重邮大学物理英文版1 (13)PPT课件

.,1,Thenetvibration,Review,Superpositionofvibration,.,2,Chapter2,Mechanicalwaves,Waves:adisturbancetravelsawayfromitssource.,Waterwaves,soundwaves,radiowaves,X-rays,Waves,MechanicalWaves,Thedisturbanceispropagatingthroughamedium.,electromagneticWaves,Donotneedamedium,.,3,Waves,TransverseWaves,Themediumoscillatesperpendiculartothedirectionthewaveismoving.,LongitudinalWaves,Waterwave,Themediumoscillatesinthesamedirectionasthewaveismoving,soundwave,.,4,MechanicalWaves,Thepropagationofadisturbanceinamedium.,Theconditionsallthemechanicalwavesrequire:,1)Somesourceofdisturbance,2)Amediumthatcanbedisturbed,3)Somephysicalmechanismthroughwhichparticlescaninfluenceoneanother.,.,5,Theessenceofmechanicalwaves:,Thedisturbanceistransferredthroughspace,butthematterdoesnot.,Thepropagationofthedisturbancealsomeansatransferofenergy.,.,6,WavesonaString,11,.,7,2-1harmonicwaves,Thecharacteristicofharmonicwaves,Everymediumelementoscillatesaroundtheequilibriumpositioninsimpleharmonicmotion,butthewavepropagatesawayfromthesourceofdisturbance.,Thepropagationofsimpleharmonicmotioninspace,.,8,2)Thephaseoftheparticlewhichoscillateslaterissmaller.,medium,disturbance,v,.,9,18,y(x,t)=Acos(wtkx),A=amplitude,=angularfrequency,k=wavenumber=2/,harmonicwavefunction,Assuming:initialphaseiszeroatx=0andt=0,.,10,Generally,Thetransversedisplacementisnotzeroatx=0andt=0,Phaseconstant,Canbedeterminedfromtheinitialconditions.,.,11,Simpleharmonicvibrationfunction:,Thevibrationyasafunctionoftimet.,.,12,Theharmonicwavefunction:,Thewavefunctiony(x,t)representstheycoordinateofanypointPlocatedatpositionxatanytimet.,Twovariablesxandt.,Iftisfixed,thewavefunctionyasafunctionofx,calledwaveform,definesacurverepresentingtheactualgeometricshapeofthepulseatthattime.,.,13,AmplitudeandWavelength,Wavelength:Thedistancebetweenidenticalpointsonthewave.,AmplitudeA:Themaximumdisplacementofapointonthewave.,19,.,14,PeriodandVelocity,21,.,15,WaveProperties.,Thespeedofawaveisaconstantthatdependsonlyonthemedium,notonamplitude,wavelengthorperiod(similartoSHM),andTarerelated!,=uTor=2u/,or=u/f,.,16,Example2-1-1,Supposetheharmonicvibrationfunctionoforiginatt,Find:theharmonicwavefunctionofpointPatt,Solution:thetimeforthevibrationtoarrivepointPis:,.,17,ThevibrationatpointPattisidenticalwiththatofpointOatt-t,ThenwehavethewavefunctionofpointP:,.,18,Example1-1-2,Supposetheharmonicvibrationfunctionoforiginatt,Find:theharmonicwavefunctionofpointPatt,.,19,ThevibrationatpointPattisidenticalwiththatofpointOatt+t,.,20,Therefore,theharmonicwavefunctioncanbewrittenas:,Or:,Ifthewavetravelsleft,usexsubstitutex.,.,21,.,22,TheparametersA，uofacertainplanarcosinewaveareknown.Calculatingt=0fromthemomentofthefollowingfigure,1)writethewavefunctiontakingOandPastheoriginrespectively.2)Findthemagnitudeanddirectionofthespeedatx1=/8andx2=3/8whent=0.,Example2-1-3,.,23,Solution:1)takingOastheorigin,ThevibrationfunctionofOis:,Whent=0,then,Thevelocityofx=0att=0:,?,.,24,Thesimpleharmonicvibrationcurve:,Thevelocityatacertaintime,istheslopeofthetangentlineofthatpoint.,.,25,Theharmonicwavecurve(displacementasafunctionofx):,t=t1,t=t2,t2t1,Iftheslopeofacertainpointofthecurvey(x)0,thevelocityatthispoint0(thewavetravelsrightwards),.,26,Solution:1)takingOastheorigin,ThevibrationfunctionofOis:,Whent=0,then,Thevelocityofx=0att=0:,thus,.,27,Therefore,thevibrationfunctionofOis:,ThewavefunctionofxtakingOasoriginis:,.,28,1)takingPastheorigin,ThevibrationfunctionofPis:,Whent=0,then,AnyoneisOk,wechoose,ThewavefunctionofxtakingPasoriginis:,.,29,ThewavefunctionofxtakingOasoriginis:,ThewavefunctionofxtakingPasoriginis:,Wemustidentifytheoriginpointclearly!,Thephaseconstantsaredifferentifwetakevariousoriginalpoints.,.,30,2)Findthemagnitudeanddirectionofthespeedatx1=/8andx2=3/8whent=0.,Thevelocityatxpoint:,Becausethevibrationis:,.,31,Thevelocityatxpointattmoment:,Takex=/8,t=0intotheaboveequation:,Alongthenegativeyaxis,Takex=3/8,t=0intotheaboveequation:,Alongthepositiveyaxis,.,32,2-2wavespeed/phasespeedu,Thespeedofawaveisaconstantthatdependsonlyonthemedium.,andTarerelated!,Note:thespeedofthewaveuisdifferentfromthevibrationvelocityofacertainmediumelementv.,.,33,Thespeedofawaveisaconstantthatdependsonlyonthemedium.,A)Wavepropagatinginliquid,gas/fluid,B:bulkelasticmodulus,:thedensityofthemedium,.,34,B)Wavepropagatinginsolid,1)Transversewave,G:shearelasticmodulus,2)longitudinalwave,Y:Youngmodulus,.,35,2-3energyofharmonicwaves,Mechanicalwave:Thedisturbanceispropagatingthroughamedium.,disturbance,Vibrationstate,phase,energy,.,36,Energyoftravelingharmonicwaves,Thewavefunction:,Thewaveform(att=t1):,SegmentABinthemedium,ThemassofAB:,themassdensityofthemedium,.,37,ThekineticenergyofAB:,.,38,ThepotentialenergyofAB:,T:tension,.,39,.,40,Themagnitudeandphaseofkineticenergyandpotentialenergyareidenticalatanytime.,.,41,Note:theenergydifferencebetweenwaveandvibration!,waveform,Maximumdeformation,Maximumvelocity,.,42,ThemechanicalenergyofAB:,Mechanicalenergyofwavechangeswithtimeperiodically,Mechanicalenergyofsimpleharmonicvibrationkeepsconstant.,.,43,energydensityofwave:,Area,massdensityofthemedium,.,44,averageenergydensityofwave:,.,45,energyflowofwave:,Theenergypassesthroughunitar