列或更多的波同时传播到在空间的.ppt

1,10InterferenceofWaves,StandingWaves,Whentwoormorewavespassthroughthesameregionofspaceatthesametime,theactualdisplacementisthevectorsumoftheseparatedisplacement.,2,ThePrincipleofSuperposition,TravelingWave:awavemovethroughspacewithoutinteractingwithanyotherwavesorobjects.,Theprincipleofsuperposition:Whentwoormorewavespassthroughthesameregionofspaceatthesametime,itisfoundthatformanywavestheactualdisplacementisthevectorsumoftheseparateoftheseparatedisplacement.,（波的叠加原理：如果两列或更多的波同时传播到在空间的同一区域中，则介质中实际位移等于每列波引起的位移之和）,3,4,InterferenceofWaves,Thecombinationofseparatewavesinthesameregionofspacetoproducearesultantwaveiscalledinterference.,（由分立的波在传播的共同区域叠加产生新的波动行为的现象称为干涉）,(Example10.1Interferenceoftwocosinewaves),5,Andwehave:,Forthecase1,wavesaresaidtobeeverywhereinphase(=0)andtointerfereconstructively.Thatis,thecrestsoftheindividualwavesoccuratthesamepositions.,（对于第一种情况，我们称两列波处处同相位并且干涉增强(相长干涉)。也就是说，每列波的波峰出现在相同的位置）,6,Ingeneral,whenthephaseconstanthasavaluebetween0and,theresultantwavehasanamplitudewhosevalueissomewherebetween0and2A.,Andforthecase2,thewavesaresaidtointerferedestructively.Thatis,thecrestofonewavecoincideswiththetroughofthesecondandtheirdisplacementscancelateverypoint.(outofphase),（第二种情况称为相消干涉。也就是说一列波的波峰和另一列波的波谷位置重叠，在空间中每一点位移相互抵消）,（一般情况下，相位介于0和之间，叠加波的振幅介于0和2A之间）,7,8,9,10,interfereconstructively,interferedestructively,11,Iftwowavesareinphaseeverywhere,weget:,interfereconstructively,interferedestructively,pathlength,pathlengthdifference,12,Twowaveswithparallelvibrationdirections,identicalfrequencyandconstantphasedifferencesuperposeinthespace.Theresultofthesuperpositionisthatthevibrationsofcertainpointsinmediumareconstructivewhilethevibrationsofotherpointsaredestructive.,InterferenceofWaves,coherentwaves（相干波）,（两列振动方向和频率相同并且具有恒定相位差的波在空间中重叠，波的叠加的结果是重叠区域的某些质点的振动增强了，而另一些质点的振动减弱了）,13,(Example10.2)Twospeakersplaced3.00mapartaredrivenbythesameoscillator.AlistenerisoriginallyatpointO,thatislocated8.00mfromthecentreofthelineconnectingthetwospeakers.ThelistenerthenmovestopointP,whichisaperpendiculardistance0.350mfromObeforereachingthefirstcancellationofwaves,resultinginaminimuminsoundintensity.Whatisthefrequencyoftheoscillator?,14,StandingWaves（驻波）,Standingwavesareformedfromthesuperpositionoftwowavesthathavethesamefrequency,amplitude,andwavelengthbutaretravelinginoppositedirections.,（两列具有相同频率、振幅和波长的波相向传播，相遇后叠加形成驻波）,15,wavefunctionofastandingwave,Thesimpleharmonicmotionofeveryparticlehasanangularfrequencyandaposition-dependentamplitude.（每一个质点作频率为简谐振动，振幅则依赖于质点的位置）,16,Theamplitudeofthesimpleharmonicmotionatxis:,Maximumamplitudeoccurswhere:,antinodes（波腹）,Zeroamplitudeoccurswhere:,nodes（波节）,Adjacentnodesandantinodesarebothseparatedbyahalfwavelength.,17,StandingWavesinString,Thereflectionofatravelingwavepulseatthefixedendofastretchedstring.Thereflectedpulseisinverted,butitsshaperemainsthesame.,P3388Fig.13-19,18,Theinversionofawaveatarigidendarenamedasaphaseshift.Atravelingwaveisreflectedatthefreeendofastretchedstringwillnotbeinverted,Ingeneral,whenatravelingwaveinamediumstrikestheboundaryofamoredensemedium,thereflectedwaveisinverted,otherwise,thewavewillnotbeinverted.Thatis,phaseshiftoccurswhilethewaveentersadensemediumfromalessdensemedium.,（一般而言，当波在介质中传播时，从波疏介质进入波密介质时，波形被反转；反之，当波由波密介质进入波疏介质时，波形不发生反转。也就是说，当波由波疏介质进入波密介质中时，反射波出现半波损失）,19,Onecanthusestablishstandingwavesonastringbycombiningincomingandreflectedwavesfromarigidend.AndItiseasilytofindthewavelengthofstandingwavesinastringhavetosatisfythefollowingcondition.,:,20,Eachpossiblewavelengthspecifyanormalmode.,（每一个可能的波长确定一种振动模式，称为简正模式）,Thelowestfrequency,correspondington=1,iscalledthefundamentalfrequency.Thehighernormalfrequenciesarecalledharmonics.,（n=1对应于振动模式频率最低的情况，该频率称为基频。其他较大的简正频率称为谐频）,21,(Example10.3)Twowavestravelinginoppositedirectionsproducesastandingwave.Theindividualwavefunctionsare,wherexandyaremeasuredincentimeters.(a)Findtheamplitudeofthesimpleharmonicmotionoftheelementofthemediumlocatedatx=2.3cm.(b)Findthepositionofthenodesandantinodesifoneendofthestringisatx=0.(c)Whatisthemaximumvalueofthepositioninthesimpleharmonicmotionofapointlocatedatananti-node?,22,Thewavefunctionofonewavepropagatingalongxaxiscanbewrittenas:,Thereflectionoccursatx=0andthereflectionpointisonenode.Finda)thewavefunctionofthereflectedwave,b)thewavefunctionofthesuperpositionofthesetwowaves,c)thepositionofthenodesandantinodes.,(Example10.4),23,24,Beats:InterferenceinTime,Atgivenlocationx0,twowavesdisturbsas:,25,TheDopplerEffect（多普勒效应）,Whenthewavesourceandtheobservermoverelatively,themeasuredfrequencybytheobserverisdifferentfromthetruefrequency(thefrequencyofthewavesource).ThisphenomenaiscalledDopplereffect.,26,Thefrequencymeasuredbytheobserverreads:,(observermovingtowardsource),(sourcemovingtowardobserver),(Boththesourceandtheobserverareinmotion),27,(Example10.5)Asubmarine(subA)travelsthroughwaterataspeedof8.00m/s,emittingasonarwaveatafrequencyof1400Hz.Thespeedofsoundinthewateris1533m/s.A2ndsubmarine(subB)islocatedsuchthatbothsubmarinesaretravelingdirectlytowardoneanother.ThesecondsubmarineBi