Waves II (Sound)
18
[SHIVOK SP211] November 1, 2015 Page 1 CH 17 Waves‐II (Sound) I. Sound Waves A. Wavefronts are surfaces over which the oscillations due to the sound wave have the same value; such surfaces are represented by whole or partial circles in a two‐dimensional drawing for a point source. B. Rays are directed lines perpendicular to the wavefronts that indicate the direction of travel of the wavefronts. C. Drawing
Transcript of Waves II (Sound)
[SHIVOK SP211] November 1, 2015
Page1
CH 17
Waves‐II(Sound)
I. SoundWaves
A. Wavefrontsaresurfacesoverwhichtheoscillationsduetothesoundwavehavethesamevalue;suchsurfacesarerepresentedbywholeorpartialcirclesinatwo‐dimensionaldrawingforapointsource.
B. Raysaredirectedlinesperpendiculartothewavefrontsthatindicatethedirectionoftravelofthewavefronts.
C. Drawing
[SHIVOK SP211] November 1, 2015
Page2
II. SpeedofSound
A. Assoundwavepassesthroughair,potentialenergyisassociatedwithperiodiccompressionsandexpansionsofsmallvolumeelementsoftheair.BulkModulus,B,determinestheextenttowhichanelementofamediumchangesinvolumewhenthepressureonitchanges.Bisdefinedas:
B. HereV/Visthefractionalchangeinvolumeproducedbyachangeinpressurep.
But,remember
C. …soifBreplacesandreplaces,
1. ThisisthespeedofsoundinamediumwithbulkmodulusBanddensity.
[SHIVOK SP211] November 1, 2015
Page3
D. SpeedofSound;Derivationofresult(nottestable)
[SHIVOK SP211] November 1, 2015
Page4
III. TravelingSoundWaves(nottestable)
IV. Interference(nottestable,buthelpfulinPhysicsII)
[SHIVOK SP211] November 1, 2015
Page5
V. IntensityandSoundLevel
A. TheintensityIofasoundwaveatasurfaceistheaveragerateperunitareaatwhichenergyistransferredbythewavethroughorontothesurface.
B. Therefore,I=P/AwherePisthetimerateofenergytransfer(thepower)ofthesoundwaveandAistheareaofthesurfaceinterceptingthesound.
C. TheintensityIisrelatedtothedisplacementamplitudesmofthe
soundwaveby
1. Proof(nottestable)
[SHIVOK SP211] November 1, 2015
Page6
D. VariationwithDistance
VI. IntensityandSoundLevel:TheDecibelScale
A.
1. HeredBistheabbreviationfordecibel,theunitofsoundlevel.
2. I0isastandardreferenceintensity(10
‐12W/m
2),chosennearthe
lowerlimitofthehumanrangeofhearing.
3. ForI=I0,gives=10log1=0,(ourstandardreferencelevel
correspondstozerodecibels).
[SHIVOK SP211] November 1, 2015
Page7
B. FamiliarExample
VII. ExampleProblems:
A. Whatisthebulkmodulusofoxygenif32.0gofoxygenoccupies22.4Landthespeedofsoundintheoxygenis317m/s?
1. Solution:
[SHIVOK SP211] November 1, 2015
Page8
B. Supposethatthesoundlevelofaconversationisinitiallyatanangry70dBandthendropstoasoothing50dB.Assumingthatthefrequencyofthesoundis500Hz,determinethe(a)initialand(b)finalsoundintensities(inμW/m2)andthe(c)initialand(d)finalsoundwaveamplitudes(innm).Assumethespeedofsoundis347m/sandtheairdensityis1.21kg/m3.
1. Solution:
[SHIVOK SP211] November 1, 2015
Page9
C. Asourceemitssoundwavesisotropically.Theintensityofthewaves2.50mfromthesourceis1.91×10‐4W/m2.Assumingthattheenergyofthewavesisconserved,findthepowerofthesource.
Isotropic Isotropy is uniformity in all orientations; it is derived from the Greek iso (equal)
and tropos (direction).
1. Solution:
[SHIVOK SP211] November 1, 2015
Page10
VIII. SourcesofMusicalSound
A. Musicalsoundscanbesetupbyoscillatingstrings(guitar,piano,violin),membranes(kettledrum,snaredrum),aircolumns(flute,oboe,pipeorgan,andthedigeridooofFig.17‐12),woodenblocksorsteelbars(marimba,xylophone),andmanyotheroscillatingbodies.Mostcommoninstrumentsinvolvemorethanasingleoscillatingpart.
B. Pipeopenatbothends
[SHIVOK SP211] November 1, 2015
Page11
C. Pipeopenatoneendonly
IX. Beats
A. Whentwosoundwaveswhosefrequenciesareclose,butnotthesame,aresuperimposed,astrikingvariationintheintensityoftheresultantsoundwaveisheard.Thisisthebeatphenomenon.Thewaveringofintensityoccursatafrequencywhichisthedifferencebetweenthetwocombiningfrequencies.
[SHIVOK SP211] November 1, 2015
Page12
B. Beatphenomenon.
X. DopplerEffect.
A. Whenthemotionofdetectororsourceistowardtheother,thesignonitsspeedmustgiveanupwardshiftinfrequency.Whenthemotionofdetectororsourceisawayfromtheother,thesignonitsspeedmustgiveadownwardshiftinfrequency.
[SHIVOK SP211] November 1, 2015
Page13
B. CalculatingreceivedFrequency
1. Heretheemittedfrequencyisf,thedetectedfrequencyf’,visthespeedofsoundthroughtheair,v
Disthedetector’sspeedrelativetotheair,
andvSisthesource’sspeedrelativetotheair.
C. Intimet,thewavefrontsmovetotherightadistancevt.ThenumberofwavelengthsinthatdistancevtisthenumberofwavelengthsinterceptedbyDintimet,andthatnumberisvt/.TherateatwhichDinterceptswavelengths,whichisthefrequencyfdetectedbyD,is
1. Inthissituation,withDstationary,thereisnoDopplereffect—thefrequencydetectedbyDisthefrequencyemittedbyS.
[SHIVOK SP211] November 1, 2015
Page14
D. DetectorMoving,SourceStationary
1. IfDmovesinthedirectionoppositethewavefrontvelocity,intimet,thewavefrontsmovetotherightadistancevt,butnowDmovestotheleftadistancev
Dt.
2. Thus,inthistimet,thedistancemovedbythewavefrontsrelativetoDisvt+v
Dt.Thenumberofwavelengthsinthisrelativedistancevt+v
Dtis(vt
+vDt)/.
3. TherateatwhichDinterceptswavelengthsinthissituationisthefrequencyf’,givenby
4. Similarly,wecanfindthefrequencydetectedbyDifDmovesawayfromthesource.Inthissituation,thewavefrontsmoveadistancevt‐v
Dt
relativetoDintimet,andf’isgivenby
[SHIVOK SP211] November 1, 2015
Page15
E. SourceMoving,DetectorStationary
1. DetectorDisstationarywithrespecttothebodyofair,andsourceSmovetowardDatspeedv
S.
2. IfT(=1/f)isthetimebetweentheemissionofanypairofsuccessivewavefrontsW
1andW
2,duringT,wavefrontW
1movesadistancevTandthe
sourcemovesadistancevST.
3. AttheendofT,wavefrontW2isemitted.
4. InthedirectioninwhichSmoves,thedistancebetweenW1andW
2,
whichisthewavelengthofthewavesmovinginthatdirection,is(vT–vST).
5. IfDdetectsthosewaves,itdetectsfrequencyfgivenby
6. InthedirectionoppositethattakenbyS,thewavelengthofthewavesisagainthedistancebetweensuccessivewavesbutnowthatdistanceis(vT–vST).Ddetectsfrequencyfgivenby
[SHIVOK SP211] November 1, 2015
Page16
F. DopplerEffectTable
XI. SupersonicSpeeds,ShockWaves
A.
B.
[SHIVOK SP211] November 1, 2015
Page17
XII. SampleProblems:
A. OrganpipeA,withbothendsopen,hasafundamentalfrequencyof300Hz.ThethirdharmonicoforganpipeB,withoneendopen,hasthesamefrequencyasthesecondharmonicofpipeA.Howlongare(a)pipeAand(b)pipeB?(Takethespeedofsoundtobe343m/s.)
1. Solution:
B. TheAstringofaviolinisalittletootightlystretched.Beatsat4.00persecondareheardwhenthestringissoundedtogetherwithatuningforkthatisoscillatingaccuratelyatconcertA(440Hz).Whatistheperiodoftheviolinstringoscillation?
1. Solution:
[SHIVOK SP211] November 1, 2015
Page18
C. Anambulancewithasirenemittingawhineat1600Hzovertakesandpassesacyclistpedalingabikeat2.44m/s.Afterbeingpassed,thecyclisthearsafrequencyof1590Hz.Howfastistheambulancemoving?(Takethespeedofsoundinairtobe343m/s.)
1. Solution:
D. Ajetplanepassesoveryouataheightof5000mandaspeedofMach1.50.(a)FindtheMachconeangle.(b)Howlongafterthejetpassesdirectlyoverheaddoestheshockwavereachyou?Use331m/sforthespeedofsound.
1. Solution:
