syllabus Class 12 Accountancy SyllabusClass 12 Business Studies SyllabusClass 12 Economics SyllabusCommerce Sample Papers Class 11 Commerce Sample PapersClass 12 Commerce Sample PapersTS Grewal Solutions TS Grewal Solutions Class 12 AccountancyTS Grewal Solutions Class 11 AccountancyStatement Of Cash FlowsWhat Is EntrepreneurshipConsumer ProtectionWhat Is A Fixed AssetWhat Is A Balance SheetWhat Is Fiscal DeficitWhat Are Equity SharesDifference Between Selling And MarketingICSEICSE Sample PapersICSE Question PapersML Aggarwal Solutions ML Aggarwal Solutions Class 10 MathsML Aggarwal Solutions Class 9 MathsML Aggarwal Solutions Class 8 MathsML Aggarwal Solutions Class 7 MathsML Aggarwal Solutions Class 6 MathsSelina Solutions Selina Solution for Class 8Selina Solutions for Class 10Selina Solution for Class 9Frank Solutions Frank Solutions for Class 10 MathsFrank Solutions for Class 9 MathsICSE Class ICSE Class 6ICSE Class 7ICSE Class 8ICSE Class 9ICSE Class 10ISC Class 11ISC Class 12IASIAS ExamUPSC ExamCivil Service ExamUPSC SyllabusIAS TopperFree IAS PrepUPSC Results UPSC Prelims ResultUPSC Mains ResultCurrent Affairs List of Current Affairs ArticlesList Of IAS ArticlesPublic Service Commission KPSC KAS ExamUPPSC PCS ExamMPSC ExamRPSC RAS ExamTNPSC Group 1APPSC Group 1BPSC ExamWBPSC ExamMPPSC ExamJPSC ExamGPSC ExamUPSC Question Papers UPSC Prelims 2022 Question PaperUPSC Prelims 2022 Answer KeyIAS Coaching IAS Coaching BangaloreIAS Coaching DelhiIAS Coaching ChennaiIAS Coaching HyderabadIAS Coaching MumbaiBest IAS coaching ChennaiBest IAS coaching BangaloreBest IAS coaching DelhiIAS QuestionsJEEJEE 2024NMTC 2023 Question PapersNMTC 2023 Sub Junior DivisionNMTC 2023 Primary DivisionNMTC 2023 Junior DivisionJEE 2023JEE Test SeriesJEE Advanced 2023JEE Advanced 2023 Question PaperJEE Advanced 2023 Paper AnalysisJEE Advanced 2022 Question PaperJEE Advanced Question PapersJEE Advanced Answer KeysJEE Advanced ResultsJEE Advanced Marks vs RankJEE Advanced Rank PredictorJEE Advanced Paper AnalysisJEE Main 2024JEE Main 2024 Mock TestJEE Main 2023 Question PapersJEE Main Toppers List 2023JEE Main 2023 Paper AnalysisJEE Main 2022 Question PapersJEE Main 2022 Paper AnalysisJEE Main Rank PredictorJEE Main ResultsJEE Sample PaperJEE Question PaperJEE Main Answer KeyBinomial TheoremJEE ArticlesQuadratic EquationJEE QuestionsNEETNEET 2024NEET 2023NEET Registration 2023NEET Admit CardNEET Test SeriesNEET 2023 Question PaperNEET 2023 Answer KeyNEET 2023 Question Paper AnalysisNEET 2022 Question PaperNEET 2022 Answer KeyNEET 2022 Question paper analysisNEET 2022 ResultsNEET Eligibility CriteriaNEET Question PapersNEET Sample PapersNEET PreparationNEET SyllabusNEET QuestionsGATE 2024GATEGATE Previous Year Question PapersGATE Syllabus GATE Syllabus For CSEGATE Syllabus For ECEGATE Syllabus For Civil EngineeringGATE Syllabus For Mechanical EngineeringGATE Aptitude SyllabusGATE Study Material GATE Notes For CSEGATE Difference Between ArticlesGATE FAQsOlympiad ExamsMaths OlympiadScience OlympiadEntrance Exams In IndiaCOMED-K COMED-K SyllabusCOMED-K Previous Year Question PapersCOMED-K Sample PapersKCET KCET SyllabusKCET Question PapersWBJEE WBJEE SyllabusWBJEE Question PapersGUJCET GUJCET SyllabusGUJCET Question PapersKVPY KVPY SyllabusMHT-CET MHT-CET SyllabusNSTSE NSTSE SyllabusNTSE NTSE SyllabusNTSE Question PaperBCECE BCECE SyllabusUPSEE UPSEE SyllabusGCETHPCETKEAMState BoardsGSEB GSEB SyllabusGSEB Question PaperGSEB Sample PaperGSEB BooksMSBSHSE MSBSHSE SyllabusMSBSHSE TextbooksMSBSHSE Sample PapersMSBSHSE Question PapersAP Board APSCERT BooksAP SSC SyllabusAP 1st Year SyllabusAP 2nd Year SyllabusMP Board MP Board SyllabusMP Board Sample PapersMP Board TextbooksAssam Board Assam Board SyllabusAssam Board TextbooksAssam Board Sample PapersBSEB Bihar Board SyllabusBihar Board TextbooksBihar Board Question PapersBihar Board Model PapersBSE Odisha Odisha Board SyllabusOdisha Board Sample PapersPSEB PSEB SyllabusPSEB TextbooksPSEB Question PapersRBSE Rajasthan Board SyllabusRBSE TextbooksRBSE Question PapersHPBOSE HPBOSE SyllabusHPBOSE TextbooksHPBOSE Question PapersJKBOSE JKBOSE SyllabusJKBOSE Sample PapersJKBOSE Exam PatternTN Board TN Board SyllabusTN Board Question PapersTN Board Sample PapersSamacheer Kalvi BooksJAC JAC SyllabusJAC TextbooksJAC Question PapersTelangana Board Telangana Board SyllabusTelangana Board TextbooksTelangana Board Question PapersKSEEB KSEEB SyllabusKSEEB Model Question PapersKBPE KBPE SyllabusKBPE TextbooksKBPE Question PapersUPMSP UP Board SyllabusUP Board BooksUP Board Question PapersWest Bengal Board West Bengal Board SyllabusWest Bengal Board TextBooksWest Bengal Board Question PapersUBSETBSEGoa BoardNBSECGBSEMBSEMeghalaya BoardManipur BoardHaryana BoardNIOSNIOS A Level Syllabus A Level EVS SyllabusA Level Basic Computer Skill SyllabusA Level Maths SyllabusNIOS B Level Syllabus B Level EVS SyllabusB Level Computer Skill SyllabusB Level Maths SyllabusNIOS C Level Syllabus C Level Social Science SyllabusC Level Science SyllabusC Level Maths SyllabusC Level Basic Computer Skills SyllabusC Level English Language SyllabusNIOS Secondary Course Secondary Course Group B SyllabusSecondary Course Group A SyllabusNIOS Senior Secondary Course Senior Secondary Group F SyllabusSenior Secondary Group E SyllabusSenior Secondary Group D SyllabusSenior Secondary Group C SyllabusSenior Secondary Group B SyllabusSenior Secondary Group A SyllabusGovernment ExamsBank Exams SBI ExamsIBPS ExamsRBI ExamsIBPS RRB ExamSSC Exams SSC JESSC GDSSC CPOSSC CHSLSSC CGLRRB Exams RRB JERRB NTPCRRB ALPInsurance Exams LIC ExamsLIC HFLLIC ADOUPSC CAPFList of Government Exams ArticlesKids LearningClass 1Class 2Class 3English LanguageLetter WritingSpeech Topics For KidsSlogans for KidsEnglish Grammar Parts of SpeechEnglish Grammar ExercisesAcademic QuestionsPhysics QuestionsChemistry QuestionsBiology QuestionsMaths QuestionsScience QuestionsGK QuestionsCommerce QuestionsEnglish QuestionsOnline TuitionHome TuitionFull FormsGeneral Full Forms Physics Full FormsChemistry Full FormsBiology Full FormsEducational Full FormsBanking Full FormsTechnology Full FormsCATCAT 2023CAT SyllabusCAT Exam PatternCAT ExamCAT Percentile PredictorFree CAT PrepByju's App Review on CATEducation NewsSupportComplaint ResolutionCustomer CareBYJU'S Answer ScholarshipBST Class 4-10BNAT Class 11-12BNST | IASMock Test | JEE MainMock Test | JEE AdvancedMock Test | NEETBTCBYJU'S Tuition CentreTuition in North ZoneTuition in Madhya Pradesh Tuition in IndoreTuition in RewaTuition in UjjainTuition in BhopalTuition in JabalpurTuition in GwaliorTuition in SagarTuition in Chhattisgarh Tuition in RaipurTuition in BilaspurTuition in BhilaiTuition in DurgTuition in DelhiTuition in Haryana Tuition in GurgaonTuition in FaridabadTuition in KarnalTuition in SonipatTuition in AmbalaTuition in HisarTuition in PanipatTuition in JagadhriTuition in SirsaTuition in PanchkulaTuition in Himachal Pradesh Tuition in ShimlaTuition in Punjab Tuition in chandigarhTuition in LudhianaTuition in JalandharTuition in AmritsarTuition in BathindaTuition in MohaliTuition in KhararTuition in Rajasthan Tuition in JaipurTuition in AjmerTuition in JodhpurTuition in BikanerTuition in UdaipurTuition in AlwarTuition in Sri GanganagarTuition in BharatpurTuition in SikarTuition in BhilwaraTuition in Uttar Pradesh Tuition in KanpurTuition in LucknowTuition in NoidaTuition in GhaziabadTuition in AligarhTuition in AgraTuition in MeerutTuition in MathuraTuition in FaizabadTuition in SaharanpurTuition in BareillyTuition in Gautam Buddha NagarTuition in RampurTuition in JhansiTuition in AllahabadMoreTuition in Uttarakhand Tuition in RudrapurTuition in HaridwarTuition in DehradunTuition in RoorkeeTuition in West ZoneTuition in Gujarat Tuition in AhmedabadTuition in SuratTuition in AnandTuition in VadodaraTuition in VapiTuition in BhavnagarTuition in RajkotTuition in JamnagarTuition in Maharashtra Tuition in MumbaiTuition in Navi MumbaiTuition in ThaneTuition in PuneTuition in NashikTuition in NagpurTuition in SolapurTuition in LaturTuition in AhmednagarTuition in AurangabadTuition in AmravatiTuition in NandedTuition in AkolaTuition in DhuleMoreTuition in East ZoneTuition in Bihar Tuition in PatnaTuition in MuzaffarpurTuition in DarbhangaTuition in GayaTuition in BhagalpurTuition in PurniaTuition in Jharkhand Tuition in JamshedpurTuition in BokaroTuition in RanchiTuition in DhanbadTuition in Odisha Tuition in BhubaneswarTuition in CuttackTuition in West Bengal Tuition in KolkataTuition in KharagpurTuition in BardhamanTuition in SiliguriTuition in AsansolTuition in Assam Tuition in DibrugarhTuition in South ZoneTuition in Andhra Pradesh Tuition in KurnoolTuition in NelloreTuition in RajahmundryTuition in VijayawadaTuition in VisakhapatnamTuition in KadapaTuition in GunturTuition in AnantapurTuition in TirupatiTuition in Karnataka Tuition in BangaloreTuition in BelagaviTuition in GulbargaTuition in DharwadTuition in MandyaTuition in BellaryTuition in HassanTuition in VijayapuraTuition in HubliTuition in ShimogaTuition in DavanagereTuition in MysoreTuition in MangaloreTuition in Kerala Tuition in TrivandrumTuition in CochinTuition in ThrissurTuition in KozhikodeTuition in KannurTuition in KollamTuition in PalakkadTuition in KottayamTuition in MalappuramTuition in Tamil Nadu Tuition in ChennaiTuition in CoimbatoreTuition in TiruchirappalliTuition in SalemTuition in VelloreTuition in ErodeTuition in KrishnagiriTuition in PuducherryTuition in Telangana Tuition in HyderabadTuition in KarimnagarTuition in KhammamTuition Centre Near YouBuy a Course Success Stories Live QuizNEWLogin+91-9243500460PhysicsDerivation of Physics Formula Diff. Between Articles Relation Between Articles Uses of Physics Concepts Types and Classification Famous Physicists Physics Constants Value of Constants Physics Syllabus Physics Index PagesClass 10 Physics Index Class 11 Physics Index Class 12 Physics Index Branches Of PhysicsMechanics Optics Electromagnetism Relativity Acoustic Thermodynamics Motion In Physics Force Work Power And Energy Current Electricity Laws Of PhysicsOhm's Law Newton's Laws Of Motion Archimedes Principle Doppler Effect Kirchhoff's Law Law Of Reflection Ampere's Law Faraday's Law Bernoulli's Principle Lenz's Law SI Unit ListUnit Of Pressure Viscosity Unit Unit Of Power Density Units Unit Of Energy Unit Of Force Unit Of Heat Conductivity Unit Unit Of Current Unit Of Magnetic Field Physics FormulasPhysics Formulas For Class 9 Physics Formulas For Class 10 Physics Formulas For Class 11 Physics Formulas For Class 12 Physics Calculators Physics Important QuestionsImportant Questions For Class 11 Physics Important Questions For Class 12 Physics CBSE Physics Important Questions Physics Marks Wise Questions Physics Concept Questions and AnswersThermodynamics Questions Thevenin Theorem Questions Equations of Motion Questions Centre of Gravity Questions Physics PracticalsCBSE Class 11 Physics Practicals CBSE Class 12 Physics Practical Syllabus CBSE Class 10 Physics Practical Syllabus Classwise Physics Experiments Viva Questions Physics MCQsClass 12 Physics MCQs Class 11 Physics MCQs Class 10 Physics MCQs Class 9 Physics MCQs

PhysicsWavesInterference Of Waves

Interference of Waves

Have you ever wondered what happens when two waves travelling in the same medium meet? Will the two waves bounce off each other, or do they pass through each other? Or, will the meeting of two waves affect the appearance of the medium? These questions about the meeting of waves pertain to the topic of wave interference. In this article, we will discuss wave interference definition and its types in detail.

Table of Contents:

What is Interference

Derivation

Check Your Understanding

Frequently Asked Questions – FAQs

What is Interference?

Interference is what happens when two or more waves meet each other. Depending on the overlapping waves’ alignment of peaks and troughs, they might add up, or they can partially or entirely cancel each other. As per the interference definition, it is defined as

, The phenomenon in which two or more waves superpose to form a resultant wave of greater, lower or the same amplitude.

The interference of waves results in the medium taking on a shape resulting from the net effect of the two individual waves. To better understand, let us consider the example of two pulses of the same amplitude travelling in different directions in the same medium. Let us consider each displaced upward by 1 unit at its crest and has the shape of a sine wave. As these sine pulses move towards each other, there will be a moment in time when they are completely overlapped. At this point, the shape of the medium would be an upward displaced sine wave with an amplitude of 2 units. After understanding the interference definition, let us learn the derivation of wave interference.

Derivation

The figure illustrates the before and during interference snapshots of the medium of two pulses. The individual sine pulses are drawn in pink and blue, and the resulting wave is green in colour.The principle of superposition of waves states that when two or more waves of the same type are incident on the same point, the resultant amplitude at that point is equal to the vector sum of the amplitudes of the individual waves. If the crest of a wave meets the crest of another wave of the same frequency at the same point, then the resultant amplitude is the sum of individual amplitudes – this is known as constructive interference. Similarly, suppose a wave’s crest meets another wave’s trough. In that case, the resultant amplitude is equal to the difference in the individual amplitudes – this is known as destructive interference. The formula for the sum of two waves can be derived as follows:

The amplitude of a sinusoidal wave travelling to the right along the x-axis is given by,

\(\begin{array}{l}W_1(x,t)=A\cos (kx-\omega t)\end{array} \)

Where A is the peak amplitude, k = 2π/λ is the wavenumber and ω = 2πf is the angular frequency of the wave.

Consider another wave of the same frequency and amplitude but with a different phase travelling to the right.

\(\begin{array}{l}W_2(x,t)=A\cos (kx-\omega t+\phi )\end{array} \)

where φ is the phase difference between the waves in radians

The two waves superimpose and add; the equation gives the resultant wave,

\(\begin{array}{l}W_1+W_2=A[\cos (kx-\omega t)+\cos (kx-\omega t+\phi)]\end{array} \) (1)

The equation gives the sum of two cosines,

\(\begin{array}{l}\cos a+\cos b=2\cos (\frac{a-b}{2})\cos (\frac{a+b}{2})\end{array} \)

Solving equation (1) using the formula, we get

\(\begin{array}{l}W_1+W_2=2A\cos \frac{\phi }{2}\cos (kx-\omega t+\frac{\phi }{2})\end{array} \)

Constructive Interference: When the phase difference is an even multiple of π (φ = ….., –4π, –2π, 0, 2π, 4π,……), then cos φ/2 =1, so the sum of the two waves is a wave with twice the amplitude.

\(\begin{array}{l}W_1+W_2=2A\cos (kx-\omega t)\end{array} \)

Destructive Interference: When the phase difference is an odd multiple of π (φ =….., –3π, –π, 0, π, 3π, 5π,……), then cos φ/2 = 0, so the sum of the two waves will be zero.

\(\begin{array}{l}W_1+W_2= 0\end{array} \)

Check Your Understanding

Two fishes create a series of circular waves by swimming in the water. The waves undergo interference and create the pattern as represented in the diagram. The thick lines represent crests, and the thin lines represent troughs. Several positions in the diagram are labelled with a letter. Categorize the labelled position as being either constructive or destructive interference.

Answer:

Constructive Interference: A and B

Destructive Interference: C

If you wish to learn more Physics concepts with the help of interactive video lessons, download BYJU’S – The Learning App.

Frequently Asked Questions-FAQsQ1 State the interference definition.

As per the interference definition, it is defined as the phenomenon in which two waves superpose to form the resultant wave of the lower, higher or same amplitude.

Q2 What are the types of light interference?

The following are the types of light interference:

Constructive interference

Destructive interference

Q3 State true or false: The interference of waves results in the medium taking shape resulting from the net effect of the two individual waves.

TRUE.

Q4 Do sound waves undergo interference?

Yes, sound waves can undergo interference.

Q5 State the principle of superposition of waves?

The principle of superposition of waves states that when two or more waves of the same type are incident on the same point, the resultant amplitude at that point is equal to the vector sum of the amplitudes of the individual waves.

Test your knowledge on Interference Of Waves

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” buttonCheck your score and answers at the end of the quiz

Start Quiz

Congrats!

Visit BYJU’S for all Physics related queries and study materials

Your result is as below

0 out of 0 arewrong

0 out of 0 are correct

0 out of 0 are Unattempted

View Quiz Answers and Analysis

Mobile Number*

Send OTP

Did not receive OTP?

Request OTP on

Voice Call

Name*

Email ID*

Grade*

Grade

City*

View Result

PHYSICS Related Links

About Spherical Mirrors

How Does A Refrigerator Work

Uniform Acceleration Graph

Applications Of Dc Shunt Generator

Visible Spectrum Wavelengths

What Is The Difference Between Voltage And Current

Pitch Of Sound Depends On

Si Unit Of Resistivity

Centripetal Acceleration Derivation

Physics All Si Units

Comments

Leave a Comment Cancel replyYour Mobile number and Email id will not be published. Required fields are marked *

Send OTP

Did not receive OTP?

Request OTP on

Voice Call

Website

Grade/Exam

Class 1

Class 2

Class 3

Class 4

Class 5

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

IAS

CAT

Bank Exam

GATE

Post My Comment

Important Physics Topics

Thermodynamics

Laws of Physics

Carnot Engine

Concave And Convex Mirrors

Centripetal And Centrifugal Force

Physics Symbols

Poissons Ratio

Frictional Force

Projectile Motion

Electric Current

Electromagnetism

Rotation And Revolution

Uniform And Non-Uniform Motion

SI Units List

Derivation Of Physics Formulas

Ohm's Law

Archimedes’ Principle

Kirchhoff's Law

Newton's Laws of Motion

Laws Of Reflection

CBSE Sample Papers

CBSE Sample Papers Class 8 Science

CBSE Sample Papers Class 9 Science

CBSE Sample Papers Class 10 Science

CBSE Sample Papers Class 11 Physics

CBSE Sample Papers Class 11 Chemistry

CBSE Sample Papers Class 11 Biology

CBSE Sample Papers Class 12 Physics

CBSE Sample Papers Class 12 Chemistry

CBSE Sample Papers Class 12 Biology

CBSE Previous Year Question Papers

CBSE Previous Year Question Papers Class 10 Science

CBSE Previous Year Question Papers Class 12 Physics

CBSE Previous Year Question Papers Class 12 Chemistry

CBSE Previous Year Question Papers Class 12 Biology

ICSE Sample Papers

ICSE Sample Papers Class 8 Physics

ICSE Sample Papers Class 8 Chemistry

ICSE Sample Papers Class 8 Biology

ICSE Sample Papers Class 9 Physics

ICSE Sample Papers Class 9 Chemistry

ICSE Sample Papers Class 9 Biology

ICSE Sample Papers Class 10 Physics

ICSE Sample Papers Class 10 Chemistry

ICSE Sample Papers Class 10 Biology

ISC Sample Papers Class 11 Physics

ISC Sample Papers Class 11 Chemistry

ISC Sample Papers Class 11 Biology

ISC Sample Papers Class 12 Physics

ISC Sample Papers Class 12 Chemistry

ISC Sample Papers Class 12 Biology

ICSE Previous Year Question Papers

ICSE Previous Year Question Papers Class 10 Physics

ICSE Previous Year Question Papers Class 10 Chemistry

ICSE Previous Year Question Papers Class 10 Maths

ISC Previous Year Question Papers class 12

ISC Previous Year Question Papers Class 12 Physics

ISC Previous Year Question Papers Class 12 Chemistry

ISC Previous Year Question Papers Class 12 Biology

BYJU'S Tuition Centre for Class 4 to 10

Class 10 Tuition Centre

Class 9 Tuition Centre

Class 8 Tuition Centre

Class 7 Tuition Centre

Class 6 Tuition Centre

Class 5 Tuition Centre

Class 4 Tuition Centre

Join BYJU'S Learning Program

Grade/Exam

Class 1

Class 2

Class 3

Class 4

Class 5

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

IAS

CAT

Bank Exam

GATE

Submit

COURSES

CBSEICSECATIASJEENEETCommerceJEE MainNCERTJEE AdvancedUPSC Prelims 2022 Question PaperUPSC Prelims 2022 Answer KeyIAS CoachingCBSE Sample PapersCBSE Question Papers

EXAMS

CAT ExamCAT 2023GATE ExamGATE 2024IAS ExamUPSC ExamUPSC SyllabusUPSC 2023Bank ExamGovernment ExamsEducation NewsCLASSES

Kids LearningClass 1st - 3rdClass 4th - 5thClass 6th - 10thClass 11th - 12thBYJU'S Tuition Centre

EXAM PREPARATION

Free CAT PrepFree IAS PrepMathsPhysicsChemistryBiologyJEE 2024JEE Advanced 2023 Question Paper with AnswersJEE Main Mock TestJEE Main 2023 Question Papers with AnswersJEE Main 2022 Question Papers with AnswersJEE Advanced 2022 Question Paper with AnswersNEET 2023 Question PaperNEET 2023 Question Paper AnalysisNEET 2022 Answer KeyRESOURCES

CAT College PredictorWorksheetsBYJU'S AnswerDSSLHome TuitionAll ProductsCalculatorsFormulas

COMPANY

About UsContact UsContact our Financial PartnersInvestorsComplianceCareersBYJU'S in MediaSocial Initiative - Education for AllBYJU'S APPFAQStudents Stories - The Learning TreeSupportFaces of BYJU'S – Life at BYJU'SBlogBYJU'S GiveFOLLOW US

FREE TEXTBOOK SOLUTIONS

NCERT SolutionsNCERT ExemplarNCERT Solutions for Class 6NCERT Solutions for Class 7NCERT Solutions for Class 8NCERT Solutions for Class 9NCERT Solutions for Class 10NCERT Solutions for Class 11NCERT Solutions for Class 11 EnglishNCERT Solutions for Class 12 EnglishNCERT Solutions for Class 12RD Sharma SolutionsRD Sharma Class 10 SolutionsICSE Selina Solutions

STATE BOARDS

MaharashtraGujaratTamil NaduKarnatakaKeralaAndhra PradeshTelanganaUttar PradeshBiharRajasthan

Madhya PradeshWest Bengal

Disclaimer

Terms of Services

Sitemap

widgets-close-button

Call Us

Send OTP

Grade

Class 1

Class 2

Class 3

Class 4

Class 5

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

IAS

CAT

Bank Exam

GATE

Download Now

Send OTP

Grade

Class 1

Class 2

Class 3

Class 4

Class 5

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

IAS

CAT

Bank Exam

GATE

Watch Now

FREE

Signup

Play&

Win

INTERFERENCE | English meaning - Cambridge Dictionary

Dictionary

Translate

Grammar

Thesaurus

+Plus

Cambridge Dictionary +Plus

Shop

Cambridge Dictionary +Plus

My profile

+Plus help

Log out

Cambridge Dictionary +Plus

My profile

+Plus help

Log out

English (UK)

English

Meaning of interference in English

interferencenoun [ U ] uk

Your browser doesn't support HTML5 audio

/ˌɪn.təˈfɪə.rəns/ us

Your browser doesn't support HTML5 audio

/ˌɪn.t̬ɚˈfɪr.əns/

Add to word list

C1 an occasion when someone tries to interfere in a situation: She seems to regard any advice or help from me as interference. The government's interference in the strike has been widely criticized.

C2 noise or other electronic signals that stop you from getting good pictures or sound on a television or radio

More examplesFewer examplesThe political subtext of her novel is a criticism of government interference in individual lives.In the end he moved to another part of the country to escape his mother's continual interference in his private life.They dreamed of a new world order, composed of co-operating independent nation states, free from outside interference.Now can I please get on with the job, without any more interference from you?I'm sorry if he sees it as interference - we were only trying to be helpful.

SMART Vocabulary: related words and phrases

Getting involved for one's own benefit or against others' will

a piece/slice of the action idiom

act

action

bandwagon

be in bed with idiom

bed

get

get in on something

get/muscle in on the act idiom

have a finger in the pie idiom

horn

horn in

interfere

intrude

intrusion

jump/climb/get on the bandwagon idiom

non-interference

snoot

stick your snoot in/into (something) idiom

See more results »

You can also find related words, phrases, and synonyms in the topics:

Communications - general words

Idiom

run interference

(Definition of interference from the Cambridge Advanced Learner's Dictionary & Thesaurus © Cambridge University Press)

interference | American Dictionary

interferencenoun [ U ] us

Your browser doesn't support HTML5 audio

/ˌɪn·tərˈfɪər·əns/

Add to word list

On the radio, television, or telephone, interference is noise, lines, etc., that prevent a clear sound or picture from being received.

physics Interference between two waves happens when they have the same frequency and produce a force that is either stronger or weaker than one wave alone.

In sports, interference is an action that is against the rules which prevents an opposing player from completing a play.

(Definition of interference from the Cambridge Academic Content Dictionary © Cambridge University Press)

Examples of interference

interference

Instead, paternalism views the interferences as justified in themselves, not merely as permissible, all things considered.

From the Cambridge English Corpus

Finally, quantum computing uses interferences between different registers as a resource.

From the Cambridge English Corpus

In sum, to have any chance of identifying interferences correctly one needs to be sure that the data collected come from a truly monolingual mode.

From the Cambridge English Corpus

We emphasise the role of computing interferences, that is, the necessity of avoiding them in order to give a causal implementation to logical operations.

From the Cambridge English Corpus

However, in real life, interferences are not always that bad.

From the Cambridge English Corpus

In the same way, spiritualism avoids logical interferences, but this does not mean that they do not make sense.

From the Cambridge English Corpus

The approaches followed in circuit design to deal with computing interferences fall into two main classes.

From the Cambridge English Corpus

Moreover, our encoding was also designed to avoid all interferences with other processes (if we restrict internal names for the request/server mechanism).

From the Cambridge English Corpus

Interlanguage errors, also called interferences, are due to the first language influencing the second language.

From the Cambridge English Corpus

Obviously, with proper design, the problem of interferences can be avoided yielding above emphasized necessary conditions of the integrated robotic system design.

From the Cambridge English Corpus

At the lowest level, the correct functioning of a single component may be endangered by computing interferences within the component itself, due to internal loops and instabilities of internal variables.

From the Cambridge English Corpus

There is a physical analogy: when you enter a plane, you are supposed to turn off your cellular phone, because of interferences: that is a smart spiritual move.

From the Cambridge English Corpus

The interferences and resonances between these influences pose aesthetic questions that are explored within the piece and its performance, while remaining open for the analyst and audience.

From the Cambridge English Corpus

To avoid unwanted interferences that might be caused by using the same sentence twice, different names were used in each of the two experimental sentences made from one stimulus sentence.

From the Cambridge English Corpus

We want to use natural causes as much as possible, because artificial interferences are often fraught with great danger.

From the Hansard archive

Example from the Hansard archive. Contains Parliamentary information licensed under the Open Parliament Licence v3.0

See all examples of interference

These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.

Collocations with interference

interference

These are words often used in combination with interference.Click on a collocation to see more examples of it.

arbitrary interferenceIn these treaties, privacy is recognized as a form of autonomy-a way to ensure protection from ' 'arbitrary interference' '1 by the state or other entities.

From the Cambridge English Corpus

bureaucratic interferenceThis is a quite monstrous case of bureaucratic interference.

From the Hansard archive

Example from the Hansard archive. Contains Parliamentary information licensed under the Open Parliament Licence v3.0

constant interferenceBut this coming and going, this constant pinpricking, this constant interference without any consecutive thought and philosophy behind it, is not something to take lightly.

From the Hansard archive

Example from the Hansard archive. Contains Parliamentary information licensed under the Open Parliament Licence v3.0

See all collocations with interference

What is the pronunciation of interference?

C1,C2

Translations of interference

in Chinese (Traditional)

干涉，干預, （雜訊或其他電子訊號對電視或收音機的）干擾…

in Chinese (Simplified)

干涉，干预, （噪声或其他电子信号对电视或收音机的）干扰…

in Spanish

intromisión, injerencia, interferencias…

in Portuguese

intromissão, interferência, intrometimento [masculine]…

in more languages

in Marathi

in Japanese

in Turkish

in French

in Catalan

in Dutch

in Tamil

in Hindi

in Gujarati

in Danish

in Swedish

in Malay

in German

in Norwegian

in Urdu

in Ukrainian

in Russian

in Telugu

in Arabic

in Bengali

in Czech

in Indonesian

in Thai

in Vietnamese

in Polish

in Korean

in Italian

हस्तक्षेप, ढवळाढवळ, गोंगाट…

干渉, 混信, 干渉（かんしょう）…

müdahale, burnunu sokma, karışma…

intrusion [feminine], ingérence [feminine], interférence [feminine]…

ingerència, intromissió, interferència…

inmenging, storing…

யாராவது ஒரு சூழ்நிலையில் தலையிட முயற்சிக்கும் ஒரு சந்தர்ப்பம், தொலைக்காட்சி அல்லது வானொலியில் நல்ல படங்கள் அல்லது ஒலியைப் பெறுவதைத் தடுக்கும் சத்தம் அல்லது பிற மின்னணு சமிக்ஞைகள்…

(एक व्यक्ति के द्वारा किसी परिस्थिति में) हस्तक्षेप, टेलीविज़न या रेडियो पर अच्छी तस्वीरें या आवाज़ को बाधित करने वाले शोर या इलेक्ट्रॉनिक संकेत…

હસ્તક્ષેપ, રુકાવટ, અવરોધ…

indblanding, forstyrrelse…

inblandning, störningar…

masuk campur, gangguan…

die Einmischung, die Störung…

innblanding [masculine], forstyrrelse [masculine], interferens [masculine]…

مداخلت, رکاوٹ, ٹیلی ویژن کے پردہ پر پیدا ہونے والی مداخلت…

втручання, перешкоди…

вмешательство, помехи…

జోక్యం/ ఎవరైనా ఒక పరిస్థితిలో జోక్యం చేసుకోవడానికి ప్రయత్నించిన ఒక సందర్భం, టెలివిజన్ లేదా రేడియోలో నుంచి మంచి చిత్రాలు లేదా ధ్వని పొందకుండా మిమ్మల్ని ఆపే శబ్దం లేదా ఇతర ఎలక్ట్రానిక్ సిగ్నల్స్…

تَدخّل, تَشويش…

হস্তক্ষেপ করা, আওয়াজ বা অন্যান্য ইলেকট্রনিক সংকেত যা আপনাকে টেলিভিশন বা রেডিওতে ভাল ছবি বা শব্দ পেতে বাধা দেয়…

zasahování, rušení, interference…

turut campur, gangguan…

สิ่งรบกวน, เสียงรบกวน…

sự can thiệp, sự nhiễu…

ingerencja, zakłócenia, mieszanie się…

간섭, 방해…

interferenza, ingerenza, intromissione…

Need a translator?

Get a quick, free translation!

Translator tool

Browse

interfamily

interfere

interfere with something

interfered

interference

interfering

interferometer

BETA

interferometric

BETA

interferometry

BETA

More meanings of interference

All

constructive interference

destructive interference

non-interference

pass interference

run interference idiom

See all meanings

Idioms and phrases

run interference idiom

Word of the Day

response

Your browser doesn't support HTML5 audio

/rɪˈspɒns/

Your browser doesn't support HTML5 audio

/rɪˈspɑːns/

an answer or reaction

About this

Blog

Forget doing it or forget to do it? Avoiding common mistakes with verb patterns (2)

March 06, 2024

New Words

inverse vaccine

March 11, 2024

More new words

has been added to list

To top

Contents

EnglishAmericanExamplesCollocationsTranslations

Learn

New Words

Help

In Print

Word of the Year 2021

Word of the Year 2022

Word of the Year 2023

Develop

Dictionary API

Double-Click Lookup

Search Widgets

License Data

About

Accessibility

Cambridge English

Cambridge University Press & Assessment

Consent Management

Cookies and Privacy

Corpus

Cambridge Dictionary +Plus

My profile

+Plus help

Log out

Dictionary

Definitions

Clear explanations of natural written and spoken English

English

Learner’s Dictionary

Essential British English

Essential American English

Translations

Click on the arrows to change the translation direction.

Bilingual Dictionaries

English–Chinese (Simplified)

Chinese (Simplified)–English

English–Chinese (Traditional)

Chinese (Traditional)–English

English–Dutch

Dutch–English

English–French

French–English

English–German

German–English

English–Indonesian

Indonesian–English

English–Italian

Italian–English

English–Japanese

Japanese–English

English–Norwegian

Norwegian–English

English–Polish

Polish–English

English–Portuguese

Portuguese–English

English–Spanish

Spanish–English

English–Swedish

Swedish–English

Semi-bilingual Dictionaries

English–Arabic

English–Bengali

English–Catalan

English–Czech

English–Danish

English–Gujarati

English–Hindi

English–Korean

English–Malay

English–Marathi

English–Russian

English–Tamil

English–Telugu

English–Thai

English–Turkish

English–Ukrainian

English–Urdu

English–Vietnamese

Translate

Grammar

Thesaurus

Pronunciation

Cambridge Dictionary +Plus

Shop

Cambridge Dictionary +Plus

My profile

+Plus help

Log out

English (UK)

Change

English (UK)

English (US)

Español

Русский

Português

Deutsch

Français

Italiano

中文 (简体)

正體中文 (繁體)

Polski

한국어

Türkçe

日本語

Tiếng Việt

Nederlands

Svenska

Dansk

Norsk

हिंदी

বাঙ্গালি

मराठी

ગુજરાતી

தமிழ்

తెలుగు

Українська

Choose a dictionary

Recent and Recommended

Definitions

Clear explanations of natural written and spoken English

English

Learner’s Dictionary

Essential British English

Essential American English

Grammar and thesaurus

Usage explanations of natural written and spoken English

Grammar

Thesaurus

Pronunciation

British and American pronunciations with audio

English Pronunciation

Translation

Click on the arrows to change the translation direction.

Bilingual Dictionaries

English–Chinese (Simplified)

Chinese (Simplified)–English

English–Chinese (Traditional)

Chinese (Traditional)–English

English–Dutch

Dutch–English

English–French

French–English

English–German

German–English

English–Indonesian

Indonesian–English

English–Italian

Italian–English

English–Japanese

Japanese–English

English–Norwegian

Norwegian–English

English–Polish

Polish–English

English–Portuguese

Portuguese–English

English–Spanish

Spanish–English

English–Swedish

Swedish–English

Semi-bilingual Dictionaries

English–Arabic

English–Bengali

English–Catalan

English–Czech

English–Danish

English–Gujarati

English–Hindi

English–Korean

English–Malay

English–Marathi

English–Russian

English–Tamil

English–Telugu

English–Thai

English–Turkish

English–Ukrainian

English–Urdu

English–Vietnamese

Dictionary +Plus

Word Lists

Choose your language

English (UK)

English (US)

Español

Русский

Português

Deutsch

Français

Italiano

中文 (简体)

正體中文 (繁體)

Polski

한국어

Türkçe

日本語

Tiếng Việt

Nederlands

Svenska

Dansk

Norsk

हिंदी

বাঙ্গালি

मराठी

ગુજરાતી

தமிழ்

తెలుగు

Українська

Contents

English

Noun

American

Noun

Examples

Collocations

Translations

Grammar

All translations

My word lists

Add interference to one of your lists below, or create a new one.

Go to your word lists

Tell us about this example sentence:

The word in the example sentence does not match the entry word.

The sentence contains offensive content.

Cancel

Submit

The word in the example sentence does not match the entry word.

The sentence contains offensive content.

Cancel

Submit

17.1 Understanding Diffraction and Interference - Physics | OpenStax

Understanding Diffraction and Interference - Physics | OpenStaxSkip to ContentGo to accessibility pageKeyboard shortcuts menuPhysics17.1 Understanding Diffraction and InterferencePhysics17.1 Understanding Diffraction and InterferenceSearchSearchCloseSearchContentsContentsHighlightsPrintTable of contentsPreface1

What is Physics?Introduction1.1 Physics: Definitions and Applications1.2 The Scientific Methods1.3 The Language of Physics: Physical Quantities and UnitsKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response2

Motion in One DimensionIntroduction2.1 Relative Motion, Distance, and Displacement2.2 Speed and Velocity2.3 Position vs. Time Graphs2.4 Velocity vs. Time GraphsKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response3

AccelerationIntroduction3.1 Acceleration3.2 Representing Acceleration with Equations and GraphsKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response4

Forces and Newton’s Laws of MotionIntroduction4.1 Force4.2 Newton's First Law of Motion: Inertia4.3 Newton's Second Law of Motion4.4 Newton's Third Law of MotionKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response5

Motion in Two DimensionsIntroduction5.1 Vector Addition and Subtraction: Graphical Methods5.2 Vector Addition and Subtraction: Analytical Methods5.3 Projectile Motion5.4 Inclined Planes5.5 Simple Harmonic MotionKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response6

Circular and Rotational MotionIntroduction6.1 Angle of Rotation and Angular Velocity6.2 Uniform Circular Motion6.3 Rotational MotionKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response7

Newton's Law of GravitationIntroduction7.1 Kepler's Laws of Planetary Motion7.2 Newton's Law of Universal Gravitation and Einstein's Theory of General RelativityKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response8

MomentumIntroduction8.1 Linear Momentum, Force, and Impulse8.2 Conservation of Momentum8.3 Elastic and Inelastic CollisionsKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response9

Work, Energy, and Simple MachinesIntroduction9.1 Work, Power, and the Work–Energy Theorem9.2 Mechanical Energy and Conservation of Energy9.3 Simple MachinesKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response10

Special RelativityIntroduction10.1 Postulates of Special Relativity10.2 Consequences of Special RelativityKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response11

Thermal Energy, Heat, and WorkIntroduction11.1 Temperature and Thermal Energy11.2 Heat, Specific Heat, and Heat Transfer11.3 Phase Change and Latent HeatKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response12

ThermodynamicsIntroduction12.1 Zeroth Law of Thermodynamics: Thermal Equilibrium12.2 First law of Thermodynamics: Thermal Energy and Work12.3 Second Law of Thermodynamics: Entropy12.4 Applications of Thermodynamics: Heat Engines, Heat Pumps, and RefrigeratorsKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response13

Waves and Their PropertiesIntroduction13.1 Types of Waves13.2 Wave Properties: Speed, Amplitude, Frequency, and Period13.3 Wave Interaction: Superposition and InterferenceKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response14

SoundIntroduction14.1 Speed of Sound, Frequency, and Wavelength14.2 Sound Intensity and Sound Level14.3 Doppler Effect and Sonic Booms14.4 Sound Interference and ResonanceKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response15

LightIntroduction15.1 The Electromagnetic Spectrum15.2 The Behavior of Electromagnetic RadiationKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response16

Mirrors and LensesIntroduction16.1 Reflection16.2 Refraction16.3 LensesKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response17

Diffraction and InterferenceIntroduction17.1 Understanding Diffraction and Interference17.2 Applications of Diffraction, Interference, and CoherenceKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response18

Static ElectricityIntroduction18.1 Electrical Charges, Conservation of Charge, and Transfer of Charge18.2 Coulomb's law18.3 Electric Field18.4 Electric Potential18.5 Capacitors and DielectricsKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response19

Electrical CircuitsIntroduction19.1 Ohm's law19.2 Series Circuits19.3 Parallel Circuits19.4 Electric PowerKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response20

MagnetismIntroduction20.1 Magnetic Fields, Field Lines, and Force20.2 Motors, Generators, and Transformers20.3 Electromagnetic InductionKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response21

The Quantum Nature of LightIntroduction21.1 Planck and Quantum Nature of Light21.2 Einstein and the Photoelectric Effect21.3 The Dual Nature of LightKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsProblemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response22

The AtomIntroduction22.1 The Structure of the Atom22.2 Nuclear Forces and Radioactivity22.3 Half Life and Radiometric Dating22.4 Nuclear Fission and Fusion22.5 Medical Applications of Radioactivity: Diagnostic Imaging and RadiationKey TermsSection SummaryKey EquationsChapter ReviewConcept ItemsCritical Thinking ItemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended Response23

Particle PhysicsIntroduction23.1 The Four Fundamental Forces23.2 Quarks23.3 The Unification of ForcesKey TermsSection SummaryChapter ReviewConcept ItemsCritical Thinking ItemsPerformance TaskTest PrepMultiple ChoiceShort AnswerExtended ResponseA | Reference TablesIndex

Section Learning Objectives

By the end of this section, you will be able to do the following:

Explain wave behavior of light, including diffraction and interference, including the role of constructive and destructive interference in Young’s single-slit and double-slit experiments

Perform calculations involving diffraction and interference, in particular the wavelength of light using data from a two-slit interference pattern

Teacher Support

The learning objectives in this section will help your students master the following standards:

(7) Science concepts. The student knows the characteristics and behavior of waves. The student is expected to:

(D)

investigate behaviors of waves, including reflection, refraction, diffraction, interference, resonance, and the Doppler effect

Section Key Terms

diffraction

Huygens’s principle

monochromatic

wavefront

Diffraction and Interference

Teacher Support

[BL]Explain constructive and destructive interference graphically on the board.

[OL]Ask students to look closely at a shadow. Ask why the edges are not sharp lines. Explain that this is caused by diffraction, one of the wave properties of electromagnetic radiation. Define the nanometer in relation to other metric length measurements.

[AL]Ask students which, among speed, frequency, and wavelength, stay the same, and which change, when a ray of light travels from one medium to another. Discuss those quantities in terms of colors (wavelengths) of visible light.

We know that visible light is the type of electromagnetic wave to which our eyes responds. As we have seen previously, light obeys the equation

c=fλ,

where

c=3.00×

m/s is the speed of light in vacuum, f is the frequency of the electromagnetic wave in Hz (or s–1), and

λ is its wavelength in m. The range of visible wavelengths is approximately 380 to 750 nm. As is true for all waves, light travels in straight lines and acts like a ray when it interacts with objects several times as large as its wavelength. However, when it interacts with smaller objects, it displays its wave characteristics prominently. Interference is the identifying behavior of a wave.

In Figure 17.2, both the ray and wave characteristics of light can be seen. The laser beam emitted by the observatory represents ray behavior, as it travels in a straight line. Passing a pure, one-wavelength beam through vertical slits with a width close to the wavelength of the beam reveals the wave character of light. Here we see the beam spreading out horizontally into a pattern of bright and dark regions that are caused by systematic constructive and destructive interference. As it is characteristic of wave behavior, interference is observed for water waves, sound waves, and light waves.

Figure

17.2

(a) The light beam emitted by a laser at the Paranal Observatory (part of the European Southern Observatory in Chile) acts like a ray, traveling in a straight line. (credit: Yuri Beletsky, European Southern Observatory) (b) A laser beam passing through a grid of vertical slits produces an interference pattern—characteristic of a wave. (credit: Shim’on and Slava Rybka, Wikimedia Commons)

That interference is a characteristic of energy propagation by waves is demonstrated more convincingly by water waves. Figure 17.3 shows water waves passing through gaps between some rocks. You can easily see that the gaps are similar in width to the wavelength of the waves and that this causes an interference pattern as the waves pass beyond the gaps. A cross-section across the waves in the foreground would show the crests and troughs characteristic of an interference pattern.

Figure

17.3

Incoming waves (at the top of the picture) pass through the gaps in the rocks and create an interference pattern (in the foreground).

Light has wave characteristics in various media as well as in a vacuum. When light goes from a vacuum to some medium, such as water, its speed and wavelength change, but its frequency, f, remains the same. The speed of light in a medium is

v=c/n

, where n is its index of refraction. If you divide both sides of the equation

c=fλ

by n, you get

c/n=v=fλ/n

. Therefore,

v=f

, where

is the wavelength in a medium, and

where

λ is the wavelength in vacuum and n is the medium’s index of refraction. It follows that the wavelength of light is smaller in any medium than it is in vacuum. In water, for example, which has n = 1.333, the range of visible wavelengths is (380 nm)/1.333 to (760 nm)/1.333, or

285–570 nm. Although wavelengths change while traveling from one medium to another, colors do not, since colors are associated with frequency.

The Dutch scientist Christiaan Huygens (1629–1695) developed a useful technique for determining in detail how and where waves propagate. He used wavefronts, which are the points on a wave’s surface that share the same, constant phase (such as all the points that make up the crest of a water wave). Huygens’s principle states, “Every point on a wavefront is a source of wavelets that spread out in the forward direction at the same speed as the wave itself. The new wavefront is a line tangent to all of the wavelets.”

Figure 17.4 shows how Huygens’s principle is applied. A wavefront is the long edge that moves; for example, the crest or the trough. Each point on the wavefront emits a semicircular wave that moves at the propagation speed v. These are drawn later at a time, t, so that they have moved a distance

s=vt

. The new wavefront is a line tangent to the wavelets and is where the wave is located at time t. Huygens’s principle works for all types of waves, including water waves, sound waves, and light waves. It will be useful not only in describing how light waves propagate, but also in how they interfere.

Figure

17.4

Huygens’s principle applied to a straight wavefront. Each point on the wavefront emits a semicircular wavelet that moves a distance

s=vt

s=vt . The new wavefront is a line tangent to the wavelets.

What happens when a wave passes through an opening, such as light shining through an open door into a dark room? For light, you expect to see a sharp shadow of the doorway on the floor of the room, and you expect no light to bend around corners into other parts of the room. When sound passes through a door, you hear it everywhere in the room and, thus, you understand that sound spreads out when passing through such an opening. What is the difference between the behavior of sound waves and light waves in this case? The answer is that the wavelengths that make up the light are very short, so that the light acts like a ray. Sound has wavelengths on the order of the size of the door, and so it bends around corners.

Teacher Support

[OL]Discuss the fact that, for a diffraction pattern to be visible, the width of a slit must be roughly the wavelength of the light. Try to give students an idea of the size of visible light wavelengths by noting that a human hair is roughly 100 times wider.

If light passes through smaller openings, often called slits, you can use Huygens’s principle to show that light bends as sound does (see Figure 17.5). The bending of a wave around the edges of an opening or an obstacle is called diffraction. Diffraction is a wave characteristic that occurs for all types of waves. If diffraction is observed for a phenomenon, it is evidence that the phenomenon is produced by waves. Thus, the horizontal diffraction of the laser beam after it passes through slits in Figure 17.2 is evidence that light has the properties of a wave.

Figure

17.5

Huygens’s principle applied to a straight wavefront striking an opening. The edges of the wavefront bend after passing through the opening, a process called diffraction. The amount of bending is more extreme for a small opening, consistent with the fact that wave characteristics are most noticeable for interactions with objects about the same size as the wavelength.

Once again, water waves present a familiar example of a wave phenomenon that is easy to observe and understand, as shown in Figure 17.6.

Figure

17.6

Ocean waves pass through an opening in a reef, resulting in a diffraction pattern. Diffraction occurs because the opening is similar in width to the wavelength of the waves.

Watch Physics

Single-Slit Interference

This video works through the math needed to predict diffraction patterns that are caused by single-slit interference.

Access multimedia content

Which values of m denote the location of destructive interference in a single-slit diffraction pattern?

whole integers, excluding zero

whole integers

real numbers excluding zero

real numbers

The fact that Huygens’s principle worked was not considered enough evidence to prove that light is a wave. People were also reluctant to accept light’s wave nature because it contradicted the ideas of Isaac Newton, who was still held in high esteem. The acceptance of the wave character of light came after 1801, when the English physicist and physician Thomas Young (1773–1829) did his now-classic double-slit experiment (see Figure 17.7).

Figure

17.7

Young’s double-slit experiment. Here, light of a single wavelength passes through a pair of vertical slits and produces a diffraction pattern on the screen—numerous vertical light and dark lines that are spread out horizontally. Without diffraction and interference, the light would simply make two lines on the screen.

When light passes through narrow slits, it is diffracted into semicircular waves, as shown in Figure 17.8 (a). Pure constructive interference occurs where the waves line up crest to crest or trough to trough. Pure destructive interference occurs where they line up crest to trough. The light must fall on a screen and be scattered into our eyes for the pattern to be visible. An analogous pattern for water waves is shown in Figure 17.8 (b). Note that regions of constructive and destructive interference move out from the slits at well-defined angles to the original beam. Those angles depend on wavelength and the distance between the slits, as you will see below.

Figure

17.8

Double slits produce two sources of waves that interfere. (a) Light spreads out (diffracts) from each slit, because the slits are narrow. The waves overlap and interfere constructively (bright lines) and destructively (dark regions). You can only see the effect if the light falls onto a screen and is scattered into your eyes. (b) The double-slit interference pattern for water waves is nearly identical to that for light. Wave action is greatest in regions of constructive interference and least in regions of destructive interference. (c) When light that has passed through double slits falls on a screen, we see a pattern such as this.

Virtual Physics

Wave Interference

Access multimedia content

This simulation demonstrates most of the wave phenomena discussed in this section. First, observe interference between two sources of electromagnetic radiation without adding slits. See how water waves, sound, and light all show interference patterns. Stay with light waves and use only one source. Create diffraction patterns with one slit and then with two. You may have to adjust slit width to see the pattern.

Visually compare the slit width to the wavelength. When do you get the best-defined diffraction pattern?

when the slit width is larger than the wavelength

when the slit width is smaller than the wavelength

when the slit width is comparable to the wavelength

when the slit width is infinite

Calculations Involving Diffraction and Interference

Teacher Support

[BL]The Greek letter

θ is spelled theta. The Greek letter

λ is spelled lamda. Both are pronounced the way you would expect from the spelling. The plurals of maximum and minimum are maxima and minima, respectively.

[OL]Explain that monochromatic means one color. Monochromatic also means one frequency. The sine of an angle is the opposite side of a right triangle divided by the hypotenuse. Opposite means opposite the given acute angle. Note that the sign of an angle is always ≥ 1.

The fact that the wavelength of light of one color, or monochromatic light, can be calculated from its two-slit diffraction pattern in Young’s experiments supports the conclusion that light has wave properties. To understand the basis of such calculations, consider how two waves travel from the slits to the screen. Each slit is a different distance from a given point on the screen. Thus different numbers of wavelengths fit into each path. Waves start out from the slits in phase (crest to crest), but they will end up out of phase (crest to trough) at the screen if the paths differ in length by half a wavelength, interfering destructively. If the paths differ by a whole wavelength, then the waves arrive in phase (crest to crest) at the screen, interfering constructively. More generally, if the paths taken by the two waves differ by any half-integral number of wavelengths

(

λ,

λ, etc.)

(

λ,

λ, etc.)

, then destructive interference occurs. Similarly, if the paths taken by the two waves differ by any integral number of wavelengths

(λ, 2λ, 3λ, etc.)

, then constructive interference occurs.

Figure 17.9 shows how to determine the path-length difference for waves traveling from two slits to a common point on a screen. If the screen is a large distance away compared with the distance between the slits, then the angle

θ between the path and a line from the slits perpendicular to the screen (see the figure) is nearly the same for each path. That approximation and simple trigonometry show the length difference,

ΔL

ΔL, to be

dsinθ

dsinθ, where d is the distance between the slits,

ΔL=dsinθ.

To obtain constructive interference for a double slit, the path-length difference must be an integral multiple of the wavelength, or

dsinθ=mλ, for m=0,1,−1,2,−2,…(constructive).

Similarly, to obtain destructive interference for a double slit, the path-length difference must be a half-integral multiple of the wavelength, or

dsinθ=(m+½)λ, for m=0,1,−1,2,−2,…(destructive).

The number m is the order of the interference. For example, m = 4 is fourth-order interference.

Figure

17.9

The paths from each slit to a common point on the screen differ by an amount

d sin θ

d sin θ, assuming the distance to the screen is much greater than the distance between the slits (not to scale here).

Figure 17.10 shows how the intensity of the bands of constructive interference decreases with increasing angle.

Figure

17.10

The interference pattern for a double slit has an intensity that falls off with angle. The photograph shows multiple bright and dark lines, or fringes, formed by light passing through a double slit.

Light passing through a single slit forms a diffraction pattern somewhat different from that formed by double slits. Figure 17.11 shows a single-slit diffraction pattern. Note that the central maximum is larger than those on either side, and that the intensity decreases rapidly on either side.

Figure

17.11

(a) Single-slit diffraction pattern. Monochromatic light passing through a single slit produces a central maximum and many smaller and dimmer maxima on either side. The central maximum is six times higher than shown. (b) The drawing shows the bright central maximum and dimmer and thinner maxima on either side. (c) The location of the minima are shown in terms of

λ and D.

The analysis of single-slit diffraction is illustrated in Figure 17.12. Assuming the screen is very far away compared with the size of the slit, rays heading toward a common destination are nearly parallel. That approximation allows a series of trigonometric operations that result in the equations for the minima produced by destructive interference.

Dsinθ=mλ

=mλ

When rays travel straight ahead, they remain in phase and a central maximum is obtained. However, when rays travel at an angle

θ relative to the original direction of the beam, each ray travels a different distance to the screen, and they can arrive in or out of phase. Thus, a ray from the center travels a distance

λ/2

farther than the ray from the top edge of the slit, they arrive out of phase, and they interfere destructively. Similarly, for every ray between the top and the center of the slit, there is a ray between the center and the bottom of the slit that travels a distance

λ/2

farther to the common point on the screen, and so interferes destructively. Symmetrically, there will be another minimum at the same angle below the direct ray.

Figure

17.12

Equations for a single-slit diffraction pattern, where λ is the wavelength of light, D is the slit width,

θ is the angle between a line from the slit to a minimum and a line perpendicular to the screen, L is the distance from the slit to the screen, y is the distance from the center of the pattern to the minimum, and m is a nonzero integer indicating the order of the minimum.

Below we summarize the equations needed for the calculations to follow.

The speed of light in a vacuum, c, the wavelength of the light,

λ, and its frequency, f, are related as follows.

c=fλ

The wavelength of light in a medium,

, compared to its wavelength in a vacuum,

λ, is given by

17.1

To calculate the positions of constructive interference for a double slit, the path-length difference must be an integral multiple, m, of the wavelength.

dsinθ=mλ, for m=0,1,−1,2,−2,…(constructive),

where d is the distance between the slits and

θ is the angle between a line from the slits to the maximum and a line perpendicular to the barrier in which the slits are located. To calculate the positions of destructive interference for a double slit, the path-length difference must be a half-integral multiple of the wavelength:

dsinθ=(m+½)λ, for m=0,1,−1,2,−2,…(destructive).

For a single-slit diffraction pattern, the width of the slit, D, the distance of the first (m = 1) destructive interference minimum, y, the distance from the slit to the screen, L, and the wavelength,

λ, are given by

=λ.

Also, for single-slit diffraction,

Dsinθ=mλ,

where

θ is the angle between a line from the slit to the minimum and a line perpendicular to the screen, and m is the order of the minimum.

Worked Example

Two-Slit Interference

Suppose you pass light from a He-Ne laser through two slits separated by 0.0100 mm, and you find that the third bright line on a screen is formed at an angle of 10.95º relative to the incident beam. What is the wavelength of the light?

Strategy

The third bright line is due to third-order constructive interference, which means that m = 3. You are given d = 0.0100 mm and

θ = 10.95º. The wavelength can thus be found using the equation

dsinθ=mλ

for constructive interference.

Solution

The equation is

dsinθ=mλ

. Solving for the wavelength,

λ, gives

λ=

dsinθ

λ=

dsinθ

17.2

Substituting known values yields

λ=

(

0.0100 mm

)(

sin 10.95°

)

=6.33×

−4

mm=633 nm.

λ=

(

0.0100 mm

)(

sin 10.95°

)

=6.33×

−4

mm=633 nm.

17.3

Discussion

To three digits, 633 nm is the wavelength of light emitted by the common He-Ne laser. Not by coincidence, this red color is similar to that emitted by neon lights. More important, however, is the fact that interference patterns can be used to measure wavelength. Young did that for visible wavelengths. His analytical technique is still widely used to measure electromagnetic spectra. For a given order, the angle for constructive interference increases with

λ, so spectra (measurements of intensity versus wavelength) can be obtained.

Worked Example

Single-Slit Diffraction

Visible light of wavelength 550 nm falls on a single slit and produces its second diffraction minimum at an angle of 45.0° relative to the incident direction of the light. What is the width of the slit?

Strategy

From the given information, and assuming the screen is far away from the slit, you can use the equation

Dsinθ=mλ

to find D.

Solution

Quantities given are

λ = 550 nm, m = 2, and

= 45.0°. Solving the equation

Dsinθ=mλ

for D and substituting known values gives

mλ

sinθ

2(550 nm)

sin45.0°

=1.56×

−6

mλ

sinθ

2(550 nm)

sin45.0°

=1.56×

−6

17.4

Discussion

You see that the slit is narrow (it is only a few times greater than the wavelength of light). That is consistent with the fact that light must interact with an object comparable in size to its wavelength in order to exhibit significant wave effects, such as this single-slit diffraction pattern.

Practice Problems

Monochromatic light from a laser passes through two slits separated by

0.00500

. The third bright line on a screen is formed at an angle of

18.0

∘

relative to the incident beam. What is the wavelength of the light?

51.5

77.3

515

773

What is the width of a single slit through which 610-nm orange light passes to form a first diffraction minimum at an angle of 30.0°?

0.863 µm

0.704 µm

0.610 µm

1.22 µm

Check Your Understanding

Teacher Support

Use these problems to assess student achievement of the section’s learning objectives. If students are struggling with a specific objective, these problems will help identify which and direct students to the relevant topics.

Which aspect of a beam of monochromatic light changes when it passes from a vacuum into water, and how does it change?

The wavelength first decreases and then increases.

The wavelength first increases and then decreases.

The wavelength increases.

The wavelength decreases.

Go outside in the sunlight and observe your shadow. It has fuzzy edges, even if you do not. Is this a diffraction effect? Explain.

This is a diffraction effect. Your whole body acts as the origin for a new wavefront.

This is a diffraction effect. Every point on the edge of your shadow acts as the origin for a new wavefront.

This is a refraction effect. Your whole body acts as the origin for a new wavefront.

This is a refraction effect. Every point on the edge of your shadow acts as the origin for a new wavefront.

Which aspect of monochromatic green light changes when it passes from a vacuum into diamond, and how does it change?

The wavelength first decreases and then increases.

The wavelength first increases and then decreases.

The wavelength increases.

The wavelength decreases.

PreviousNextOrder a print copyAs an Amazon Associate we earn from qualifying purchases.Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the

Creative Commons Attribution License

and you must attribute Texas Education Agency (TEA). The original material is available at:

https://www.texasgateway.org/book/tea-physics

. Changes were made to the original material, including updates to art, structure, and other content updates.

Attribution information

If you are redistributing all or part of this book in a print format,

then you must include on every physical page the following attribution:

Access for free at https://openstax.org/books/physics/pages/1-introduction

If you are redistributing all or part of this book in a digital format,

then you must include on every digital page view the following attribution:

Access for free at https://openstax.org/books/physics/pages/1-introduction

Citation information

Use the information below to generate a citation. We recommend using a

citation tool such as

this one.

Authors: Paul Peter Urone, Roger Hinrichs

Publisher/website: OpenStax

Book title: Physics

Publication date: Mar 26, 2020

Location: Houston, Texas

Book URL: https://openstax.org/books/physics/pages/1-introduction

Section URL: https://openstax.org/books/physics/pages/17-1-understanding-diffraction-and-interference

are not subject to the Creative Commons license and may not be reproduced without the prior and express written

consent of Rice University.

Our mission is to improve educational access and learning for everyone.

OpenStax is part of Rice University, which is a 501(c)(3) nonprofit.

Give today and help us reach more students.

HelpContact UsSupport CenterFAQOpenStaxPressNewsletterCareersPoliciesAccessibility StatementTerms of UseLicensingPrivacy Policy

are licensed under a

Creative Commons Attribution 4.0 International License.

Advanced Placement® and AP® are trademarks registered and/or owned by the College Board,

which is not affiliated with, and does not endorse, this site.

13.3 Wave Interaction: Superposition and Interference - Physics | OpenStax

Wave Interaction: Superposition and Interference - Physics | OpenStaxSkip to ContentGo to accessibility pageKeyboard shortcuts menuPhysics13.3 Wave Interaction: Superposition and InterferencePhysics13.3 Wave Interaction: Superposition and InterferenceSearchSearchCloseSearchContentsContentsHighlightsPrintTable of contentsPreface1

Section Learning Objectives

By the end of this section, you will be able to do the following:

Describe superposition of waves

Describe interference of waves and distinguish between constructive and destructive interference of waves

Describe the characteristics of standing waves

Distinguish reflection from refraction of waves

Teacher Support

The learning objectives in this section will help your students master the following standards:

(7) Science concepts. The student knows the characteristics and behavior of waves. The student is expected to:

(D) investigate the behaviors of waves, including reflection, refraction, diffraction, interference, resonance, and the Doppler effect.

In addition, the High School Physics Laboratory Manual addresses content in this section in the lab titled: Waves, as well as the following standards:

(7) Science concepts. The student knows the characteristics and behavior of waves. The student is expected to:

(D) investigate behaviors of waves, including reflection, refraction, diffraction, interference, resonance, and the Doppler effect.

Section Key Terms

antinode

constructive interference

destructive interference

inversion

nodes

reflection

refraction

standing wave

superposition

Teacher Support

[BL][OL] Review waves, their types, and their properties, as covered in the previous sections.

Superposition of Waves

Most waves do not look very simple. They look more like the waves in Figure 13.10, rather than the simple water wave considered in the previous sections, which has a perfect sinusoidal shape.

Figure

13.10

These waves result from the superposition of several waves from different sources, producing a complex pattern. (Waterborough, Wikimedia Commons)

Teacher Support

The horizontal waves in the picture bounce off the wall of the lake seen in the front part of the picture. These superimpose or combine with waves moving in a different direction. When they combine, their energies get added, forming higher peaks and lower crests in specific places. This is why the water has a crisscross pattern.

Most waves appear complex because they result from two or more simple waves that combine as they come together at the same place at the same time—a phenomenon called superposition.

Waves superimpose by adding their disturbances; each disturbance corresponds to a force, and all the forces add. If the disturbances are along the same line, then the resulting wave is a simple addition of the disturbances of the individual waves, that is, their amplitudes add.

Wave InterferenceThe two special cases of superposition that produce the simplest results are pure constructive interference and pure destructive interference.

Pure constructive interference occurs when two identical waves arrive at the same point exactly in phase. When waves are exactly in phase, the crests of the two waves are precisely aligned, as are the troughs. Refer to Figure 13.11. Because the disturbances add, the pure constructive interference of two waves with the same amplitude produces a wave that has twice the amplitude of the two individual waves, but has the same wavelength.

Figure

13.11

The pure constructive interference of two identical waves produces a wave with twice the amplitude but the same wavelength.

Figure 13.12 shows two identical waves that arrive exactly out of phase—that is, precisely aligned crest to trough—producing pure destructive interference. Because the disturbances are in opposite directions for this superposition, the resulting amplitude is zero for pure destructive interference; that is, the waves completely cancel out each other.

Figure

13.12

The pure destructive interference of two identical waves produces zero amplitude, or complete cancellation.

While pure constructive interference and pure destructive interference can occur, they are not very common because they require precisely aligned identical waves. The superposition of most waves that we see in nature produces a combination of constructive and destructive interferences.

Waves that are not results of pure constructive or destructive interference can vary from place to place and time to time. The sound from a stereo, for example, can be loud in one spot and soft in another. The varying loudness means that the sound waves add partially constructively and partially destructively at different locations. A stereo has at least two speakers that create sound waves, and waves can reflect from walls. All these waves superimpose.

An example of sounds that vary over time from constructive to destructive is found in the combined whine of jet engines heard by a stationary passenger. The volume of the combined sound can fluctuate up and down as the sound from the two engines varies in time from constructive to destructive.

The two previous examples considered waves that are similar—both stereo speakers generate sound waves with the same amplitude and wavelength, as do the jet engines. But what happens when two waves that are not similar, that is, having different amplitudes and wavelengths, are superimposed? An example of the superposition of two dissimilar waves is shown in Figure 13.13. Here again, the disturbances add and subtract, but they produce an even more complicated-looking wave. The resultant wave from the combined disturbances of two dissimilar waves looks much different than the idealized sinusoidal shape of a periodic wave.

Figure

13.13

The superposition of nonidentical waves exhibits both constructive and destructive interferences.

Virtual Physics

Wave Interference

Access multimedia content

In this simulation, make waves with a dripping faucet, an audio speaker, or a laser by switching between the water, sound, and light tabs. Contrast and compare how the different types of waves behave. Try rotating the view from top to side to make observations. Then experiment with adding a second source or a pair of slits to create an interference pattern.

PhET Explorations: Wave Interference.

Make waves with a dripping faucet, audio speaker, or laser! Add a second source or a pair of slits to create an interference pattern.

Access multimedia content

In the water tab, compare the waves generated by one drip versus two drips. What happens to the amplitude of the waves when there are two drips? Is this constructive or destructive interference? Why would this be the case?

The amplitude of the water waves remains same because of the destructive interference as the drips of water hit the surface at the same time.

The amplitude of the water waves is canceled because of the destructive interference as the drips of water hit the surface at the same time.

The amplitude of water waves remains same because of the constructive interference as the drips of water hit the surface at the same time.

The amplitude of water waves doubles because of the constructive interference as the drips of water hit the surface at the same time.

Standing Waves

Sometimes waves do not seem to move and they appear to just stand in place, vibrating. Such waves are called standing waves and are formed by the superposition of two or more waves moving in opposite directions. The waves move through each other with their disturbances adding as they go by. If the two waves have the same amplitude and wavelength, then they alternate between constructive and destructive interference. Standing waves created by the superposition of two identical waves moving in opposite directions are illustrated in Figure 13.14.

Figure

13.14

A standing wave is created by the superposition of two identical waves moving in opposite directions. The oscillations are at fixed locations in space and result from alternating constructive and destructive interferences.

As an example, standing waves can be seen on the surface of a glass of milk in a refrigerator. The vibrations from the refrigerator motor create waves on the milk that oscillate up and down but do not seem to move across the surface. The two waves that produce standing waves may be due to the reflections from the side of the glass.

Earthquakes can create standing waves and cause constructive and destructive interferences. As the earthquake waves travel along the surface of Earth and reflect off denser rocks, constructive interference occurs at certain points. As a result, areas closer to the epicenter are not damaged while areas farther from the epicenter are damaged.

Standing waves are also found on the strings of musical instruments and are due to reflections of waves from the ends of the string. Figure 13.15 and Figure 13.16 show three standing waves that can be created on a string that is fixed at both ends. When the wave reaches the fixed end, it has nowhere else to go but back where it came from, causing the reflection. The nodes are the points where the string does not move; more generally, the nodes are the points where the wave disturbance is zero in a standing wave. The fixed ends of strings must be nodes, too, because the string cannot move there.

The antinode is the location of maximum amplitude in standing waves. The standing waves on a string have a frequency that is related to the propagation speed

of the disturbance on the string. The wavelength

λ is determined by the distance between the points where the string is fixed in place.

Figure

13.15

The figure shows a string oscillating with its maximum disturbance as the antinode.

Figure

13.16

The figure shows a string oscillating with multiple nodes.

Reflection and Refraction of Waves

As we saw in the case of standing waves on the strings of a musical instrument, reflection is the change in direction of a wave when it bounces off a barrier, such as a fixed end. When the wave hits the fixed end, it changes direction, returning to its source. As it is reflected, the wave experiences an inversion, which means that it flips vertically. If a wave hits the fixed end with a crest, it will return as a trough, and vice versa (Henderson 2015). Refer to Figure 13.17.

Figure

13.17

A wave is inverted after reflection from a fixed end.

Tips For Success

If the end is not fixed, it is said to be a free end, and no inversion occurs. When the end is loosely attached, it reflects without inversion, and when the end is not attached to anything, it does not reflect at all. You may have noticed this while changing the settings from Fixed End to Loose End to No End in the Waves on a String PhET simulation.

Rather than encountering a fixed end or barrier, waves sometimes pass from one medium into another, for instance, from air into water. Different types of media have different properties, such as density or depth, that affect how a wave travels through them. At the boundary between media, waves experience refraction—they change their path of propagation. As the wave bends, it also changes its speed and wavelength upon entering the new medium. Refer to Figure 13.18.

Figure

13.18

A wave refracts as it enters a different medium.

For example, water waves traveling from the deep end to the shallow end of a swimming pool experience refraction. They bend in a path closer to perpendicular to the surface of the water, propagate slower, and decrease in wavelength as they enter shallower water.

Check Your Understanding

Teacher Support

Use these questions to assess students’ achievement of the section’s learning objectives. If students are struggling with a specific objective, these questions will help identify such objective and direct them to the relevant content.

13.

What is the superposition of waves?

When a single wave splits into two different waves at a point

When two waves combine at the same place at the same time

14.

How do waves superimpose on one another?

By adding their frequencies

By adding their wavelengths

By adding their disturbances

By adding their speeds

What is interference of waves?

Interference is a superposition of two waves to form a resultant wave with higher or lower frequency.

Interference is a superposition of two waves to form a wave of larger or smaller amplitude.

Interference is a superposition of two waves to form a resultant wave with higher or lower velocity.

Interference is a superposition of two waves to form a resultant wave with longer or shorter wavelength.

16.

Is the following statement true or false? The two types of interference are constructive and destructive interferences.

True

False

17.

What are standing waves?

Waves that appear to remain in one place and do not seem to move

Waves that seem to move along a trajectory

How are standing waves formed?

Standing waves are formed by the superposition of two or more waves moving in opposite directions.

Standing waves are formed by the superposition of two or more waves moving in the same direction.

Standing waves are formed by the superposition of two or more waves moving in perpendicular directions.

Standing waves are formed by the superposition of two or more waves moving in arbitrary directions.

What is the reflection of a wave?

The reflection of a wave is the change in amplitude of a wave when it bounces off a barrier.

The reflection of a wave is the change in frequency of a wave when it bounces off a barrier.

The reflection of a wave is the change in velocity of a wave when it bounces off a barrier.

The reflection of a wave is the change in direction of a wave when it bounces off a barrier.

What is inversion of a wave?

Inversion occurs when a wave reflects off a fixed end and the wave amplitude changes sign.

Inversion occurs when a wave reflects off a loose end and the wave amplitude changes sign.

Inversion occurs when a wave reflects off a fixed end without the wave amplitude changing sign.

Inversion occurs when a wave reflects off a loose end without the wave amplitude changing sign.

PreviousNextOrder a print copyAs an Amazon Associate we earn from qualifying purchases.Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the

Creative Commons Attribution License

and you must attribute Texas Education Agency (TEA). The original material is available at:

https://www.texasgateway.org/book/tea-physics

. Changes were made to the original material, including updates to art, structure, and other content updates.

Attribution information

If you are redistributing all or part of this book in a print format,

then you must include on every physical page the following attribution:

Access for free at https://openstax.org/books/physics/pages/1-introduction

If you are redistributing all or part of this book in a digital format,

then you must include on every digital page view the following attribution:

Access for free at https://openstax.org/books/physics/pages/1-introduction

Citation information

Use the information below to generate a citation. We recommend using a

citation tool such as

this one.

Authors: Paul Peter Urone, Roger Hinrichs

Publisher/website: OpenStax

Book title: Physics

Publication date: Mar 26, 2020

Location: Houston, Texas

Book URL: https://openstax.org/books/physics/pages/1-introduction

Section URL: https://openstax.org/books/physics/pages/13-3-wave-interaction-superposition-and-interference

are not subject to the Creative Commons license and may not be reproduced without the prior and express written

consent of Rice University.

Our mission is to improve educational access and learning for everyone.

OpenStax is part of Rice University, which is a 501(c)(3) nonprofit.

Give today and help us reach more students.

HelpContact UsSupport CenterFAQOpenStaxPressNewsletterCareersPoliciesAccessibility StatementTerms of UseLicensingPrivacy Policy

are licensed under a

Creative Commons Attribution 4.0 International License.

Advanced Placement® and AP® are trademarks registered and/or owned by the College Board,

which is not affiliated with, and does not endorse, this site.

Just a moment...

a moment...Enable JavaScript and cookies to conti

Wave interference - Wikipedia

Jump to content

Main menu

move to sidebar

hide

Navigation

Main pageContentsCurrent eventsRandom articleAbout WikipediaContact usDonate

Contribute

HelpLearn to editCommunity portalRecent changesUpload file

Create account

Personal tools

Create account Log in

Pages for logged out editors learn more

ContributionsTalk

Contents

move to sidebar

hide

(Top)

1Etymology

2Mechanisms

Toggle Mechanisms subsection

2.1Real-valued wave functions

2.2Between two plane waves

2.3Between two spherical waves

2.4Multiple beams

3Complex valued wave functions

Toggle Complex valued wave functions subsection

3.1Optical wave interference

3.1.1Light source requirements

3.1.2Optical arrangements

3.2Quantum interference

4Applications

Toggle Applications subsection

4.1Beat

4.2Optical interferometry

4.3Radio interferometry

4.4Acoustic interferometry

5See also

6References

7External links

Toggle the table of contents

Wave interference

70 languages

አማርኛالعربيةAsturianuAzərbaycancaবাংলাBân-lâm-gúБеларускаяБългарскиBosanskiCatalàЧӑвашлаČeštinaCymraegDanskDeutschEestiΕλληνικάEspañolEsperantoEuskaraفارسیFrançaisGaeilgeGalego한국어Հայերենहिन्दीHrvatskiIdoBahasa IndonesiaInterlinguaItalianoעבריתಕನ್ನಡKreyòl ayisyenLatviešuLëtzebuergeschLietuviųMagyarМакедонскиമലയാളംBahasa MelayuNederlands日本語Norsk bokmålNorsk nynorskOʻzbekcha / ўзбекчаਪੰਜਾਬੀPolskiPortuguêsRomânăРусскийSimple EnglishSlovenčinaSlovenščinaСрпски / srpskiSrpskohrvatski / српскохрватскиSuomiSvenskaTagalogதமிழ்Татарча / tatarçaไทยTürkçeУкраїнськаاردوTiếng Việt吴语粵語中文

Edit links

ArticleTalk

English

ReadEditView history

Tools

move to sidebar

hide

Actions

ReadEditView history

General

What links hereRelated changesUpload fileSpecial pagesPermanent linkPage informationCite this pageGet shortened URLDownload QR codeWikidata item

Print/export

Download as PDFPrintable version

In other projects

Wikimedia Commons

From Wikipedia, the free encyclopedia

Phenomenon resulting from the superposition of two waves

For interference in radio communications, see Interference (communication).

"Interference pattern" redirects here. For Moiré patterns, see Moiré pattern.

This article may be too technical for most readers to understand. Please help improve it to make it understandable to non-experts, without removing the technical details. (February 2022) (Learn how and when to remove this template message)

The interference of two waves. In phase: the two lower waves combine (left panel), resulting in a wave of added amplitude (constructive interference). Out of phase: (here by 180 degrees), the two lower waves combine (right panel), resulting in a wave of zero amplitude (destructive interference).

In physics, interference is a phenomenon in which two coherent waves are combined by adding their intensities or displacements with due consideration for their phase difference. The resultant wave may have greater intensity (constructive interference) or lower amplitude (destructive interference) if the two waves are in phase or out of phase, respectively.

Interference effects can be observed with all types of waves, for example, light, radio, acoustic, surface water waves, gravity waves, or matter waves as well as in loudspeakers as electrical waves.

Etymology[edit]

The word interference is derived from the Latin words inter which means "between" and fere which means "hit or strike", and was coined by Thomas Young in 1801.[1][2][3]

Mechanisms[edit]

Interference of right traveling (green) and left traveling (blue) waves in Two-dimensional space, resulting in final (red) wave

Interference of waves from two point sources.

Cropped tomography scan animation of laser light interference passing through two pinholes (side edges).

The principle of superposition of waves states that when two or more propagating waves of the same type are incident on the same point, the resultant amplitude at that point is equal to the vector sum of the amplitudes of the individual waves.[4] If a crest of a wave meets a crest of another wave of the same frequency at the same point, then the amplitude is the sum of the individual amplitudes—this is constructive interference. If a crest of one wave meets a trough of another wave, then the amplitude is equal to the difference in the individual amplitudes—this is known as destructive interference. In ideal mediums (water, air are almost ideal) energy is always conserved, at points of destructive interference energy is stored in the elasticity of the medium. For example when we drop 2 pebbles in a pond we see a pattern but eventually waves continue and only when they reach the shore is the energy absorbed away from the medium.

A magnified image of a coloured interference pattern in a soap film. The "black holes" are areas of almost total destructive interference (antiphase).

Constructive interference occurs when the phase difference between the waves is an even multiple of π (180°), whereas destructive interference occurs when the difference is an odd multiple of π. If the difference between the phases is intermediate between these two extremes, then the magnitude of the displacement of the summed waves lies between the minimum and maximum values.

Consider, for example, what happens when two identical stones are dropped into a still pool of water at different locations. Each stone generates a circular wave propagating outwards from the point where the stone was dropped. When the two waves overlap, the net displacement at a particular point is the sum of the displacements of the individual waves. At some points, these will be in phase, and will produce a maximum displacement. In other places, the waves will be in anti-phase, and there will be no net displacement at these points. Thus, parts of the surface will be stationary—these are seen in the figure above and to the right as stationary blue-green lines radiating from the centre.

Interference of light is a unique phenomenon in that we can never observe superposition of the EM field directly as we can, for example, in water. Superposition in the EM field is an assumed phenomenon and necessary to explain how two light beams pass through each other and continue on their respective paths. Prime examples of light interference are the famous double-slit experiment, laser speckle, anti-reflective coatings and interferometers.

In addition to classical wave model for understanding optical interference, quantum matter waves also demonstrate interference.

Real-valued wave functions[edit]

The above can be demonstrated in one dimension by deriving the formula for the sum of two waves. The equation for the amplitude of a sinusoidal wave traveling to the right along the x-axis is

(

)

cos

⁡

(

−

)

{\displaystyle W_{1}(x,t)=A\cos(kx-\omega t)}

where

{\displaystyle A}

is the peak amplitude,

{\displaystyle k=2\pi /\lambda }

is the wavenumber and

{\displaystyle \omega =2\pi f}

is the angular frequency of the wave. Suppose a second wave of the same frequency and amplitude but with a different phase is also traveling to the right

(

)

cos

⁡

(

−

)

{\displaystyle W_{2}(x,t)=A\cos(kx-\omega t+\varphi )}

where

{\displaystyle \varphi }

is the phase difference between the waves in radians. The two waves will superpose and add: the sum of the two waves is

[

cos

⁡

(

−

)

cos

⁡

(

−

)

]

{\displaystyle W_{1}+W_{2}=A[\cos(kx-\omega t)+\cos(kx-\omega t+\varphi )].}

Using the trigonometric identity for the sum of two cosines:

cos

⁡

cos

⁡

cos

⁡

(

−

)

cos

⁡

(

)

{\textstyle \cos a+\cos b=2\cos \left({a-b \over 2}\right)\cos \left({a+b \over 2}\right),}

this can be written

cos

⁡

(

)

cos

⁡

(

−

)

{\displaystyle W_{1}+W_{2}=2A\cos \left({\varphi \over 2}\right)\cos \left(kx-\omega t+{\varphi \over 2}\right).}

This represents a wave at the original frequency, traveling to the right like its components, whose amplitude is proportional to the cosine of

{\displaystyle \varphi /2}

Constructive interference: If the phase difference is an even multiple of π:

…

−

…

{\displaystyle \varphi =\ldots ,-4\pi ,-2\pi ,0,2\pi ,4\pi ,\ldots }

then

cos

⁡

(

)

{\displaystyle \left|\cos(\varphi /2)\right|=1}

, so the sum of the two waves is a wave with twice the amplitude

cos

⁡

(

−

)

{\displaystyle W_{1}+W_{2}=2A\cos(kx-\omega t)}

Destructive interference: If the phase difference is an odd multiple of π:

…

−

…

{\displaystyle \varphi =\ldots ,-3\pi ,\,-\pi ,\,\pi ,\,3\pi ,\,5\pi ,\ldots }

then

cos

⁡

(

)

{\displaystyle \cos(\varphi /2)=0\,}

, so the sum of the two waves is zero

{\displaystyle W_{1}+W_{2}=0}

Between two plane waves[edit]

Geometrical arrangement for two plane wave interference

Interference fringes in overlapping plane waves

A simple form of interference pattern is obtained if two plane waves of the same frequency intersect at an angle.

Interference is essentially an energy redistribution process. The energy which is lost at the destructive interference is regained at the constructive interference.

One wave is travelling horizontally, and the other is travelling downwards at an angle θ to the first wave. Assuming that the two waves are in phase at the point B, then the relative phase changes along the x-axis. The phase difference at the point A is given by

sin

⁡

{\displaystyle \Delta \varphi ={\frac {2\pi d}{\lambda }}={\frac {2\pi x\sin \theta }{\lambda }}.}

It can be seen that the two waves are in phase when

sin

⁡

…

{\displaystyle {\frac {x\sin \theta }{\lambda }}=0,\pm 1,\pm 2,\ldots ,}

and are half a cycle out of phase when

sin

⁡

…

{\displaystyle {\frac {x\sin \theta }{\lambda }}=\pm {\frac {1}{2}},\pm {\frac {3}{2}},\ldots }

Constructive interference occurs when the waves are in phase, and destructive interference when they are half a cycle out of phase. Thus, an interference fringe pattern is produced, where the separation of the maxima is

sin

⁡

{\displaystyle d_{f}={\frac {\lambda }{\sin \theta }}}

and df is known as the fringe spacing. The fringe spacing increases with increase in wavelength, and with decreasing angle θ.

The fringes are observed wherever the two waves overlap and the fringe spacing is uniform throughout.

Between two spherical waves[edit]

Optical interference between two point sources that have different wavelengths and separations of sources.

A point source produces a spherical wave. If the light from two point sources overlaps, the interference pattern maps out the way in which the phase difference between the two waves varies in space. This depends on the wavelength and on the separation of the point sources. The figure to the right shows interference between two spherical waves. The wavelength increases from top to bottom, and the distance between the sources increases from left to right.

When the plane of observation is far enough away, the fringe pattern will be a series of almost straight lines, since the waves will then be almost planar.

Multiple beams[edit]

Interference occurs when several waves are added together provided that the phase differences between them remain constant over the observation time.

It is sometimes desirable for several waves of the same frequency and amplitude to sum to zero (that is, interfere destructively, cancel). This is the principle behind, for example, 3-phase power and the diffraction grating. In both of these cases, the result is achieved by uniform spacing of the phases.

It is easy to see that a set of waves will cancel if they have the same amplitude and their phases are spaced equally in angle. Using phasors, each wave can be represented as

{\displaystyle Ae^{i\varphi _{n}}}

for

{\displaystyle N}

waves from

{\displaystyle n=0}

−

{\displaystyle n=N-1}

, where

−

{\displaystyle \varphi _{n}-\varphi _{n-1}={\frac {2\pi }{N}}.}

To show that

∑

−

{\displaystyle \sum _{n=0}^{N-1}Ae^{i\varphi _{n}}=0}

one merely assumes the converse, then multiplies both sides by

{\displaystyle e^{i{\frac {2\pi }{N}}}.}

The Fabry–Pérot interferometer uses interference between multiple reflections.

A diffraction grating can be considered to be a multiple-beam interferometer; since the peaks which it produces are generated by interference between the light transmitted by each of the elements in the grating; see interference vs. diffraction for further discussion.

Complex valued wave functions[edit]

Mechanical and gravity waves can be directly observed: they are real-valued wave functions; optical and matter waves cannot be directly observed: they are complex valued wave functions. Some of the differences between real valued and complex valued wave interference include:

The interference involves different types of mathematical functions: A classical wave is a real function representing the displacement from an equilibrium position; an optical or quantum wavefunction is a complex function. A classical wave at any point can be positive or negative; the quantum probability function is non-negative.

Any two different real waves in the same medium interfere; complex waves must be coherent to interfere. In practice this means the wave must come from the same source and have similar frequencies

Real wave interference is obtained simply by adding the displacements from equilibrium (or amplitudes) of the two waves; In complex wave interference, we measure the modulus of the wavefunction squared.

Optical wave interference[edit]

Creation of interference fringes by an optical flat on a reflective surface. Light rays from a monochromatic source pass through the glass and reflect off both the bottom surface of the flat and the supporting surface. The tiny gap between the surfaces means the two reflected rays have different path lengths. In addition the ray reflected from the bottom plate undergoes a 180° phase reversal. As a result, at locations (a) where the path difference is an odd multiple of λ/2, the waves reinforce. At locations (b) where the path difference is an even multiple of λ/2 the waves cancel. Since the gap between the surfaces varies slightly in width at different points, a series of alternating bright and dark bands, interference fringes, are seen.

Because the frequency of light waves (~1014 Hz) is too high for currently available detectors to detect the variation of the electric field of the light, it is possible to observe only the intensity of an optical interference pattern. The intensity of the light at a given point is proportional to the square of the average amplitude of the wave. This can be expressed mathematically as follows. The displacement of the two waves at a point r is:

(

)

(

)

[

(

)

−

]

{\displaystyle U_{1}(\mathbf {r} ,t)=A_{1}(\mathbf {r} )e^{i[\varphi _{1}(\mathbf {r} )-\omega t]}}

(

)

(

)

[

(

)

−

]

{\displaystyle U_{2}(\mathbf {r} ,t)=A_{2}(\mathbf {r} )e^{i[\varphi _{2}(\mathbf {r} )-\omega t]}}

where A represents the magnitude of the displacement, φ represents the phase and ω represents the angular frequency.

The displacement of the summed waves is

(

)

(

)

[

(

)

−

]

(

)

[

(

)

−

]

{\displaystyle U(\mathbf {r} ,t)=A_{1}(\mathbf {r} )e^{i[\varphi _{1}(\mathbf {r} )-\omega t]}+A_{2}(\mathbf {r} )e^{i[\varphi _{2}(\mathbf {r} )-\omega t]}.}

The intensity of the light at r is given by

(

)

∫

(

)

∗

(

)

∝

(

)

(

)

(

)

(

)

cos

⁡

[

(

)

−

(

)

]

{\displaystyle I(\mathbf {r} )=\int U(\mathbf {r} ,t)U^{*}(\mathbf {r} ,t)\,dt\propto A_{1}^{2}(\mathbf {r} )+A_{2}^{2}(\mathbf {r} )+2A_{1}(\mathbf {r} )A_{2}(\mathbf {r} )\cos[\varphi _{1}(\mathbf {r} )-\varphi _{2}(\mathbf {r} )].}

This can be expressed in terms of the intensities of the individual waves as

(

)

(

)

(

)

(

)

(

)

cos

⁡

[

(

)

−

(

)

]

{\displaystyle I(\mathbf {r} )=I_{1}(\mathbf {r} )+I_{2}(\mathbf {r} )+2{\sqrt {I_{1}(\mathbf {r} )I_{2}(\mathbf {r} )}}\cos[\varphi _{1}(\mathbf {r} )-\varphi _{2}(\mathbf {r} )].}

Thus, the interference pattern maps out the difference in phase between the two waves, with maxima occurring when the phase difference is a multiple of 2π. If the two beams are of equal intensity, the maxima are four times as bright as the individual beams, and the minima have zero intensity.

Classically the two waves must have the same polarization to give rise to interference fringes since it is not possible for waves of different polarizations to cancel one another out or add together. Instead, when waves of different polarization are added together, they give rise to a wave of a different polarization state.

Quantum mechanically the theories of Paul Dirac and Richard Feynman offer a more modern approach. Dirac showed that every quanta or photon of light acts on its own which he famously stated as "every photon interferes with itself". Richard Feynman showed that by evaluating a path integral where all possible paths are considered, that a number of higher probability paths will emerge. In thin films for example, film thickness which is not a multiple of light wavelength will not allow the quanta to traverse, only reflection is possible.

Light source requirements[edit]

The discussion above assumes that the waves which interfere with one another are monochromatic, i.e. have a single frequency—this requires that they are infinite in time. This is not, however, either practical or necessary. Two identical waves of finite duration whose frequency is fixed over that period will give rise to an interference pattern while they overlap. Two identical waves which consist of a narrow spectrum of frequency waves of finite duration (but shorter than their coherence time), will give a series of fringe patterns of slightly differing spacings, and provided the spread of spacings is significantly less than the average fringe spacing, a fringe pattern will again be observed during the time when the two waves overlap.

Conventional light sources emit waves of differing frequencies and at different times from different points in the source. If the light is split into two waves and then re-combined, each individual light wave may generate an interference pattern with its other half, but the individual fringe patterns generated will have different phases and spacings, and normally no overall fringe pattern will be observable. However, single-element light sources, such as sodium- or mercury-vapor lamps have emission lines with quite narrow frequency spectra. When these are spatially and colour filtered, and then split into two waves, they can be superimposed to generate interference fringes.[5] All interferometry prior to the invention of the laser was done using such sources and had a wide range of successful applications.

A laser beam generally approximates much more closely to a monochromatic source, and thus it is much more straightforward to generate interference fringes using a laser. The ease with which interference fringes can be observed with a laser beam can sometimes cause problems in that stray reflections may give spurious interference fringes which can result in errors.

Normally, a single laser beam is used in interferometry, though interference has been observed using two independent lasers whose frequencies were sufficiently matched to satisfy the phase requirements.[6]

This has also been observed for widefield interference between two incoherent laser sources.[7]

It is also possible to observe interference fringes using white light. A white light fringe pattern can be considered to be made up of a 'spectrum' of fringe patterns each of slightly different spacing. If all the fringe patterns are in phase in the centre, then the fringes will increase in size as the wavelength decreases and the summed intensity will show three to four fringes of varying colour. Young describes this very elegantly in his discussion of two slit interference. Since white light fringes are obtained only when the two waves have travelled equal distances from the light source, they can be very useful in interferometry, as they allow the zero path difference fringe to be identified.[8]

Optical arrangements[edit]

To generate interference fringes, light from the source has to be divided into two waves which then have to be re-combined. Traditionally, interferometers have been classified as either amplitude-division or wavefront-division systems.

In an amplitude-division system, a beam splitter is used to divide the light into two beams travelling in different directions, which are then superimposed to produce the interference pattern. The Michelson interferometer and the Mach–Zehnder interferometer are examples of amplitude-division systems.

In wavefront-division systems, the wave is divided in space—examples are Young's double slit interferometer and Lloyd's mirror.

Interference can also be seen in everyday phenomena such as iridescence and structural coloration. For example, the colours seen in a soap bubble arise from interference of light reflecting off the front and back surfaces of the thin soap film. Depending on the thickness of the film, different colours interfere constructively and destructively.

Iridiscence caused by thin-film interference

Smartphone with iridescent back panel

An oil spill

White light interference in a soap bubble.

Quantum interference[edit]

See also: Double-slit experiment and Matter wave

Part of a series of articles aboutQuantum mechanics

ℏ

∂

(

)

⟩

(

)

⟩

{\displaystyle i\hbar {\frac {\partial }{\partial t}}|\psi (t)\rangle ={\hat {H}}|\psi (t)\rangle }

Schrödinger equation

Introduction

Glossary

History

Background

Classical mechanics

Old quantum theory

Bra–ket notation

Hamiltonian

Interference

Fundamentals

Complementarity

Decoherence

Entanglement

Energy level

Measurement

Nonlocality

Quantum number

State

Superposition

Symmetry

Tunnelling

Uncertainty

Wave function

Collapse

Experiments

Bell's inequality

Davisson–Germer

Double-slit

Elitzur–Vaidman

Franck–Hertz

Leggett–Garg inequality

Mach–Zehnder

Popper

Quantum eraser

Delayed-choice

Schrödinger's cat

Stern–Gerlach

Wheeler's delayed-choice

Formulations

Overview

Heisenberg

Interaction

Matrix

Phase-space

Schrödinger

Sum-over-histories (path integral)

Equations

Dirac

Klein–Gordon

Pauli

Rydberg

Schrödinger

Interpretations

Bayesian

Consistent histories

Copenhagen

de Broglie–Bohm

Ensemble

Hidden-variable

Local

Superdeterminism

Many-worlds

Objective collapse

Quantum logic

Relational

Transactional

Von Neumann–Wigner

Advanced topics

Relativistic quantum mechanics

Quantum field theory

Quantum information science

Quantum computing

Quantum chaos

EPR paradox

Density matrix

Scattering theory

Quantum statistical mechanics

Quantum machine learning

Scientists

Aharonov

Bell

Bethe

Blackett

Bloch

Bohm

Bohr

Born

Bose

de Broglie

Compton

Dirac

Davisson

Debye

Ehrenfest

Einstein

Everett

Fock

Fermi

Feynman

Glauber

Gutzwiller

Heisenberg

Hilbert

Jordan

Kramers

Pauli

Lamb

Landau

Laue

Moseley

Millikan

Onnes

Planck

Rabi

Raman

Rydberg

Schrödinger

Simmons

Sommerfeld

von Neumann

Weyl

Wien

Wigner

Zeeman

Zeilinger

vte

Quantum interference – the observed wave-behavior of matter[9] – resembles optical interference. Let

(

)

{\displaystyle \Psi (x,t)}

be a wavefunction solution of the Schrödinger equation for a quantum mechanical object. Then the probability

(

)

{\displaystyle P(x)}

of observing the object at position

{\displaystyle x}

(

)

(

)

∗

(

)

(

)

{\displaystyle P(x)=|\Psi (x,t)|^{2}=\Psi ^{*}(x,t)\Psi (x,t)}

where * indicates complex conjugation. Quantum interference concerns the issue of this probability when the wavefunction is expressed as a sum or linear superposition of two terms

(

)

(

)

(

)

{\displaystyle \Psi (x,t)=\Psi _{A}(x,t)+\Psi _{B}(x,t)}

(

)

(

)

(

)

(

)

(

∗

(

)

(

)

(

)

∗

(

)

{\displaystyle P(x)=|\Psi (x,t)|^{2}=|\Psi _{A}(x,t)|^{2}+|\Psi _{B}(x,t)|^{2}+(\Psi _{A}^{*}(x,t)\Psi _{B}(x,t)+\Psi _{A}(x,t)\Psi _{B}^{*}(x,t))}

Usually,

(

)

{\displaystyle \Psi _{A}(x,t)}

and

(

)

{\displaystyle \Psi _{B}(x,t)}

correspond to distinct situations A and B. When this is the case, the equation

(

)

(

)

(

)

{\displaystyle \Psi (x,t)=\Psi _{A}(x,t)+\Psi _{B}(x,t)}

indicates that the object can be in situation A or situation B. The above equation can then be interpreted as: The probability of finding the object at

{\displaystyle x}

is the probability of finding the object at

{\displaystyle x}

when it is in situation A plus the probability of finding the object at

{\displaystyle x}

when it is in situation B plus an extra term. This extra term, which is called the quantum interference term, is

∗

(

)

(

)

(

)

∗

(

)

{\displaystyle \Psi _{A}^{*}(x,t)\Psi _{B}(x,t)+\Psi _{A}(x,t)\Psi _{B}^{*}(x,t)}

in the above equation. As in the classical wave case above, the quantum interference term can add (constructive interference) or subtract (destructive interference) from

(

)

(

)

{\displaystyle |\Psi _{A}(x,t)|^{2}+|\Psi _{B}(x,t)|^{2}}

in the above equation depending on whether the quantum interference term is positive or negative. If this term is absent for all

{\displaystyle x}

, then there is no quantum mechanical interference associated with situations A and B.

The best known example of quantum interference is the double-slit experiment. In this experiment, matter waves from electrons, atoms or molecules approach a barrier with two slits in it. One slit becomes

(

)

{\displaystyle \Psi _{A}(x,t)}

and the other becomes

(

)

{\displaystyle \Psi _{B}(x,t)}

. The interference pattern occurs on the far side, observed by detectors suitable to the particles originating the matter wave.[10] The pattern matches the optical double slit pattern.

Applications[edit]

Beat[edit]

Main article: Beat (acoustics)

In acoustics, a beat is an interference pattern between two sounds of slightly different frequencies, perceived as a periodic variation in volume whose rate is the difference of the two frequencies.

With tuning instruments that can produce sustained tones, beats can be readily recognized. Tuning two tones to a unison will present a peculiar effect: when the two tones are close in pitch but not identical, the difference in frequency generates the beating. The volume varies like in a tremolo as the sounds alternately interfere constructively and destructively. As the two tones gradually approach unison, the beating slows down and may become so slow as to be imperceptible. As the two tones get further apart, their beat frequency starts to approach the range of human pitch perception,[11] the beating starts to sound like a note, and a combination tone is produced. This combination tone can also be referred to as a missing fundamental, as the beat frequency of any two tones is equivalent to the frequency of their implied fundamental frequency.

Main article: Interferometry

Optical interferometry[edit]

Main article: Optical interferometry

Interferometry has played an important role in the advancement of physics, and also has a wide range of applications in physical and engineering measurement.

Thomas Young's double slit interferometer in 1803 demonstrated interference fringes when two small holes were illuminated by light from another small hole which was illuminated by sunlight. Young was able to estimate the wavelength of different colours in the spectrum from the spacing of the fringes. The experiment played a major role in the general acceptance of the wave theory of light.[8]

In quantum mechanics, this experiment is considered to demonstrate the inseparability of the wave and particle natures of light and other quantum particles (wave–particle duality). Richard Feynman was fond of saying that all of quantum mechanics can be gleaned from carefully thinking through the implications of this single experiment.[12]

The results of the Michelson–Morley experiment are generally considered to be the first strong evidence against the theory of a luminiferous aether and in favor of special relativity.

Interferometry has been used in defining and calibrating length standards. When the metre was defined as the distance between two marks on a platinum-iridium bar, Michelson and Benoît used interferometry to measure the wavelength of the red cadmium line in the new standard, and also showed that it could be used as a length standard. Sixty years later, in 1960, the metre in the new SI system was defined to be equal to 1,650,763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum. This definition was replaced in 1983 by defining the metre as the distance travelled by light in vacuum during a specific time interval. Interferometry is still fundamental in establishing the calibration chain in length measurement.

Interferometry is used in the calibration of slip gauges (called gauge blocks in the US) and in coordinate-measuring machines. It is also used in the testing of optical components.[13]

Radio interferometry[edit]

Main article: Astronomical interferometer

The Very Large Array, an interferometric array formed from many smaller telescopes, like many larger radio telescopes.

In 1946, a technique called astronomical interferometry was developed. Astronomical radio interferometers usually consist either of arrays of parabolic dishes or two-dimensional arrays of omni-directional antennas. All of the telescopes in the array are widely separated and are usually connected together using coaxial cable, waveguide, optical fiber, or other type of transmission line. Interferometry increases the total signal collected, but its primary purpose is to vastly increase the resolution through a process called Aperture synthesis. This technique works by superposing (interfering) the signal waves from the different telescopes on the principle that waves that coincide with the same phase will add to each other while two waves that have opposite phases will cancel each other out. This creates a combined telescope that is equivalent in resolution (though not in sensitivity) to a single antenna whose diameter is equal to the spacing of the antennas farthest apart in the array.

Acoustic interferometry[edit]

An acoustic interferometer is an instrument for measuring the physical characteristics of sound waves in a gas or liquid, such velocity, wavelength, absorption, or impedance. A vibrating crystal creates ultrasonic waves that are radiated into the medium. The waves strike a reflector placed parallel to the crystal, reflected back to the source and measured.

3: Interference - Physics LibreTexts

Table of Contents menu

search Searchbuild_circle Toolbarfact_check Homeworkcancel Exit Reader Mode

school Campus Bookshelves

menu_book Bookshelves

perm_media Learning Objects

how_to_reg Request Instructor Account

hub Instructor Commons

Search this book

Submit Search

Downloads expand_more

Download Page (PDF)

Download Full Book (PDF)

Resources expand_more

Periodic Table

Physics Constants

Scientific Calculator

Reference expand_more

Reference & Cite

Tools expand_more

Help expand_more

Get Help

Feedback

Readability

selected template will load here

Error

This action is not available.

chrome_reader_mode Enter Reader Mode

University Physics III - Optics and Modern Physics (OpenStax)University Physics (OpenStax){ "3.01:_Prelude_to_Interference" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "3.02:_Young\'s_Double-Slit_Interference" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "3.03:_Mathematics_of_Interference" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "3.04:_Multiple-Slit_Interference" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "3.05:_Interference_in_Thin_Films" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "3.06:_The_Michelson_Interferometer" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "3.0A:_3.A:_Interference_(Answers)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "3.0E:_3.E:_Interference_(Exercises)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "3.0S:_3.S:_Interference_(Summary)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()" }{ "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "01:_The_Nature_of_Light" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "02:_Geometric_Optics_and_Image_Formation" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "03:_Interference" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "04:_Diffraction" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "05:__Relativity" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "06:_Photons_and_Matter_Waves" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "07:_Quantum_Mechanics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "08:_Atomic_Structure" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "09:_Condensed_Matter_Physics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "10:__Nuclear_Physics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "11:_Particle_Physics_and_Cosmology" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()" }{ "Book:_University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "Book:_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()" }Sun, 20 Feb 2022 16:01:41 GMT3: Interference45054505admin{ }AnonymousAnonymous2falsefalse[ "article:topic-guide", "authorname:openstax", "license:ccby", "showtoc:no", "program:openstax", "licenseversion:40", "source@https://openstax.org/details/books/university-physics-volume-3" ][ "article:topic-guide", "authorname:openstax", "license:ccby", "showtoc:no", "program:openstax", "licenseversion:40", "source@https://openstax.org/details/books/university-physics-volume-3" ]https://phys.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FBookshelves%2FUniversity_Physics%2FUniversity_Physics_(OpenStax)%2FUniversity_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)%2F03%253A_Interference

Search site

Go back to previous article

Username

Password

Forgot password

Expand/collapse global hierarchy

Home

Bookshelves

University Physics

University Physics (OpenStax)

University Physics III - Optics and Modern Physics (OpenStax)

3: Interference

Expand/collapse global location

3: Interference

Last updated

Save as PDF

Page ID4505

OpenStaxOpenStax

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

No headers

The most certain indication of a wave is interference. This wave characteristic is most prominent when the wave interacts with an object that is not large compared with the wavelength. Interference is observed for water waves, sound waves, light waves, and, in fact, all types of waves.

3.1: Prelude to InterferenceIf you have ever looked at the reds, blues, and greens in a sunlit soap bubble and wondered how straw-colored soapy water could produce them, you have hit upon one of the many phenomena that can only be explained by the wave character of light. The same is true for the colors seen in an oil slick or in the light reflected from a DVD. These and other interesting phenomena cannot be explained fully by geometric optics. In these cases, light interacts with objects and exhibits wave characteristics.3.2: Young's Double-Slit InterferenceYoung’s double-slit experiment gave definitive proof of the wave character of light. An interference pattern is obtained by the superposition of light from two slits. When light passes through narrow slits, the slits act as sources of coherent waves and light spreads out as semicircular waves. Pure constructive interference occurs where the waves are crest to crest or trough to trough. Pure destructive interference occurs where they are crest to trough.3.3: Mathematics of InterferenceIn double-slit diffraction, constructive interference occurs when d sin θ = mλ (for m=0,±1,±2,±3…), where d is the distance between the slits, θ is the angle relative to the incident direction, and m is the order of the interference. Destructive interference occurs when \(d \space sin \space \theta = (m + \frac{1}{2}) \lambda\), for m = 0,±1,±2,±3,…3.4: Multiple-Slit InterferenceAnalyzing the interference of light passing through two slits lays out the theoretical framework of interference and gives us a historical insight into Thomas Young’s experiments. Much of the modern-day application of slit interference uses not just two slits but many, approaching infinity for practical purposes. We start the analysis of multiple-slit interference by taking the results from our analysis of the double slit (N = 2) and extending it to configurations with numbers of slits.3.5: Interference in Thin FilmsWhen light reflects from a medium having an index of refraction greater than that of the medium in which it is traveling, a 180° phase change (or a λ/2 shift) occurs. Thin-film interference occurs between the light reflected from the top and bottom surfaces of a film. In addition to the path length difference, there can be a phase change.3.6: The Michelson InterferometerThe Michelson interferometer (invented by the American physicist Albert A. Michelson, 1852–1931) is a precision instrument that produces interference fringes by splitting a light beam into two parts and then recombining them after they have traveled different optical paths.3.A: Interference (Answers)3.E: Interference (Exercises)3.S: Interference (Summary)

This page titled 3: Interference is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

2.S: Geometric Optics and Image Formation (Summary)

3.1: Prelude to Interference

Was this article helpful?YesNo

INTERFERENCE definition | Cambridge English Dictionary

Dictionary

Translate

Grammar

Thesaurus

+Plus

Cambridge Dictionary +Plus

Shop

Cambridge Dictionary +Plus

My profile

+Plus help

Log out

Cambridge Dictionary +Plus

My profile

+Plus help

Log out

English (US)

English

Meaning of interference in English

interferencenoun [ U ] us

Your browser doesn't support HTML5 audio

/ˌɪn.t̬ɚˈfɪr.əns/ uk

Your browser doesn't support HTML5 audio

/ˌɪn.təˈfɪə.rəns/

Add to word list

C1 an occasion when someone tries to interfere in a situation: She seems to regard any advice or help from me as interference. The government's interference in the strike has been widely criticized.

C2 noise or other electronic signals that stop you from getting good pictures or sound on a television or radio

SMART Vocabulary: related words and phrases

Getting involved for one's own benefit or against others' will

a piece/slice of the action idiom

act

action

bandwagon

be in bed with idiom

bed

get

get in on something

get/muscle in on the act idiom

have a finger in the pie idiom

horn

horn in

interfere

intrude

intrusion

jump/climb/get on the bandwagon idiom

non-interference

snoot

stick your snoot in/into (something) idiom

See more results »

You can also find related words, phrases, and synonyms in the topics:

Communications - general words

Idiom

run interference

interference | Intermediate English

interferencenoun [ U ] us

Your browser doesn't support HTML5 audio

/ˌɪn·tərˈfɪər·əns/

Add to word list

On the radio, television, or telephone, interference is noise, lines, etc., that prevent a clear sound or picture from being received.

physics Interference between two waves happens when they have the same frequency and produce a force that is either stronger or weaker than one wave alone.

In sports, interference is an action that is against the rules which prevents an opposing player from completing a play.

Examples of interference

interference

They want to work together on those problems, without interference of outside militia.

From OregonLive.com

Word is out around the league about the interference in football operations.

From cleveland.com

It's pretty violent: there's no penalty for pass interference or late hits, and it's no fun unless you're hurting someone on every play.

From The Verge

Defensive pass interference is called approximately seven million times more than offensive pass interference (rough estimate).

From ESPN

It's been a ridiculous government interference on family issues.

From CNN

Their interference in the market prevents small companies from competing with large ones.

From CNN

We are not their family members and do not know what repercussions they could face by our individual interference.

From NPR

It does not seem to help answer why, when single photons pass through the grid, they still show interference.

From Phys.Org

I get to be a teacher without any interference.

From CNN

In licensed spectrum, interference disputes tend to get resolved without such loud, public fights.

From The Hill

Prosecutors are concentrating on proving that their case against him has been weakened by interference with witnesses.

From Reuters

We believe this is the first time such a quantum two-photon interference based on a parametric effect (an active process) has been demonstrated.

From Phys.Org

It just requires placing one fiber in the gas flow stream -- even in locations with strong magnetic interference.

From Phys.Org

Collocations with interference

interference

These are words often used in combination with interference. Click on a collocation to see more examples of it.

arbitrary interferenceIn these treaties, privacy is recognized as a form of autonomy-a way to ensure protection from ' 'arbitrary interference' '1 by the state or other entities.

From the Cambridge English Corpus

bureaucratic interferenceThis is a quite monstrous case of bureaucratic interference.

From the Hansard archive

Example from the Hansard archive. Contains Parliamentary information licensed under the Open Parliament Licence v3.0

constant interferenceBut this coming and going, this constant pinpricking, this constant interference without any consecutive thought and philosophy behind it, is not something to take lightly.

From the Hansard archive

Example from the Hansard archive. Contains Parliamentary information licensed under the Open Parliament Licence v3.0

See all collocations with interference

What is the pronunciation of interference?

C1,C2

Translations of interference

in Chinese (Traditional)

干涉，干預, （雜訊或其他電子訊號對電視或收音機的）干擾…

in Chinese (Simplified)

干涉，干预, （噪声或其他电子信号对电视或收音机的）干扰…

in Spanish

intromisión, injerencia, interferencias…

in Portuguese

intromissão, interferência, intrometimento [masculine]…

in more languages

in Marathi

in Japanese

in Turkish

in French

in Catalan

in Dutch

in Tamil

in Hindi

in Gujarati

in Danish

in Swedish

in Malay

in German

in Norwegian

in Urdu

in Ukrainian

in Russian

in Telugu

in Arabic

in Bengali

in Czech

in Indonesian

in Thai

in Vietnamese

in Polish

in Korean

in Italian

हस्तक्षेप, ढवळाढवळ, गोंगाट…

干渉, 混信, 干渉（かんしょう）…

müdahale, burnunu sokma, karışma…

intrusion [feminine], ingérence [feminine], interférence [feminine]…

ingerència, intromissió, interferència…

inmenging, storing…

હસ્તક્ષેપ, રુકાવટ, અવરોધ…

indblanding, forstyrrelse…

inblandning, störningar…

masuk campur, gangguan…

die Einmischung, die Störung…

innblanding [masculine], forstyrrelse [masculine], interferens [masculine]…

مداخلت, رکاوٹ, ٹیلی ویژن کے پردہ پر پیدا ہونے والی مداخلت…

втручання, перешкоди…

вмешательство, помехи…

تَدخّل, تَشويش…

zasahování, rušení, interference…

turut campur, gangguan…

สิ่งรบกวน, เสียงรบกวน…

sự can thiệp, sự nhiễu…

ingerencja, zakłócenia, mieszanie się…

간섭, 방해…

interferenza, ingerenza, intromissione…

Need a translator?

Get a quick, free translation!

Translator tool

Browse

interfamily

interfere

interfere with something

interfered

interference

interfering

interferometer

BETA

interferometric

BETA

interferometry

BETA

More meanings of interference

All

constructive interference

destructive interference

non-interference

pass interference

run interference idiom

See all meanings

Idioms and phrases

run interference idiom

Word of the Day

response

Your browser doesn't support HTML5 audio

/rɪˈspɒns/

Your browser doesn't support HTML5 audio

/rɪˈspɑːns/

an answer or reaction

About this

Blog

Forget doing it or forget to do it? Avoiding common mistakes with verb patterns (2)

March 06, 2024

New Words

inverse vaccine

March 11, 2024

More new words

has been added to list

To top

Contents

EnglishIntermediateExamplesCollocationsTranslations

Learn

New Words

Help

In Print

Word of the Year 2021

Word of the Year 2022

Word of the Year 2023

Develop

Dictionary API

Double-Click Lookup

Search Widgets

License Data

About

Accessibility

Cambridge English

Cambridge University Press & Assessment

Consent Management

Cookies and Privacy

Corpus

Cambridge Dictionary +Plus

My profile

+Plus help

Log out

Dictionary

Definitions

Clear explanations of natural written and spoken English

English

Learner’s Dictionary

Essential British English

Essential American English

Translations

Click on the arrows to change the translation direction.

Bilingual Dictionaries

English–Chinese (Simplified)

Chinese (Simplified)–English

English–Chinese (Traditional)

Chinese (Traditional)–English

English–Dutch

Dutch–English

English–French

French–English

English–German

German–English

English–Indonesian

Indonesian–English

English–Italian

Italian–English

English–Japanese

Japanese–English

English–Norwegian

Norwegian–English

English–Polish

Polish–English

English–Portuguese

Portuguese–English

English–Spanish

Spanish–English

English–Swedish

Swedish–English

Semi-bilingual Dictionaries

English–Arabic

English–Bengali

English–Catalan

English–Czech

English–Danish

English–Gujarati

English–Hindi

English–Korean

English–Malay

English–Marathi

English–Russian

English–Tamil

English–Telugu

English–Thai

English–Turkish

English–Ukrainian

English–Urdu

English–Vietnamese

Translate

Grammar

Thesaurus

Pronunciation

Cambridge Dictionary +Plus

Shop

Cambridge Dictionary +Plus

My profile

+Plus help

Log out

English (US)

Change

English (UK)

English (US)

Español

Русский

Português

Deutsch

Français

Italiano

中文 (简体)

正體中文 (繁體)

Polski

한국어

Türkçe

日本語

Tiếng Việt

Nederlands

Svenska

Dansk

Norsk

हिंदी

বাঙ্গালি

मराठी

ગુજરાતી

தமிழ்

తెలుగు

Українська

Choose a dictionary

Recent and Recommended

Definitions

Clear explanations of natural written and spoken English

English

Learner’s Dictionary

Essential British English

Essential American English

Grammar and thesaurus

Usage explanations of natural written and spoken English

Grammar

Thesaurus

Pronunciation

British and American pronunciations with audio

English Pronunciation

Translation

Click on the arrows to change the translation direction.

Bilingual Dictionaries

English–Chinese (Simplified)

Chinese (Simplified)–English

English–Chinese (Traditional)

Chinese (Traditional)–English

English–Dutch

Dutch–English

English–French

French–English

English–German

German–English

English–Indonesian

Indonesian–English

English–Italian

Italian–English

English–Japanese

Japanese–English

English–Norwegian

Norwegian–English

English–Polish

Polish–English

English–Portuguese

Portuguese–English

English–Spanish

Spanish–English

English–Swedish

Swedish–English

Semi-bilingual Dictionaries

English–Arabic

English–Bengali

English–Catalan

English–Czech

English–Danish

English–Gujarati

English–Hindi

English–Korean

English–Malay

English–Marathi

English–Russian

English–Tamil

English–Telugu

English–Thai

English–Turkish

English–Ukrainian

English–Urdu

English–Vietnamese

Dictionary +Plus

Word Lists

Choose your language

English (US)

English (UK)

Español

Русский

Português

Deutsch

Français

Italiano

中文 (简体)

正體中文 (繁體)

Polski

한국어

Türkçe

日本語

Tiếng Việt

Nederlands

Svenska

Dansk

Norsk

हिंदी

বাঙ্গালি

मराठी

ગુજરાતી

தமிழ்

తెలుగు

Українська

Contents

English

Noun

Intermediate

Noun

Examples

Collocations

Translations

Grammar

All translations

My word lists

Add interference to one of your lists below, or create a new one.

Go to your word lists

Tell us about this example sentence:

The word in the example sentence does not match the entry word.

The sentence contains offensive content.

Cancel

Submit

The word in the example sentence does not match the entry word.

The sentence contains offensive content.

Cancel

Submit

比特派app官方下载网站安卓|interference

比特派app官方下载网站安卓|interference

Interference | Definition, Examples, & Facts | Britannica

Interference Definition & Meaning - Merriam-Webster

Interference of Waves - Interference Definition, Derivation, Review Question, Video and FAQs

INTERFERENCE | English meaning - Cambridge Dictionary

17.1 Understanding Diffraction and Interference - Physics | OpenStax

13.3 Wave Interaction: Superposition and Interference - Physics | OpenStax

Just a moment...

Wave interference - Wikipedia

3: Interference - Physics LibreTexts

INTERFERENCE definition | Cambridge English Dictionary

菜单

支持

Follow

比特派app官方下载网站安卓|interference

比特派app官方下载网站安卓|interference

Interference | Definition, Examples, & Facts | Britannica

Interference Definition & Meaning - Merriam-Webster

Interference of Waves - Interference Definition, Derivation, Review Question, Video and FAQs

INTERFERENCE | English meaning - Cambridge Dictionary

17.1 Understanding Diffraction and Interference - Physics | OpenStax

13.3 Wave Interaction: Superposition and Interference - Physics | OpenStax

Just a moment...

Wave interference - Wikipedia

3: Interference - Physics LibreTexts

INTERFERENCE definition | Cambridge English Dictionary

最近的新闻

您可能喜欢的文章

比特派安卓版下载|massacre

下载网站比特派app下载|soccer

比特派转错地址了怎么办

比特派二维码怎么找

bitpie比特派转不了账怎么办

比特派扫码被盗怎么办啊

比特派被攻击了怎么办啊