RaymondA.SerwayChrisVuille

ChapterFourteenSound

SoundWaves

•  Soundwavesarelongitudinalwaves•  Characteris=csofsoundwaveswillhelpyouunderstandhowwehear

Introduc=on

ProducingaSoundWave

•  Anysoundwavehasitssourceinavibra=ngobject•  Soundwavesarelongitudinalwavestravelingthroughamedium

•  Atuningforkcanbeusedasanexampleofproducingasoundwave

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UsingaTuningForktoProduceaSoundWave

•  Atuningforkwillproduceapuremusicalnote

•  Asthe=nesvibrate,theydisturbtheairnearthem

•  Asthe=neswingstotheright,itforcestheairmoleculesnearitclosertogether

•  Thisproducesahighdensityareaintheair–  Thisisanareaofcompression

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UsingaTuningFork,cont.

•  Asthe=nemovestowardtheleJ,theairmoleculestotherightofthe=nespreadout

•  Thisproducesanareaoflowdensity–  Thisareaiscalledararefac&on

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UsingaTuningFork,final

•  Asthetuningforkcon=nuestovibrate,asuccessionofcompressionsandrarefac=onsspreadoutfromthefork

•  Asinusoidalcurvecanbeusedtorepresentthelongitudinalwave–  Crestscorrespondtocompressionsandtroughstorarefac=ons

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CategoriesofSoundWaves

•  Audiblewaves–  Laywithinthenormalrangeofhearingofthehumanear–  Normallybetween20Hzto20000Hz

•  Infrasonicwaves–  Frequenciesarebelowtheaudiblerange–  Earthquakesareanexample

•  Ultrasonicwaves–  Frequenciesareabovetheaudiblerange–  Dogwhistlesareanexample

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Applica=onsofUltrasound

•  Canbeusedtoproduceimagesofsmallobjects•  Widelyusedasadiagnos=candtreatmenttoolinmedicine–  Ultrasonicflowmetertomeasurebloodflow–  Mayusepiezoelectricdevicesthattransformelectricalenergyinto

mechanicalenergy•  Reversible:mechanicaltoelectrical

–  Ultrasoundstoobservebabiesinthewomb–  CavitronUltrasonicSurgicalAspirator(CUSA)usedtosurgically

removebraintumors–  High-intensityFocusedUltrasound(HIFU)isalsousedforbrainsurgery

•  Ultrasonicrangingunitforcameras

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SpeedofSoundinaLiquid

•  Inafluid,thespeeddependsonthefluid’scompressibilityandiner=a

–  BistheBulkModulusoftheliquid–  ρisthedensityoftheliquid–  Compareswiththeequa=onforatransversewaveonastring

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SpeedofSound,General

•  Thespeedofsoundishigherinsolidsthaningases–  Themoleculesinasolidinteractmorestrongly

•  Thespeedisslowerinliquidsthaninsolids–  Liquidsaremorecompressible

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SpeedofSoundinaSolidRod

•  Thespeeddependsontherod’scompressibilityandiner=alproper=es

–  YistheYoung’sModulusofthematerial–  ρisthedensityofthematerial

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SpeedofSoundinAir

•  331m/sisthespeedofsoundat0°C•  Tistheabsolutetemperature

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IntensityofSoundWaves•  TheaverageintensityIofawaveonagivensurfaceisdefined

astherateatwhichtheenergyflowsthroughthesurface,ΔE/Δtdividedbythesurfacearea,A

•  Thedirec=onofenergyflowisperpendiculartothesurfaceateverypoint

•  Therateofenergytransferisthepower•  SIunit:W/m2

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VariousIntensi=esofSound

•  Thresholdofhearing–  Faintestsoundmosthumanscanhear–  About1x10-12W/m2

•  Thresholdofpain–  Loudestsoundmosthumanscantolerate–  About1W/m2

•  Theearisaverysensi=vedetectorofsoundwaves–  Itcandetectpressurefluctua=onsassmallasabout3partsin1010

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IntensityLevelofSoundWaves

•  Thesensa=onofloudnessislogarithmicinthehumanear

•  βistheintensitylevelorthedecibellevelofthesound

•  Ioisthethresholdofhearing

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Intensityvs.IntensityLevel

•  Intensityisaphysicalquan=ty•  Intensitylevelisaconvenientmathema=caltransforma=onofintensitytoalogarithmicscale

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VariousIntensityLevels

•  Thresholdofhearingis0dB•  Thresholdofpainis120dB•  Jetairplanesareabout150dB•  Table14.2listsintensitylevelsofvarioussounds– Mul=plyingagivenintensityby10adds10dBtotheintensitylevel

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SphericalWaves

•  Asphericalwavepropagatesradiallyoutwardfromtheoscilla=ngsphere

•  Theenergypropagatesequallyinalldirec=ons

•  Theintensityis

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IntensityofaPointSource

•  Sincetheintensityvariesas1/r2,thisisaninversesquarerela&onship

•  Theaveragepoweristhesamethroughanysphericalsurfacecenteredonthesource

•  Tocompareintensi=esattwoloca=ons,theinversesquarerela=onshipcanbeused

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Representa=onsofWaves

•  Wavefrontsaretheconcentricarcs–  Thedistancebetweensuccessivewavefrontsisthewavelength

•  Raysaretheradiallinespoin=ngoutfromthesourceandperpendiculartothewavefronts

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PlaneWave

•  Farawayfromthesource,thewavefrontsarenearlyparallelplanes

•  Theraysarenearlyparallellines

•  Asmallsegmentofthewavefrontisapproximatelyaplanewave

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PlaneWaves,cont

•  Anysmallpor=onofasphericalwavethatisfarfromthesourcecanbeconsideredaplanewave

•  Thisshowsaplanewavemovingintheposi=vexdirec=on–  Thewavefrontsareparalleltotheplanecontainingthey-andz-axes

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DopplerEffect

•  ADopplereffectisexperiencedwheneverthereisrela=vemo=onbetweenasourceofwavesandanobserver.– Whenthesourceandtheobserveraremovingtowardeachother,theobserverhearsahigherfrequency

– Whenthesourceandtheobserveraremovingawayfromeachother,theobserverhearsalowerfrequency

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DopplerEffect,cont.

•  AlthoughtheDopplerEffectiscommonlyexperiencedwithsoundwaves,itisaphenomenacommontoallwaves

•  Assump=ons:– Theairissta=onary– Allspeedmeasurementsaremaderela=vetothesta=onarymedium

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DopplerEffect,Case1(ObserverTowardSource)

•  Anobserverismovingtowardasta=onarysource

•  Duetohismovement,theobserverdetectsanaddi=onalnumberofwavefronts

•  Thefrequencyheardisincreased

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DopplerEffect,Case1(ObserverAwayfromSource)

•  Anobserverismovingawayfromasta=onarysource

•  Theobserverdetectsfewerwavefrontspersecond

•  Thefrequencyappearslower

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DopplerEffect,Case1–Equa=on

•  Whenmovingtowardthesta=onarysource,theobservedfrequencyis

•  Whenmovingawayfromthesta=onarysource,subs=tute–voforvointheaboveequa=on

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DopplerEffect,Case2(SourceinMo=on)

•  Asthesourcemovestowardtheobserver(A),thewavelengthappearsshorterandthefrequencyincreases

•  Asthesourcemovesawayfromtheobserver(B),thewavelengthappearslongerandthefrequencyappearstobelower

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DopplerEffect,SourceMoving–Equa=on

•  Usethe–vswhenthesourceismovingtowardtheobserverand+vswhenthesourceismovingawayfromtheobserver

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DopplerEffect,GeneralCase

•  Boththesourceandtheobservercouldbemoving

•  Useposi=vevaluesofvoandvsifthemo=onistoward–  Frequencyappearshigher

•  Usenega=vevaluesofvoandvsifthemo=onisaway–  Frequencyappearslower

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DopplerEffect,FinalNotes

•  TheDopplerEffectdoesnotdependondistance– Asyougetcloser,theintensitywillincrease– Theapparentfrequencywillnotchange

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ShockWaves

•  Ashockwaveresultswhenthesourcevelocityexceedsthespeedofthewaveitself

•  Thecirclesrepresentthewavefrontsemijedbythesource

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ShockWaves,cont

•  TangentlinesaredrawnfromSntothewavefrontcenteredonSo

•  Theanglebetweenoneofthesetangentlinesandthedirec=onoftravelisgivenbysinθ=v/vs

•  Thera=ovs/viscalledtheMachNumber•  Theconicalwavefrontistheshockwave

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ShockWaves,final

•  Shockwavescarryenergyconcentratedonthesurfaceofthecone,withcorrespondinglygreatpressurevaria=ons

•  Ajetproducesashockwaveseenasafogofwatervapor

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InterferenceofSoundWaves

•  Soundwavesinterfere– Construc=veinterferenceoccurswhenthepathdifferencebetweentwowaves’mo=oniszeroorsomeintegermul=pleofwavelengths•  Pathdifference=nλ(n=0,1,2,…)

– Destruc=veinterferenceoccurswhenthepathdifferencebetweentwowaves’mo=onisanoddhalfwavelength•  Pathdifference=(n+½)λ(n=0,1,2,…)

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StandingWaves

•  Whenatravelingwavereflectsbackonitself,itcreatestravelingwavesinbothdirec=ons

•  Thewaveanditsreflec=oninterfereaccordingtothesuperposi=onprinciple

•  Withexactlytherightfrequency,thewavewillappeartostands=ll– Thisiscalledastandingwave

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StandingWaves,cont

•  Anodeoccurswherethetwotravelingwaveshavethesamemagnitudeofdisplacement,butthedisplacementsareinoppositedirec=ons–  Netdisplacementiszeroatthatpoint–  Thedistancebetweentwonodesis½λ

•  Anan&nodeoccurswherethestandingwavevibratesatmaximumamplitude

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StandingWavesonaString

•  Nodesmustoccurattheendsofthestringbecausethesepointsarefixed

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StandingWaves,cont.

•  Thepinkarrowsindicatethedirec=onofmo=onofthepartsofthestring

•  Allpointsonthestringoscillatetogetherver=callywiththesamefrequency,butdifferentpointshavedifferentamplitudesofmo=on

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StandingWavesonaString,final

•  Thelowestfrequencyofvibra=on(b)iscalledthefundamentalfrequency(ƒ1)

•  Higherharmonicsareposi=veintegermul=plesofthefundamental

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StandingWavesonaString–Frequencies

•  ƒ1,ƒ2,ƒ3formaharmonicseries–  ƒ1isthefundamentalandalsothefirstharmonic–  ƒ2isthesecondharmonicorthefirstovertone

•  Wavesinthestringthatarenotintheharmonicseriesarequicklydampedout–  Ineffect,whenthestringisdisturbed,it“selects”thestandingwavefrequencies

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ForcedVibra=ons

•  Asystemwithadrivingforcewillcauseavibra=onatthefrequencyofthedrivingforce

•  Whenthefrequencyofthedrivingforceequalsthenaturalfrequencyofthesystem,thesystemissaidtobeinresonance

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AnExampleofResonance

•  PendulumAissetinmo=on

•  Theothersbegintovibrateduetothevibra=onsintheflexiblebeam

•  PendulumCoscillatesatthegreatestamplitudesinceitslength,andthereforeitsnaturalfrequency,matchesthatofA

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OtherExamplesofResonance

•  Childbeingpushedonaswing•  Shajeringglasses•  TacomaNarrowsBridgecollapseduetooscilla=onscausedbythewind

•  UpperdeckoftheNimitzFreewaycollapseduetotheLomaPrietaearthquake

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StandingWavesinAirColumns

•  Ifoneendoftheaircolumnisclosed,anodemustexistatthisendsincethemovementoftheairisrestricted

•  Iftheendisopen,theelementsoftheairhavecompletefreedomofmovementandanan=nodeexists

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TubeOpenatBothEnds

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ResonanceinAirColumnOpenatBothEnds

•  Inapipeopenatbothends,thenaturalfrequencyofvibra=onformsaserieswhoseharmonicsareequaltointegralmul=plesofthefundamentalfrequency

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TubeClosedatOneEnd

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ResonanceinanAirColumnClosedatOneEnd

•  Theclosedendmustbeanode•  Theopenendisanan=node

•  Therearenoevenmul=plesofthefundamentalharmonic

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Beats

•  Beatsarealterna=onsinloudness,duetointerference

•  Waveshaveslightlydifferentfrequenciesandthe=mebetweenconstruc=veanddestruc=veinterferencealternates

•  Thebeatfrequencyequalsthedifferenceinfrequencybetweenthetwosources:

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Beats,cont.

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QualityofSound–TuningFork

•  Tuningforkproducesonlythefundamentalfrequency

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QualityofSound–Flute

•  Thesamenoteplayedonaflutesoundsdifferently

•  Thesecondharmonicisverystrong

•  Thefourthharmoniciscloseinstrengthtothefirst

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QualityofSound–Clarinet

•  ThefiJhharmonicisverystrong

•  Thefirstandfourthharmonicsareverysimilar,withthethirdbeingclosetothem

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Timbre

•  Inmusic,thecharacteris=csoundofanyinstrumentisreferredtoasthequalityofsound,orthe&mbre,ofthesound

•  Thequalitydependsonthemixtureofharmonicsinthesound

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Pitch

•  Pitchisrelatedmainly,althoughnotcompletely,tothefrequencyofthesound

•  Pitchisnotaphysicalpropertyofthesound•  Frequencyisthes=mulusandpitchistheresponse–  Itisapsychologicalreac=onthatallowshumanstoplacethesoundonascale

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TheEar

•  Theouterearconsistsoftheearcanalthatterminatesattheeardrum

•  Justbehindtheeardrumisthemiddleear

•  Thebonesinthemiddleeartransmitsoundstotheinnerear

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FrequencyResponseCurves•  Bojomcurveisthe

thresholdofhearing–  Thresholdofhearingis

stronglydependentonfrequency

–  Easiestfrequencytohearisabout3300Hz

•  Whenthesoundisloud(topcurve,thresholdofpain)allfrequenciescanbeheardequallywell

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