《大学物理》英文课件16 WavesI

?大学物理?英文课件16Waves-IWavesandParticles

Atelephonecalltakesinformationandenergytoyourfriend,butnotanymaterialtoher(him)Particleandwavearethetwogreatconceptsinclassicalphysics

Theredarrowmovestotherightwiththewaveshape

Thered-dyedstringelementmovesparalleltotheyaxisThewavedescriptionfunctiongivestheshapeofthewave

andtocompletelydescribeawaveonastring.WaveDescriptionFunctionAmplitude,Phase,Wavelength,AngularWaveNumber

Amplitude:ymPhase:kx-ωt+ϕPhaseconstant:ϕWavelength:λAngularwavenumber:k

Period:T

Angularfrequency:ωFrequency:f

Period,AngularFrequency,Frequency

TheSpeedofaTravelingWaveSampleProblem–Transversewave,amplitude,wavelength,period,velocityProblem:

awavetravelingalongastringisdescribedbyy(xxt),inwhichthenumericalconstantareinSIunits.(a)Whatistheamplitudeofthewave?(b)Whatarethewavelength,period,andfrequencyofthewave?©Whatisthevelocityofthiswave?Solution:(a)(b)(c)SampleProblem–Transversewave,transversevelocity,transverseaccelerationProblem:

awavetravelingalongastringisdescribedbyy(xxt),inwhichthenumericalconstantareinSIunits.Weshowthatatt=18.9sthetransversedisplacementyoftheelementofthestringatx=22.5cmduetothewaveis1.92mm.(a)Whatisthetransversevelocityuintheydirection?(b)Whatisthetransverseaccelerationayofthesameelementatthattime?Solution:(a)(b)String’stensionandlineardensitywilldeterminethespeed.WaveSpeedonaStretchedStringKineticEnergy:

associatedwithtransversevelocityofstringelement(Max&zero)ElasticPotentialEnergy:withstringlengthchangeEnergyTransport:tensionforcescontinuouslydoworktotransferenergyEnergyandPowerofTravelingStringWaveTheRateofEnergyTransmission

OverlappingwavesalgebraicallyaddtoproducearesultantwaveOverlappingwavesdonotalterthetravelofeachotherThePrincipleofSuperpositionforWavesInterfereandInterference

ϕ

=0(inphase)fullyconstructiveinterferenceϕ

=π(outofphase)fullydestructiveinterference0<ϕ<πintermediateinterference

inphaseoutofphasephase-shifted

InterferenceofWavesSampleProblem–Interferenceoftwowaves,samedirection,sameamplitudeProblem:Twoidenticalsinusoidalwaves,movinginthesamedirectionalongastretchedstring,interferewitheachother.Theamplitudeymofeachwaveis9.8mm,andthephasedifferenceϕbetweenthemis100o.(a)Whatistheamplitudey’m

oftheresultantwaveduetotheinterference,andwhatisthetypeofthisinterference?(b)Whatphasedifference,inradiansandwavelengths,willgivetheresultantwaveanamplitudeof4.9mm?Solution:(a)(b)Nodes:wherethestringnevermoves.Antinodes:wheretheamplitudeoftheresultantwaveisamaximum.Standingwave:thewavepatterndonotmoveleftorright.StandingWavesTravelingwavesy1,y2:Superposition:Nodes:Antinodes:ReflectionsataBoundary“hard〞reflection-anodeatthesupport“soft〞reflection-anantinodeatthestringendReflectionsataBoundaryStandingWavesandResonanceNodeexistsatbothendsFundamentalmode(firstharmonic):

n=1Harmonicseries:

collectionofallpossibleoscillationmodesHarmonicnumber:n

SampleProblemProblem:astring,tiedtoasinusoidaloscillatoratPandrunningoverasupportatQ,isstretchedbyablockofmassm.SeparationL=m,lineardensityμ=1.6g/m,andtheoscillatorfrequencyf=120Hz.TheamplitudeofthemotionatPissmallenoughforthatpointtobeconsideredanode.AnodealsoexistsatQ.(a)What