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1、FUNDAMENTALSOFACOUSTICS(11)聲學基礎（英文版教學課件）Whensoundwavesaretravelingthroughamedium,theymaybereflectedorrefracted,diffractedorscattered,interferedorabsorbed.Thetransmissionofsoundinvolvesthetransferofacousticenergythroughthemediuminwhichsoundwavestravel.Wecan
2、defineplaneacousticwavesasone-dimensionalfreeprogressivewavestravelinginthexdirection.Theyaredescribedbytheone-dimensionalwaveequationThegeneralsolutionfortheone-dimensionalwaveequationcanbewritteninprogressivewavesformWhich,whenstrikingtheboundary,generat
3、esareflectedwaveAndatransmittedwaveNote:Thetransmittedwavehasthesamefrequencyastheincidentwavebut,becauseofthedifferentphasespeedsc1andc2,thewavenumbersk1influidIandk2influidIIaredifferentInthefirstmedium,soundpressureisInthesecondmedium,soundpressureisThe
4、yaredescribedbythewaveequationTherearetwoboundaryconditionsthatmustbesatisfiedforalltimesatallpointontheboundary:(2)Theparticlevelocitiesnormaltotheboundaryareequal.Thesecondcondition,continuityofnormalvelocity,requiresthatthefluidremainincontact.(1)theaco
5、usticpressuresonbothsidesoftheboundaryareequalThefirstcondition,continuityofpressure,meansthattherecanbenonetforceonthe(massless)planeseparatingthefluid.Wehavedefinedtheratioofacousticpressureinamediumtotheassociatedparticlevelocityastheacousticimpedance.Z
6、=p/u,thenThepressureandnormalparticlevelocityinfluidIarepi+prand(ui+ur)sothattwoboundaryconditionsarepi+pr=ptatx=0ui+ur=utatx=0FromtheequationofmotionWedefinethepressuretransmission(refraction)andreflectioncoefficients,soobtain:Fromthereflectioncoefficient
7、,weknowthatRisalwaysreal:PositivewhenZ1Z2.Consequently,attheboundarytheacousticpressureofthereflectedwaveiseitherinphaseor1800outofphasewiththatoftheincidentwave.WhenthecharacteristicacousticimpedanceoffluidIIisgreaterthanthatoffluidI,
8、apositivepressureintheincidentwaveisreflectedasapositivepressure.whenZ1=Z2thenR=0,andthereiscompletetransmission.For,thewaveisreflectedwithonlyaslightreductioninamplitudeandnochangeinphase.Theresultingwaveinf
