您好,欢迎访问三七文档
当前位置:首页 > 办公文档 > 会议纪要 > FUNDAMENTALS OF ACOUSTICS(11)
Fundamentalsofacoustics(11)Reflection,refractionandtransmissionofplanewaves•Whensoundwavesaretravelingthroughamedium,theymaybereflectedorrefracted,diffractedorscattered,interferedorabsorbed.Thetransmissionofsoundinvolvesthetransferofacousticenergythroughthemediuminwhichsoundwavestravel.222022ppctx1200()()xxpftftccWecandefineplaneacousticwavesasone-dimensionalfreeprogressivewavestravelinginthexdirection.Theyaredescribedbytheone-dimensionalwaveequationThegeneralsolutionfortheone-dimensionalwaveequationcanbewritteninprogressivewavesform)(2)(1kxtikxtieAeAp00()()12xxjtjtccpAeAeWhichconsistsoftwoparts:thefirstpartrepresentsawaveofarbitraryshapetravelinginthexdirectionwithvelocityco,andthesecondpartrepresentsawavealsoofarbitraryshapetravelinginthenegativexdirectionwithvelocityc0.Incomplexexponentialform,thegeneralsolutioncanbewrittenasChangeinmedia•Whenanacousticwavetravelinginonemediumencounterstheboundaryofasecondmedium,reflectedandtransmitted(orrefracted)wavesaregenerated.•DiscussionofthisphenomenonisgreatlysimplifiedifitisassumedthatboththeincidentwaveandtheboundarybetweenthemediaareplanarandthatallmediaarefluidTransmissionfromonefluidtoanother:normalincidence•AssuggestedinFig.,lettheplanex=0betheboundarybetweenfluidIofcharacteristicacousticimpedanceZ1andfluidIIofcharacteristicacousticimpedanceZ2.•Lettherebeanincidentwavetravelinginthepositivexdirection1()1(,)jtkxipxtAeiprptp111Zc222ZcWhich,whenstrikingtheboundary,generatesareflectedwave1()1jtktrpBeAndatransmittedwave2()2jtkttpAe1()1(,)jtkxipxtAeNote:Thetransmittedwavehasthesamefrequencyastheincidentwavebut,becauseofthedifferentphasespeedsc1andc2,thewavenumbersk1influidIandk2influidIIaredifferentInthefirstmedium,soundpressureis11()()111jtkxjtkxirpppAeBeInthesecondmedium,soundpressureis2()22jtkxtppAeTheyaredescribedbythewaveequation•Therearetwoboundaryconditionsthatmustbesatisfiedforalltimesatallpointontheboundary:21221212xpctp22222222xpctp)0(x)0(x(2)Theparticlevelocitiesnormaltotheboundaryareequal.Thesecondcondition,continuityofnormalvelocity,requiresthatthefluidremainincontact.•(1)theacousticpressuresonbothsidesoftheboundaryareequal•Thefirstcondition,continuityofpressure,meansthattherecanbenonetforceonthe(massless)planeseparatingthefluid.1200(,)(,)xxpxtpxt1200(,)(,)nnxxuxtuxt•Wehavedefinedtheratioofacousticpressureinamediumtotheassociatedparticlevelocityastheacousticimpedance.•Z=p/u,then111122/,//iirrttupcupcupc•ThepressureandnormalparticlevelocityinfluidIarepi+prand(ui+ur)sothattwoboundaryconditionsaredtxpu0111()()1111111jtkxjtkxABueecc2()2222jtkxAuecpi+pr=ptatx=0ui+ur=utatx=0Fromtheequationofmotion•Wedefinethepressuretransmission(refraction)andreflectioncoefficients,soobtain:12111AAAB2112111ZZAAAB12121122112211ZZZZccccABR2222122112122AcZDAccZZ•Fromthereflectioncoefficient,weknowthatRisalwaysreal:•PositivewhenZ1Z2andnegativewhenZ1Z2.Consequently,attheboundarytheacousticpressureofthereflectedwaveiseitherinphaseor1800outofphasewiththatoftheincidentwave.•WhenthecharacteristicacousticimpedanceoffluidIIisgreaterthanthatoffluidI,apositivepressureintheincidentwaveisreflectedasapositivepressure.12121122112211ZZZZccccABR2222122112122AcZDAccZZ•whenZ1=Z2thenR=0,andthereiscompletetransmission.•For,thewaveisreflectedwithonlyaslightreductioninamplitudeandnochangeinphase.TheresultingwaveinfluidIIhasamaximumpressureamplitudealmosttwicePiandaparticlespeedattheboundarythatisalmostzero.Becauseofthislatterfact,suchaboundaryistermedrigid222ZcSincetheintensityofaharmonicplaneprogressivewaveisTheintensitytransmissionisrealandisdefinedby22mpIc22222221111221122221122tIiAIcAccTDAIAcccThetransmissionlosswillbe2112210lg10lg10lg[]ittiIIcTLDIIcAwaveinwaterincidentonthewater-airinterface6111105.1cZ420222cZ1105.1420105.142066R4621106.5420105.1420212ZZD)00112.0log(10105.1420105.14204log104log10)2(log106622121212221ZZZZZZZZZTL29TL•Abeamofsoundwavesisincidentnormallyonaplaneinterfaceofairandaninfinitebodyoffluidofunknownimpedance.Ifhalfofthesoundenergyisreflected,findtheunknownimpedance.Textbook3-14Soundenergyreflectedisdescribedbythesoundpowerreflectioncoefficient,andsoundenergyisproportionaltoitsintensity.Theintensityreflectionis22211211122rriAIcRAIc22212212415()()0.5415rZZZZZZZ2=72MKSraylsTransmissionformonefluidtoanother:obliqueincidence•Assumethattheboundaryseparatingtwofluidsistheplanex=0andthattheincident,reflected,andtransmittedwavesmaketherespectiveangles,showninFig.ritoxz11I()c22II()c•Inthefirstmedium,p1=pi+pr•Inthesecondmedium,p2=pt•Theycanbedescribedbywaveequations111(sincos)()11iijtkxkzjtkripAeAe11(sincos)1rrjtkxkzrpBe22(sincos)2ttjtkxkytpAe222111222211pppxzct222222222221pppxzctritoxz11I()c22II()cOntheboundary,theyaretwoboundaryconditions(1)continuityofpressure1200(,,)(,,)zzpxztpxzt121(sin)(sin)(sin)112itrjt
本文标题:FUNDAMENTALS OF ACOUSTICS(11)
链接地址:https://www.777doc.com/doc-4601045 .html