《大學物理簡明教程》 課件 8-1 Mechanical Waves

MechanicalWavesMechanicalwaves.commonexamplesincludewaterwaves,soundwaves,andseismicwaves.Electromagneticwaves.commonexamplesincludevisibleandultravioletlight,radioandtelevisionwaves,microwaves,xrays,andradarwaves.AwaveisatravelingdisturbancethattransportsenergyMatterwaves.

Thesewavesareassociatedwithelectrons,protons,andotherfundamentalparticles,andevenatomsandmolecules.2AmechanicalwavemustbeassociatedwithAsourceofoscillationAmaterialwhichcantransmitoscillations(medium)PhysicalmechanismthroughwhichparticlesofthemediumcaninfluenceoneanotherTheparticlesinthemediumareNOTtransmitting!EnergyandstatesofmotionaretransmittingthroughtheinteractionsbetweenparticlesEachparticle–(forced)simpleharmonicoscillation1.Theparticlesofmediumdonotmoveforwardwiththewave.Theyonlyoscillatearoundtheirequilibriumpositions.2.EachparticleisdoingtheSAME

simpleharmonicmotionwithdifferentinitialphases(neglectingtheenergydissipation)Specialcase–continuousperiodicwaves

Intransversewaves-theoscillationofthemediumisperpendiculartothedirectionofthewave1.TransverseWavesTypesofMechanicalWavesThecrestofawaveisthepointinthemediumwhichexhibitsthemaximumamountofpositiveorupwardsdisplacementfromtheequilibriumpositionThetroughofawaveisthepointinthemediumwhichexhibitsthemaximumamountofnegativeordownwardsdisplacementfromtheequilibriumposition.creststroughsInlongitudinalwaves-theoscillationofthemediumisparalleltothedirectionofthemotionofthewave2.LongitudinalWavesTypesofMechanicalWavescompressionsrarefactionsTravellingwave=thedistancebetweenacrestandtheadjacent

crest(ortroughtoadjacenttrough)Wavelength

：Thedistancebetweenidenticalpointsonthewave.

Period

T-theperiodoftheharmonicoscillationoftheparticleinthemedium

Frequencyf

T–Alsothetimeneededforthewavetomoveforonewavelength

WavefrontNewwavefrontItdependssolelyonthemechanicalpropertiesofthemediumWavespeedinsteel

inwater

soundwaveinair

Whatdeterminethewavespeed?TransversewaveLongitudinalwaveWaveonastringYoung’smodulusshearmodulusdensitydensitytensionmassperunitlengthShearmodulusSolidliquidgasYoung’smodulusShearmodulusBulkmodulusTransversewaveLongitudinalwaveWaterwave?20ExampleSoundwavesarelongitudinalwavesinair.Thespeedofsounddependsonthetemperature.At20℃

itis344m/s.Whatisthewavelengthofasoundwaveinairat20℃ifthefrequencyis262Hz?Solution22WaveFunctionThemotionofparticlesinthemediumcanbedescribedbythewavefunction:-themotionoftheparticleatpositionx0-thepositionsoftheparticlesinmediumatt0-thedisplacementoftheparticleatpositionx0andtheinstancet0.displacementofaparticlewhichhastheequilibriumpositionatx

displacementattimet

23HarmonicWaveSimpleHarmonicWave-thepropagationofsimpleharmonicmotioninmediumThewavefunctionoftheharmonicwave:phaseconstantamplitudeangularfrequencyWavespeed24AlternativeExpressionsofWaveFunctionComparingwithSHM:+φ+φ+φ)Simpleharmonicmotionoftwoparticles-changeinthephaseangle

Thephasechangewaveformoft=0vThinkaboutthewavefunction

Consistent!

v

Alongthedirectionofpropagationofthewave,thephasefallsbehindCausality–thephaseofparticles“infront”iscausedbytheparticles“behind”it.Wavepropagatestothenegativedirection?

y5612-5Thewaveform