Chapter13 Vibrationsandwaves

Waveparameters:(λ)Wavelength–thedistancebetweentwoconsecutivepointswhichareinphase(f)Frequency–thenumberofcyclesleavingthesourceeachsecondAmplitude–themaximumheightofthewaveaboveitsrestposition(T)Period–theamountoftimerequiredtogenerateonecycle

Awaveisatravellingdisturbance

Period=1/frequencyfrequency=1/period

Periodicmotionismotionthatrepeatsregularly.Anexampleofperiodicmotionisthesimplependulum

http://en.wikipedia.org/wikiSimple_harmonic_motion

SimpleHarmonicMotion-therestoringforceisproportionalto�thedisplacementfromtheequilibriumposition

http://www.ionaphysics.org/lab/Pend%20ALT%20Approach/TenSecOneSwing.html

Definition:Period:Theamountoftimeittakesfor1completecycle

T=2π√(L/g)T=PeriodL=lengthg=accel.ofgravity

https://phet.colorado.edu/sims/html/pendulum-lab/latest/pendulum-lab_en.html

AnotherperiodicmotionisamassonaspringForamassonaspringT=periodm=massk=springconstant𝑇=2π√(m/k)

https://phet.colorado.edu/sims/html/masses-and-springs/latest/masses-and-springs_en.html

Resonance: Largeamplitudeofmotionwhena�systemisdrivenatitsnaturalfrequency.

TacomaNarrowsBridgeVideo

https://www.youtube.com/watch?v=j-zczJXSxnw

https://www.youtube.com/watch?feature=player_detailpage&v=j-zczJXSxnw

(Copythelinkandpasteitintoyourbrowser)

ApulseisasingletravelingdisturbanceAwaveisperiodictravelingdisturbancesDirectionofpropagation:thedirectionthewaveismoving.Transversewave: Themediummovesperpendiculartothedirectionofpropagationofthewave.Longitudinalwave: Themediummovesparalleltothedirectionof�propagationofthewave.

https://www.youtube.com/watch?v=7cDAYFTXq3EThefollowingvideodemonstratesbothlongitudinalandtransversemechanicalwaves

Vocabularyreview:AmplitudeFrequencyHertzLongitudinalWavePeriodPeriodicMotionPulseResonanceTransverseWaveWaveWavelengthImportantReminders:Period=1/frequencyT=1/fFrequency=1/periodf=1/T

Questions:1.Ifthefrequencyisdoubled,whathappenstotheperiod?2.Supposeatennisballishitbackandforthbetweentwoplayers.Ifittakes2.3secondsfortheballtogofromoneplayertotheother,whataretheperiodandfrequencyoftheball'smotion?

Wavespeed (howfastitmovesfromthesourcetothe�  observer.)v=distance/timev=wavelength/periodperiod=1/frequency

 v=fλ

Thespeedofthewavedependsuponthematerialinwhichthewaveismovingandpossiblyothervariables,likethetemperature.(Thematerialinwhichthewaveismovingiscalledthe�medium.)

Thisappearsonyourradio.Whatarethefrequencyandperiodofthebroadcastingstation?

Vocabularyreview:AmplitudeFrequencyHertzLongitudinalWaveMediumPeriodPeriodicMotionPulseResonanceTransverseWaveWaveWavelength

Superpositionandinterference-whentwo�ormorewavespassthroughthesame�spacetheysimplyaddup(asvectors).Thatmeansthattheymayreinforceeachotherorcanceleachother.

ConstructiveInterference:Thewavesmeetinphase(instep)andcombinetoformawavewithincreasedamplitude.

Destructiveinterference-whentwowaves�meetoutofphase(outofstep)witheachotherandcombinetoformawaveof�decreasedamplitude.

Standingwaves:Awaveisreflectedbackon�itself.-nodes(minimummotion)-antinodes(maximummotion)

Soundtravelsatabout340m/s.Lighttravelsat3.00x10^8m/s.1.Whatisthewavelengthofthewavetransmittedbyradiostation1010WINS?(f=1010kHz)2.Whatisthewavelengthofthemusicalnote�calledconcertA(frequency=440Hz)?

Vocabularyreview:AmplitudeConstructiveInterferenceDestructiveInterferenceFrequencyHertzInterferenceLongitudinalWaveMediumPeriodPeriodicMotionPulseResonanceStandingWaveSuperpositionTransverseWaveWaveWavelength

3.Whatisthefrequencyofredlightwhichhasawavelengthof6.00x10^-9meters?

Soundtravelsatabout340m/s.Lighttravelsat3.00x10^8m/s.4.Howlongdoesittakelightningtotravel1mile(1mile=1609meters)?5.Howlongdoesittakethundertotravel1�mile?

Problems:(Page486)60.Apersoninarockingchaircompletes12cyclesin21�seconds.Whatistheperiodandthefrequencyofthemotion?63.Ifyoudribbleabasketballwithafrequencyof1.8Hz,(A)howlongdoesittakeforyoutocomplete12dribbles?(B)Howlongdoesittakefortheballtogofromthefloortoyour�hand?64.Ifyoutakeyourpulseandobserve74heartbeatsina�minute,whataretheperiodandfrequencyoftheheartbeat?66.Supposea0.46kilogrammassisattachedtoaspringand�undergoessimpleharmonicmotionwithaperiodof0.77s.�(A)Whatisthefrequencyofthemotion?(B)Whatisthespringconstantofthespring?69.Apendulumswingsbackandforth.Howmanytimes�doesitpassthroughtheequilibriumpositionduringone�completecycleofitsmotion,assumingthecyclebeginswhenthependulumisatmaximumdisplacementfromequilibrium?87.Youdipyourfingerintothewaterofapondtwicea�second.Thewavesyouproducehavecreststhatareseparatedby0.18m.Determinethefrequency,period,andspeedofthewaves.

ANSWERStothemathematicalproblems:P19#1=297m;#2=0.77mP20#23=5x10^16HzP.22#45.36x10^-6sec#5=4.7secP23#60T=1.75sec;f=0.57Hz#63T=0.55sec;Timefor12=7.7sec;timetofloor=0.275sec#641.2Hz;0.81sec#66A=1.29HzB=OMIT#69TWICE#87f=2Hz;wavelength=0.18m;v=0.36m/s