Unit 7 – Waves and Sound

Lesson4:DecibelsandDopplerEffect

SuggestedReadings SoundIntensityandDecibels:•  PhysicsClassroom.com->Tutorial->SoundWavesandMusic->

Lesson2(secFonbonly)

DopplerEffect:•  PhysicsClassroom.com->Tutorial->Waves->Lesson3(secFond

only)•  PhysicsClassroom.com->Tutorial->SoundWavesandMusic->

Lesson3(secFonbonly)Both:•  HoltPhysicstextbook->Chapter12(Sound)->Pg.412-417

SoundIntensity

InordertoquanFfythe“loudness”ofasound,mustfirstthinkaboutthesound’sintensity

SoundIntensity

IntensityisameasureoftherateatwhichenergyisbeingtransmiXedoveragivenarea

SoundIntensity

Remember,theword“rate”indicateshowmuchofsomething(energyhere)istransmiXedoverFme.

SoundIntensity

Remember,theword“rate”indicateshowmuchofsomething(energyhere)istransmiXedoverFme.So“intensity”israteofenergytransmissionoversomeareainspace.

SoundIntensity

EquaFonforintensity:

Energytime

SoundIntensity

Energytime

AreaRateofenergytransmission

SoundIntensity

Energytime

AreaAreaofsurfacetheenergyistransmiXedthrough

SoundIntensity

Energytime

SoundIntensity

EquaFonforintensity:UnitsofPower:WaXs(Joules/second)UnitsofArea:meters2=>SoUnitsofIntensity:WaXs/m2

I =Energytime

SoundIntensity

EquaFonforintensity:Asitstands,thisequaFonisnotreallyusefulforourpurposes.Forexample,howdowecalculatearea,especiallyifwedon’thaveanactualsurfaceinmind?

I =Energytime

SoundIntensity–PointSourceWecanstarttomakesomesimplificaFonstomakethingseasier:First,let’sdefinea“pointsource”

SoundIntensity–PointSourceWecanstarttomakesomesimplificaFonstomakethingseasier:First,let’sdefinea“pointsource”WemaketheassumpFonthatsoundisemiXedfromasinglepointinspace.

=>ThisdrasFcallysimplifiesthings,becausenowwedon’thavetothinkabout

complicatedsoundemission

SoundIntensity–PointSourcePointSource:Sothesourceiswhateverisemibngthesound,andweassumethatitcomesfromasinglepointinspace.

=>NOTE:Suchasourcedoesn’treallyexist,butitisaveryusefulsimplificaFon

=>NOTE:Suchasourcedoesn’treallyexist,butitisaveryusefulsimplificaFon=>Theclosestthingtoimaginewouldbeaverysmallspeakeremibngsound

Then,weimaginethatsoundasemanaFngin3-dimensionsoutwardfromthepointsource

hXp://dev.physicslab.org/Document.aspx?doctype=2&filename=WavesSound_DopplerEffectSourceMoving.xml

Picturethesourceinthemiddleofaneverexpanding3-dimensionalsphere

SoundIntensity–PointSourceThismeansthatthesurfacethesoundenergyispassingthroughisthesurfaceofthatsphere!

SoundIntensity–PointSourceThismeansthatthesurfacethesoundenergyispassingthroughisthesurfaceofthatsphere!WhatistheequaFonforthesurfaceareaofasphere?

=>4πr2 whereristheradiusofthesphere

SoundIntensity–PointSourceThismeansthatthesurfacethesoundenergyispassingthroughisthesurfaceofthatsphere!WhatistheequaFonforthesurfaceareaofasphere?

=>4πr2 whereristheradiusofthesphereSoIntensity,

I =Power

4⇡r2

IntensityWhathappenstotheintensityofasoundwaveasyoutripleyourdistanceawayfromthesource?A.  Increasesby9xB.  Increasesby3xC.  StaysthesameD.  Decreasesby1/3xE.  Decreasesby1/9x

Intensity

hXp://hyperphysics.phy-astr.gsu.edu/hbase/AcousFc/invsqs.html

IntensitySothefartherawayyougetfromapointsource,thesameamountofenergygetsspreadoutoveranincreasinglylargesurface.

IntensitySothefartherawayyougetfromapointsource,thesameamountofenergygetsspreadoutoveranincreasinglylargesurface.Thismeansthattheintensityofthesounddecreasesthefartherawayyougetfromthesource.

IntensitySothefartherawayyougetfromapointsource,thesameamountofenergygetsspreadoutoveranincreasinglylargesurface.Thismeansthattheintensityofthesounddecreasesthefartherawayyougetfromthesource.So,inotherwords,theintensityofsoundyouheardependsonhowfarawayyouarefromthesource

IntensitySothefartherawayyougetfromapointsource,thesameamountofenergygetsspreadoutoveranincreasinglylargesurface.Thismeansthattheintensityofthesounddecreasesthefartherawayyougetfromthesource.(Thisisaclassicexampleofan“inversesquarelaw”)

IntensityIfthereismorethanonesourceofsound,thentofindthetotalintensityyouwould…

=>justaddtheintensiFesfromeachindividualsource!

IntensityIftherewasaguitarplayerjammingwhoproducesanintensityof400W/m2,whatwouldtheintensitybeiftherewere3guitaristplaying?A.  400W/m2B.  403W/m2C.  1200W/m2D.  400,000W/m2E.  64,000,000W/m2

PerceivedVolumeofSound

NowwecanuseintensitytotryandquanFfythe“loudness”ofasound.

NowwecanuseintensitytotryandquanFfythe“loudness”ofasound.“Fun”fact:Perceivedvolumeandintensityare

related…inaweirdway.

NowwecanuseintensitytotryandquanFfythe“loudness”ofasound.“Fun”fact:Perceivedvolumeandintensityare related…inaweirdway.Ifyouhearasound,andyouperceivethatthesoundhasdoubleditsvolume,thenitsintensityasactuallyincreasedbyafactorof10!!

IntensityIfasingleguitarplayerjammingproducesanintensityof400W/m2,whatwouldtheintensitybeiftheperceivedvolumewasdoubled?A.  402W/m2B.  800W/m2C.  4,000W/m2D.  160,000W/m2E.  4,000,000W/m2

IntensityIftherewasaguitarplayerjamming,howmanyguitarplayersjammingwiththesameintensitywouldbeneededtodoubletheperceivedvolume?A.  2B.  4C.  10D.  20E.  100

IntensityHowmanyguitarplayersjammingwouldbeneededtodoubletheperceivedvolumeof2guitarplayers?A.  4B.  8C.  14D.  20E.  100

IntensityHowmanyguitarplayersjammingwouldbeneededtohavehalfoftheperceivedvolumeof30guitarplayers?A.  3B.  9C.  10D.  15E.  20

LogarithmsReview

FromAlgebra,whereB=Base:

logB (x) = yBy = x

LogarithmsReview

FromAlgebra,whereB=Base:ThesetwofuncFonsareinversesofeachother

logB (x) = yBy = x

LogarithmsReview

FromAlgebra,whereB=Base:We’llbeusingthemostcommonbase,base10

logB (x) = yBy = x

LogarithmsReview

Fory=1:

101 = 10log10(10) = 1

10y = x

log10(x) = y

LogarithmsReview

Fory=1:Fory=2:

101 = 10log10(10) = 1

log10(100) = 2102 = 100

10y = x

log10(x) = y

LogarithmsReview

Fory=1:Fory=2:Fory=3:

101 = 10log10(10) = 1

log10(100) = 2

log10(1000) = 3

102 = 100

103 = 1000

10y = x

log10(x) = y

LogarithmsReview

Sothegoaloflogarithms:1)  Youhaveanumber,like100or53,whichis“x”

10y = x

log10(x) = y

LogarithmsReview

Sothegoaloflogarithms:1)  Youhaveanumber,like100or53,whichis“x”2)  Youwanttofigureoutwhatexponenttoraise

“10”totogetthatnumber,x,out!

10y = x

log10(x) = y

LogarithmsReview

“10”totogetthatnumber,x,out!3)  Soyouaretryingtosolvefor“y”

10y = x

log10(x) = y

LogarithmsReview

“10”totogetthatnumber,x,out!3)  Soyouaretryingtosolvefor“y”4)  Youdothisbyjusttyping“logx”intoyour

calculator,anditwillspitout“y”!

10y = x

log10(x) = y

LogarithmicscalesThismightseemarbitrary,soyoumightwonderwhythisseeminglyrandommathemaFcalfuncFonissouseful.Thekeythatitisnon-linear.

hXp://freemat.sourceforge.net/help/mathfuncFons_log10.html

log10(x) = y

x=10y=1

log10(x) = y

x=10y=1

x=100y=2

LogarithmicscalesNon-linearfuncFonsarereallyusefulinscience

LogarithmicscalesNon-linearfuncFonsarereallyusefulinscience1)  WhenyouhaveaHUGEspreadofdatathat

youwanttorepresentgraphically

2)  WhentheresponseofasystemisNOTlinear

2)  WhentheresponseofasystemisNOTlinearThatlastoneiswhatwearedealingwith.

LogarithmicscalesAgreatexampleistheRichterScaleusedtoquanFfythe“intensity”ofearthquakes.

LogarithmicscalesAgreatexampleistheRichterScaleusedtoquanFfythe“intensity”ofearthquakes.Ifyouhaveanearthquakethatmeasures“7”ontheRichterscale,andanotherearthquakethatmeasures“8”,youhaven’tdoubledintensityorjustaddedonsomeconstant

LogarithmicscalesAgreatexampleistheRichterScaleusedtoquanFfythe“intensity”ofearthquakes.Ifyouhaveanearthquakethatmeasures“7”ontheRichterscale,andanotherearthquakethatmeasures“8”,youhaven’tdoubledintensityorjustaddedonsomeconstantRather,yourintensityhasgoneupbyafactorof

LogarithmicscalesAnearthquakethatmeasures“9”is1000=mesmoreintensethananearthquakethatmeasures“6”

LogarithmicscalesAnearthquakethatmeasures“9”is1000=mesmoreintensethananearthquakethatmeasures“6”Thedecibelscaleisanotherexampleofanon-linearscale,andiswhyI’vebeenbabblingonaboutlogarithms.

LogarithmicscalesAnearthquakethatmeasures“9”is1000=mesmoreintensethananearthquakethatmeasures“6”Thedecibelscaleisanotherexampleofanon-linearscale,andiswhyI’vebeenbabblingonaboutlogarithms.Decibelsmeasurethe“loudness”ofasound

Loudness,βFirstlet’sidenFfythefaintestintensityofsoundhumanscanhear:Io=10-12W/m2

Loudness,βFirstlet’sidenFfythefaintestintensityofsoundhumanscanhear:Io=10-12W/m2So,wecanmeasureloudness,β,as: β=10log(I/Io)

Loudness,βFirstlet’sidenFfythefaintestintensityofsoundhumanscanhear:Io=10-12W/m2So,wecanmeasureloudness,β,as:Theunitofβis:decibels(dB)

β=10log(I/Io)

Loudness,βFirstlet’sidenFfythefaintestintensityofsoundhumanscanhear:Io=10-12W/m2So,wecanmeasureloudness,β,as:Theunitofβis:decibels(dB)=>NOTE:βisNOT“perceivedvolume,”butamathemaFcalquanFtycalled“loudness”

β=10log(I/Io)

I=Io:I=10Io:I=100Io:I=1000Io:

β=10log(I/Io)

� = 10 log(I

) = 10 log(1) = 10 (0) = 0 dB

β=10log(I/Io)

� = 10 log(I

) = 10 log(1) = 10 (0) = 0 dB

� = 10 log(10I

) = 10 log(10) = 10 (1) = 10 dB

β=10log(I/Io)

� = 10 log(I

) = 10 log(1) = 10 (0) = 0 dB

� = 10 log(10I

) = 10 log(10) = 10 (1) = 10 dB

� = 10 log(100I

) = 10 log(100) = 10 (2) = 20 dB

β=10log(I/Io)

� = 10 log(I

) = 10 log(1) = 10 (0) = 0 dB

� = 10 log(10I

) = 10 log(10) = 10 (1) = 10 dB

� = 10 log(100I

) = 10 log(100) = 10 (2) = 20 dB

� = 10 log(1000I

) = 10 log(1000) = 10 (3) = 30 dB

β=10log(I/Io)

Forevery10dBofloudness,theintensityismulFpliedby10andthe“perceivedvolume”doubles!

� = 10 log(I

) = 10 log(1) = 10 (0) = 0 dB

� = 10 log(10I

) = 10 log(10) = 10 (1) = 10 dB

� = 10 log(100I

) = 10 log(100) = 10 (2) = 20 dB

� = 10 log(1000I

) = 10 log(1000) = 10 (3) = 30 dB

Whatistheloudnessofasoundwithanintensityof1x10-6W/m2?

Answer:60dB

Thereare4blaringcarhornsproducingatotalsoundof70dB.Whatistheintensityofthissound?

A) 10-7W/m2B) 10-5W/m2C) 1W/m2D) 10W/m2E) 105W/m2F) 107W/m2

So,whatistheintensityofoneblaringcarhorn?

Answer:0.25x10-5W/m2

Howmanydecibelsisonecarhornblaring?(Wecalculateditsintensitytobe0.25x10-5W/m2)

A) 10dBB) 62dBC) 64dBD) 68dBE) 70dBF) 74dB

Howmanydecibelsisonecarhornblaring?(Wecalculateditsintensitytobe0.25x10-5W/m2)

A) 10dBB) 62dBC) 64dBD) 68dBE) 70dBF) 74dB

Ifyoudoubledthevolumeofoneblaringcarhorn,howmanydecibelsisthat?A.  74dBB.  128dBC.  640dBD.  4096dBE.  Noneofthese

Ifyoudoubledthevolumeof4blaringcarhorns,whichproducedatotalof70dB,howmanyhornswouldbeneededandhowmanydecibelswouldthatbe?A.  8horns,140dBB.  8horns,80dBC.  40horns,140dBD.  40horns,80dBE.  Noneofthese

Ifyourheadphonesproduced95dB,andthenyouturnedthemdownto75dB,byhowmuchdidtheintensitychange?A.  Decreasedto1/4oftheintensityB.  Decreasedto1/20oftheintensityC.  Decreasedto1/100oftheintensityD.  Decreasedto1/200oftheintensityE.  Decreasedto1/400oftheintensityF.  Decreasedto1/1000oftheintensity

Torestatethegeneralrules:Youarestandingsomewhere,listeningtoasound.Theperceivedvolumethatyouheardoubles,andthesound’sintensitythatyouexperienceismulFpliedby10,and10dBhavebeenaddedtothesound’sloudness(β)thatyouexperience.

hXps://noiselimiters.co.uk/buy/noise-levels-what-is-noise.php

hXp://sound.whsites.net/arFcles/fadb.htm

DamagetoHearing

hXps://chicagoent.com/dangerous-decibels-how-loud-is-too-loud/

DamagetoHearing

hXps://chicagoent.com/dangerous-decibels-how-loud-is-too-loud/

Regularearbudscanreachupto115dB,theyshouldbesetat85dB

hXp://www.sightandhearing.org/Store/tabid/999/ProdID/1/

Default.aspx

SomeGuinnessBookofWorldRecords

DopplerEffect

SofarwehaveassumedthatthesourceofthesoundhasbeenstandingsFll.

DopplerEffect

SofarwehaveassumedthatthesourceofthesoundhasbeenstandingsFll.WehavealsoassumedthatyoudetecFngthesoundhavealsobeenstandingsFll.

Source

SourceDetector

DopplerEffect

SofarwehaveassumedthatthesourceofthesoundhasbeenstandingsFll.WehavealsoassumedthatyoudetecFngthesoundhavealsobeenstandingsFll.However,whathappenswhenone(orboth)aremoving??

hXp://www.school-for-champions.com/science/waves_doppler_effect.htm#.WK2qwhiZPVo

Source

Ifdetectorishere

Source

Ifdetectorishere

Source

Ifdetectorishere

Source

Ifdetectorishere

Source

Ifdetectorishere

DopplerEffectWhenthesourceismovingtowardsyou,thewavesget“squishedtogether,”resulFnginashorterwavelengthandahigherpitch.Whenthesourceismovingawayfromyou,thewavesget“stretchedout,”resulFnginalongerwavelengthandalowerpitch.

DopplerEffectWhenthesourceismovingtowardsyou,thewavesget“squishedtogether,”resulFnginashorterwavelengthandahigherpitch.Whenthesourceismovingawayfromyou,thewavesget“stretchedout,”resulFnginalongerwavelengthandalowerpitch.Note:ThisdoesNOTaffectthevolumeofthesound,justthewavelength/pitch

DopplerEffect

Screechingcarhorn:hXps://www.youtube.com/watch?v=a3RfULw7aAYEuropeansiren:hXps://www.youtube.com/watch?v=imoxDcn2Sgo

DopplerEffect

ThesamethinghappensifthesourceisstaFonaryandyou(thedetector)aremoving.Ifyouaremovingtowardthedetector,then…

DopplerEffect

ThesamethinghappensifthesourceisstaFonaryandyou(thedetector)aremoving.Ifyouaremovingtowardthedetector,then…thepitchyouheargetshigher

DopplerEffect

ThesamethinghappensifthesourceisstaFonaryandyou(thedetector)aremoving.Ifyouaremovingtowardthedetector,then…thepitchyouheargetshigherIfyouaremovingawayfromthedetector,then…

DopplerEffect

ThesamethinghappensifthesourceisstaFonaryandyou(thedetector)aremoving.Ifyouaremovingtowardthedetector,then…thepitchyouheargetshigherIfyouaremovingawayfromthedetector,then…thepitchyouheargetslower.

DopplerEffect

DopplerEffectinAstronomy=>Redshiw

DopplerEffect

DopplerEffectinAstronomy=>Redshiw

hXps://www.quora.com/How-does-the-Doppler-effect-prove-that-the-universe-is-expanding

DopplerEffectForwhichobjectistheDopplerEffectgoingtobedemonstratedinamoredrasFcway(greaterchangeinfrequency)?A.  AnobjectemibngaloudersoundB.  AnobjectmovingfasterC.  AnobjectemibngahigherpitchsoundD.  Allofthese

WhistleswereputonbombsthatweredroppedfromairplanesinWWIIasameansofpsychologicalwarfare.Whenrecordedfromtheplaneasabombfell,itsoundedlikethis:Why?hXp://soundbible.com/30-Bomb-Dropping.html hXp://www.youtube.com/watch?v=cGigkA-Xh5E

A.  ItwasmovingawayfromtheplaneB.  ItwasspeedingupC.  BothA&BD.  ItwasfallingdownE.  Itwasmadetosoundlikethat

WhistleswereputonbombsthatweredroppedfromairplanesinWWIIasameansofpsychologicalwarfare.Whenrecordedfromtheplaneasabombfell,itsoundedlikethis:Why?hXp://soundbible.com/30-Bomb-Dropping.html hXp://www.youtube.com/watch?v=cGigkA-Xh5E

A.  ItwasmovingawayfromtheplaneB.  ItwasspeedingupC.  BothA&BD.  ItwasfallingdownE.  Itwasmadetosoundlikethat

DopplerEffectIfyouwereonthegroundasawhistlingbombapproachedyouawerbeingreleasedfromaplane,whatwouldyouhearbeforethebombhittheground?A.  Adecreasingpitch(justlikewejustheard)B.  AconstanthigherpitchC.  Anincreasingpitch(reversetowhatwejust

heard)D.  Nothing

DopplerEffectIfyouwereonthegroundasawhistlingbombapproachedyouawerbeingreleasedfromaplane,whatwouldyouhearbeforethebombhittheground?A.  Adecreasingpitch(justlikewejustheard)B.  AconstanthigherpitchC.  Anincreasingpitch(reversetowhatwejust

heard)D.  Nothing

Aspeakerisatrestatthesideofastraightroad.Thespeakerproducesasteadysoundofconstantfrequency.AstudentisstandingsFllnearthespeaker.Twovehiclesaredrivendowntheroad:atruckapproachingthespeakerandacarmovingawayfromthespeaker.Ifthesoundisrepresentedbywavefronts,thestudentandthevehicledriverseachobserveadifferentamountofFmebetweensuccessivewavefronts:tsforthestudent,ttforthetruckdriver,andtcforthecardriver.WhichofthefollowingcorrectlyrankstheFmes?

A)ts<tt<tcB)tc<ts<ttC)tt<ts<tcD)tt<tc<ts

Aspeakerisatrestatthesideofastraightroad.Thespeakerproducesasteadysoundofconstantfrequency.AstudentisstandingsFllnearthespeaker.Twovehiclesaredrivendowntheroad:atruckapproachingthespeakerandacarmovingawayfromthespeaker.Ifthesoundisrepresentedbywavefronts,thestudentandthevehicledriverseachobserveadifferentamountofFmebetweensuccessivewavefronts:tsforthestudent,ttforthetruckdriver,andtcforthecardriver.WhichofthefollowingcorrectlyrankstheFmes?

A)ts<tt<tcB)tc<ts<ttC)tt<ts<tcD)tt<tc<ts

Unit 7 – Waves and Sound

Documents

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