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answers to test yourself questionstopic 44.1 oscilliations
1 a Anoscillationisanymotioninwhichthedisplacementofaparticlefromafixedpointkeepschangingdirectionandthereisaperiodicityinthemotioni.e.themotionrepeatsinsomeway.
b Insimpleharmonicmotion,thedisplacementfromanequilibriumpositionandtheaccelerationareproportionalandoppositeeachother.
8 a Wavelength–thelengthofafullwave;thedistancebetweentwoconsecutivecrestsortroughs b Period–thetimeneededtoproduceonefulloscillationorwave c Amplitude–thelargestvalueofthedisplacementfromequilibriumofanoscillation d Crest–apointonawaveofmaximumdisplacement e Trough–apointonawaveofminimumdisplacement
Distance /m
Dis
plac
emen
t /cm 2
4
–4
–2
00.5 1.0 1.5 2.0
λ amplitude A
Time / ms
Dis
plac
emen
t /cm 2
4
–4
–2
0
period T
642 108
9 a Inwavemotiondisplacementreferstothedifferenceinthevalueofaquantitysuchasposition,pressure,densityetcwhenthewaveispresentandwhenthewaveisabsent.
b Inatransversewavethedisplacementisatrightanglestothedirectionofenergytransfer,inalongitudinalitisparalleltotheenergytransferdirection.
c Thefallingstoneimpartskineticenergytothewateratthepointofimpactandsothatwatermoves.Itwillcontinuemoving(creatingmanyripples)untiltheenergyisdissipated.
d Wemustrecallthattheintensityofawaveisproportionaltothesquareoftheamplitude.Theamplitudewilldecreasefortworeasons:first,someenergyisboundtobedissipatedasthewavemovesawayandsotheamplitudehastodecrease.Second,evenintheabsenceofanyenergylosses,theamplitudewillstilldecreasebecausethewavefrontsgetbiggerastheymoveawayfromthepointofimpactoftheripple.Theenergycarriedbythewaveisnowdistributedonalongerwavefrontandsotheenergyperunitwavefrontlengthdecreases.Theamplitudemustthendecreaseaswell.
10 a Fromlefttoright:down,down,up. b Fromlefttoright:up,up,down.
13 a Awaveinwhichthedisplacementisparalleltothedirectionofenergytransferredbythewave. b i
20 4 6 8 x /cm
ii Atx=4.0cm
c i 92 3 5 710 4 86 x/cm
ii Thecompressionisnowatx=5.0cm.
14 a fv
= = =λ
340
0 40850
.Hz
b i Acompressionoccursatx=0.30m.Moleculesjusttotheleftofthispointhavepositivedisplacementandsomovetotheright.Moleculesjusttotherightmovetotheleftcreatingthecompressionatx=0.30m.
ii Bysimilarreasoningx=0.10misapointwhereararefactionoccurs.
b Arayisthedirectionnormaltowavefrontsthatcorrespondstothedirectionofenergytransfer.
a b
source of disturbance
point source
20 a Polarisedlightislightinwhichtheelectricfieldoscillatesonthesameplane. b Lightcanbepolarisedbypassagethroughapolariserandbyreflectionoffanon-metallicsurface.
22 a Thelightisnotpolarised.Inthecaseofunpolarisedlightincidentonananalyser,theintensityofthetransmittedlightwouldbehalftheincidentintensityandsoconstantasrequiredinthequestion.
b Sincethereisanorientation(callitX)oftheanalyserthatmakesthetransmittedintensityzero,itfollowsthattheincidentlightwaspolarisedinadirectionatrightanglestothedirectionX.
c Sincetheintensityneverbecomeszerothelightwasnotpolarised.Sincetheintensityvarieshowever,itfollowsthattheincidentlighthasunequalcomponentsinvariousdirectionssoitispartiallypolarised.
23 a ThisrelatesthetransmittedintensityItotheincidentintensityI0whenpolarisedlightisincidentandthentransmittedthroughananalyser.TherelationisI=I0cos2θwhereθistheanglebetweenthetransmissionaxisandthedirectionoftheincidentelectricfield.
bI
I 0
2 2 25 0 82= = ° =cos cos .θ
24 a Thelighttransmittedthroughthefirstpolariserwillbepolarisedinagivendirection.Thesecondpolariser’saxisisatrightanglestothisdirectionsotheelectricfieldhaszerocomponentalongtheaxisofthesecondpolariser.Hencenolightgetstransmitted.
b Lightwillbetransmittedsincenowtherewillbeacomponentoftheelectricfieldalongthesecondpolariser’saxis.
c Thesituationisnowidenticaltoaandsonolightgoesthrough.
4.4 Wave behaviour
25 a From1 00 38 1 583 2. sin . sin× ° = × θ wefindsin. sin
34 a Anodeisapointinthemediumwherethedisplacementisalwayszero. b Anantinodeisapointinthemediumwherethedisplacement,atsomeinstant,willassumeitsmaximumvalue. c Speedreferstothespeedofthetravellingwaveswhosesuperpositiongivesthestandingwave.