Waves I (Interference; Beats; Doppler Effect)

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1、SJPOTrainingWavesMarkThengJune19&26,2014Contents1AMathematicalDescriptionofWaves12PhysicalMeaning22.1PhysicalQuantities..........................................22.2TypesofWaves............................................33Superposition53.1ConstructiveandDestructiveInterference

2、.............................53.2StandingWaves............................................53.3Beats.................................................64TheDopplerEect85SpecialRoundQuestions91AMathematicalDescriptionofWavesA1-dimensionalwavecanbedescribedbythefollowingequation:f(

3、x;t)=Acos(!t+kx+)(1)whereAistheamplitude!istheangularfrequencykisthewavenumberisthephase1Anexampleofsuchawaveisplottedbelow:f(x;t)=cos(100x+200t)42t02442024xThehorizontallinedepictstheshapeofthewaveatagivenpointintime,whiletheverticallinedepictstheoscillationoftheeldatag

4、ivenpointinspace.Botharesinusoids.2PhysicalMeaning2.1PhysicalQuantitiesTheenergycarriedbyawave,knownasitsintensity,isproportionaltothesquareofitsamplitude.TheangularfrequencyandthewavenumberarerelatedinverselytotheperiodTandwavelengthbyafactorof2.Theycanbethoughtofasscalingfa

5、ctors.Atagivenpointinspaceandtime,thevalue!t+kx+isknownasthephase.Notethatforanytwopointsinspace,thephasedierenceisconstantregardlessoftime.Astincreases,theentirewavemovesrightwardsmonotonically.Thevelocityofthewaveisknownasthephasevelocity,andisgivenby:!c==(2)TkPage21.Theg

6、ureshowsatransversewaveataparticularinstantintime.IfweknowthatpointFismovingdownwardsatthattime,wecandeducethatA.thewaveistravellingtowardstheright.B.thepointHismovinginthesamedirectionaspointFC.CwillreachtheequilibriumpositionealierthanB.D.theaccelerationatDatthispointisthemax

7、imum.E.Aisnotmovingatall2.(a)Atransversewaveispropagatedinastringstretchedalongthex-axis.Theequationofthewave,inSIunits,isgivenbyy=0:020cos(29t3:5x)(3)TheamplitudeofthewaveisA.0:020mB.16mC.3:5mD.4:6mE.0:22m(b)Forthewaveinpart(a)itsfrequencyisclosesttoA.0:020HzB.16HzC.3:5HzD.4:

8、6HzE.0:22Hz2.2TypesofWavesThereareafewwaystoclassifyty