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.ThesecondsubmarineBismovingat9.00m/s.(a)WhatfrequencyisdetectedbyanobserverridingonsubBasthesubsapproacheachother?(b)Thesubsbarelymisseachotherandpass.WhatfrequencyisdetectedbyanobserverridingonsubBasthesubsrecedefromeachother?,28,28,Homework7,P34735,46,49,P36835,39,60,29,29,TheEnd,