《大学物理简明教程》 课件 8-2 Superposition of Waves

SuperpositionofWavesWhathappened?

Twomechanicalwavesofthesamefrequency2harmonicmotionsforoneparticleinthemedium

Themotionoftheparticle

Phasedifferenceisimportant!TwoSHM“inphase”TwoSHM“outofphase”Specialsituations6Whathappensifacontinuouswaveisreflected?ReflectionuuIncidentwavereflectedwaveBothwavesareofthesamefrequency,samespeedandsamewavelength.Ifnoenergylossduringthereflection,thenthesameamplitudeButoppositedirection!uuPhasechangeatreflectionpointFixedpointAtthereflectionpointPhaseshifty5612-5Thewaveformatt=0

isshowninthegraph.Thewavespeedis18.Thedirectionofmotionofaparticleinthemediumisgiveninthegraph.Findthewavefunction.(allquantitiesareinSIunits)Example

Submityouranswersbyscanit

Wavefunctions

Simpleharmonicmotion“Amplitude”ofSHMStandingWaveTwowaves-oppositedirection-samefrequency-sameamplitudeConstructiveinterferenceDestructiveinterferencenodeantinodeNodesAntinodes

y1y2y=

y1+y2String–bothendsfixedBothendsmustbenodes!

Integernumberofantinodes

n=1,2,3….

tensioninthestringmassperunitlengthofthestring

Fundamentalfrequency“nth”harmonicpossiblewavelengthsofastandingwaveonthestringOrganPipeAn

organpipe

isasound-producingelementofthe

pipeorgan

that

resonates

ataspecific

pitch

whenpressurizedairisdriventhroughit.Eachpipeistunedtoaspecificnoteofthe

musicalscale.resonate=formstandingwavesStandingwaveofthesoundOneendclosedNodesAntinodes

Fundamentalfrequency“nth”harmonicBothendsopenAntinodesAntinodesWhatarethefrequenciesofsound?Giventhepipelengthof1m.

n=1:1stharmonicmodefundamentalmoden=2:2ndharmonicmode1stovertonen=3:3rdharmonicmode2ndovertonen=4:4thharmonicmode3rdovertonehigherfrequency&shorterwavelengthterminologyaboutstandingwaveAE25BeatsTheinterferencebetweentwooscillationswithdifferentbutclosefrequenciesBeatperiodChangingfastChangingslowly“Changeofamplitude”Amplitude:BeatfrequencyOscillation1Oscillation2CombinedoscillationDopplerEffectAlthoughtheDopplerEffectiscommonlyexperiencedwithsoundwaves,itisaphenomenacommontoallwavesAssumptions:ThemediumisstationaryAllspeedmeasurementsaremaderelativetothestationarymediumWhatisthefrequencydetectedbythereceiver?NumberofwavecrestsreceivedtimeFrequency=DopplerEffect,Case1

(Observermoving

towardSource)AnobserverismovingtowardastationarysourceDuetohismovement,theobserverdetectsanadditionalnumberofwavefronts(crests)ThefrequencyheardisincreasedDopplerEffect,Case1.5

(ObservermovingAWAYfromSource)AnobserverismovingawayfromastationarysourceTheobserverdetectsfewerwavefrontspersecondThefrequencyappearslowerDopplerEffect,Case1–EquationWhenmovingtowardthestationarysource,theobservedfrequencyisWhenmovingawayfromthestationarysource,substitute–vrforvrintheaboveequation

DopplerEffect,Case2(SourceinMotion)Asthesourcemovestowardtheobserver(A),thewavelengthappearsshorterandthefrequencyincreasesAsthesourcemovesawayfromtheobserver(B),thewavelengthappearslongerandthefrequencyappearstobelowerDopplerEffect,SourceMoving–EquationUsethe–vs

whenthesourceismovingtowardtheobserverand+vs

whenthesourceismovingawayfromtheobserver

DopplerEffect,GeneralCaseBoththesourceandtheobservercouldbemovingUsepositivevaluesofvrandvsifthemotionistowardeachotherFrequencyappearshigherUsenegativevaluesofvr

andvsifthemotionisawayfromeachotherFrequencyappearslower

Whatisthefrequencyheardbyapersondrivingat15m/sectowardablowingfactorywhistle(f=800hz)ifthespeedofsoundis340m/sec?Think–whatifthesource