重郵大學物理英文版 最新版本ppt課件

Thenetvibration Review Superpositionofvibration Chapter2 Mechanicalwaves Waves adisturbancetravelsawayfromitssource Waterwaves soundwaves radiowaves X rays Waves MechanicalWaves Thedisturbanceispropagatingthroughamedium electromagneticWaves Donotneedamedium Waves TransverseWaves Themediumoscillatesperpendiculartothedirectionthewaveismoving LongitudinalWaves Waterwave Themediumoscillatesinthesamedirectionasthewaveismoving soundwave MechanicalWaves Thepropagationofadisturbanceinamedium Theconditionsallthemechanicalwavesrequire 1 Somesourceofdisturbance 2 Amediumthatcanbedisturbed 3 Somephysicalmechanismthroughwhichparticlescaninfluenceoneanother Theessenceofmechanicalwaves Thedisturbanceistransferredthroughspace butthematterdoesnot Thepropagationofthedisturbancealsomeansatransferofenergy WavesonaString 11 2 1harmonicwaves Thecharacteristicofharmonicwaves Everymediumelementoscillatesaroundtheequilibriumpositioninsimpleharmonicmotion butthewavepropagatesawayfromthesourceofdisturbance Thepropagationofsimpleharmonicmotioninspace 2 Thephaseoftheparticlewhichoscillateslaterissmaller medium disturbance v 18 y x t Acos wt kx A amplitude angularfrequency k wavenumber 2 harmonicwavefunction Assuming initialphaseiszeroatx 0andt 0 Generally Thetransversedisplacementisnotzeroatx 0andt 0 Phaseconstant Canbedeterminedfromtheinitialconditions Simpleharmonicvibrationfunction Thevibrationyasafunctionoftimet Theharmonicwavefunction Thewavefunctiony x t representstheycoordinateofanypointPlocatedatpositionxatanytimet Twovariablesxandt Iftisfixed thewavefunctionyasafunctionofx calledwaveform definesacurverepresentingtheactualgeometricshapeofthepulseatthattime AmplitudeandWavelength Wavelength Thedistancebetweenidenticalpointsonthewave AmplitudeA Themaximumdisplacementofapointonthewave 19 PeriodandVelocity 21 WaveProperties Thespeedofawaveisaconstantthatdependsonlyonthemedium notonamplitude wavelengthorperiod similartoSHM andTarerelated uTor 2 u or u f Example2 1 1 Supposetheharmonicvibrationfunctionoforiginatt Find theharmonicwavefunctionofpointPatt Solution thetimeforthevibrationtoarrivepointPis ThevibrationatpointPattisidenticalwiththatofpointOatt t ThenwehavethewavefunctionofpointP Example1 1 2 Supposetheharmonicvibrationfunctionoforiginatt Find theharmonicwavefunctionofpointP att ThevibrationatpointP attisidenticalwiththatofpointOatt t Therefore theharmonicwavefunctioncanbewrittenas Or Ifthewavetravelsleft use xsubstitutex TheparametersA uofacertainplanarcosinewaveareknown Calculatingt 0fromthemomentofthefollowingfigure 1 writethewavefunctiontakingOandPastheoriginrespectively 2 Findthemagnitudeanddirectionofthespeedatx1 8andx2 3 8whent 0 Example2 1 3 Solution 1 takingOastheorigin ThevibrationfunctionofOis Whent 0 then Thevelocityofx 0att 0 Thesimpleharmonicvibrationcurve Thevelocityatacertaintime istheslopeofthetangentlineofthatpoint Theharmonicwavecurve displacementasafunctionofx t t1 t t2 t2 t1 Iftheslopeofacertainpointofthecurvey x 0 thevelocityatthispoint 0 thewavetravelsrightwards Solution 1 takingOastheorigin ThevibrationfunctionofOis Whent 0 then Thevelocityofx 0att 0 thus Therefore thevibrationfunctionofOis ThewavefunctionofxtakingOasoriginis 1 takingPastheorigin ThevibrationfunctionofPis Whent 0 then AnyoneisOk wechoose ThewavefunctionofxtakingPasoriginis ThewavefunctionofxtakingOasoriginis ThewavefunctionofxtakingPasoriginis Wemustidentifytheoriginpointclearly Thephaseconstantsaredifferentifwetakevariousoriginalpoints 2 Findthemagnitudeanddirectionofthespeedatx1 8andx2 3 8whent 0 Thevelocityatxpoint Becausethevibrationis Thevelocityatxpointattmoment Takex 8 t 0intotheaboveequation Alongthenegativeyaxis Takex 3 8 t 0intotheaboveequation Alongthepositiveyaxis 2 2wavespeed phasespeedu Thespeedofawaveisaconstantthatdependsonlyonthemedium andTarerelated Note thespeedofthewaveuisdifferentfromthevibrationvelocityofacertainmediumelementv Thespeedofawaveisaconstantthatdependsonlyonthemedium A Wavepropagatinginliquid gas fluid B bulkelasticmodulus thedensityofthemedium B Wavepropagatinginsolid 1 Transversewave G shearelasticmodulus 2 longitudinalwave Y Youngmodulus 2 3energyofharmonicwaves Mechanicalwave Thedisturbanceispropagatingthroughamedium disturbance Vibrationstate phase energy Energyoftravelingharmonicwaves Thewavefunction Thewaveform att t1 SegmentABinthemedium ThemassofAB themassdensityofthemedium ThekineticenergyofAB ThepotentialenergyofAB T tension Themagnitudeandphaseofkineticenergyandpotentialenergyareidenticalatanytime Note theenergydifferencebetweenwaveandvibration waveform Maximumdeformation Maximumvelocity ThemechanicalenergyofAB Mechanicalenergyofwavechangeswithtimeperiodically Mechanicalenergyofsimpleharmonicvibrationkeepsconstant energydensityofwave Area massdensityofthemedium averageenergydensityofwave energyflowofwave Theenergypassesthroughunitareainunittime energyflowofwavechangeswith