physicslab1

physicslab1 - Williams 1 Lab1:ResonanceTube StaciWilliams

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Unformatted text preview: Williams 1 Lab1:ResonanceTube StaciWilliams KevinSchesing,NicoleHarty,CaitlinKubota Section015 PerformedFebruary2,2010 DueFebruary13,2010 Williams 2 Theory: 2.1AirAsASpring Gasisaspringymaterial,andwhenplacedinacylinderwithpistonsoneachsideitcanbe compressedaspistonspushin,raisingthepressureinside.Therewillbeanetforcefromthe pressuretopushthepistonbackout.Sincegashasmassitcansupportoscillationsandwaves. 2.2TravelingSoundWavesinAir Whenaconeofaspeakermovesout,itcompressesairnexttoisandimpartsanoutwardvelocitytotheair moleculesaroundit,inadditiontotherandomthermalvelocitiesofairmolecules.Themoleculesnearestto thespeakerwillcollidewiththosenearthemandimpartthosemoleculesintomotion,propagatingaway fromthespeakerproducingsound.Similarstatementsapplytowhentheconeismovedinaswell.If speakerconevibratessinusoidally,atravelingwavewillbeemittedformthespeakerandthewaverelation f=v<=wavelength,f=frequencyofwave,v=velocityofwave>issatisfied.ASthemotion ofthewavemoleculesmovealongthedirectionofthepropagationofthewavearecalled longitudinalwaves,whichiscontrastingtotransversewaveswhichareonstrings.Thewavesas theelementsofthestringmovetransversetothedirectioninwhichthewavestravel.Intraveling wavesthedisplacementofairsatisfiesthewaveequation.V=(P/)<v=velocityof wave,=specificheatsatconstantpressure/"constantvolume=Cp/Cv,P=airpressure,=air massdensity>.WiththeidealgaslawitcanbewrittenasV=(RT/M)<R=molargas constant,T=absolutetemperature,M=Molarmass>.Foragivengasthespeedwillbe proportionaltothesquarerootofthetemperaturegivingtheequationvrms=(3RT/M)<vrms ~thermalspeedofthegasmolecules>.Thespeedofsoundingasisclosetothethermalspeedof moleculesingas,sothevelocityofpropagationisessentiallythethermalspeedsofthemolecules givingthisequationV=331.5+.606Tm/s<Temperatureisincentigrade>. 2.3TravelingSoundWavesinaTube Soundwavesareabletotravelinatubeofaconstantcrosssectionmuchsimilartohowthey travelinopenair.Thetubeisassumedtohaverigidwallsthatwillnotflexunderpressure variations,aswellasbesmoothsothatthereisnotmuchattenuationofthewave,allowingthe speedofthewavestobenearlythesameasinopenair. 2.4StandingSoundWavesinaFiniteTube Travelingsoundwavesinafiniteclosedtubewillreflectattheends,allowingforresonanceto occuratcertainconditionscalledresonantfrequencies(normalmodes).Resonancewilloccur whenthereflectedwavesatbothendsreinforceoneanother.The"pressure"oftheairinthe waveisthechangeofpressurefromtheaveragevalue,withthe"displacement"ofairtobeits displacementfromtheequilibriumposition,withbothpressureanddisplacementvarying sinusoidallyinspaceandtime.Pointswherepressureismaximumarecalledpressureantinodes, andzeroarecalledpressurenodes.Likewise,pointswheredisplacementismaximumarecalled displacementantinodesandzerodisplacementarecalleddisplacementnodes.Instandingsound wavespressurenodesoccuratdisplacementantinodesandpressureantinodesoccurat displacementnodes.Anopenendofafinitetubewillbeapressurenodebecauseofthenormalair pressureoutsideofthetube,makingthesamepointadisplacementantinode,whiletheendofa Williams 3 closedtubemustbeadisplacementnodeandapressureantinode.Frequenciescanbecalculated fortubeswithbothendsclosed,oneendclosedandoneendopened,andbothendsopen. Resonancewavelengthscanbecalculatedyfittingstandardwavesintothetubesothatboundary conditionsaresettled.Thelowestresonancefrequencyiscalledthefundamentalfrequencyorthe 1stharmonic.Thenthharmonicisnmultipliedbythefundamentalfrequency,andnotall harmonicsmustbepresent. Dataand Calculations: 4MeasuringWavelength Frequency D1 D2 D3 D4 (Hz) (m) (m) (m) (m) 500 .159 .513 1000 .059 .248 .412 .582 1500 .038 .152 .268 .384 SampleCalculations1500Hz: D5 (m) .759 .501 D6 (m) .618 D7 (m) .736 (m) .708 .350 .233 Velocity (m/s) 343 343 343 Theoretical (m) .686 .343 .229 Percent Error(%) 3.21 2.04 1.75 Williams 4 .513m.159m=.354mSincewavelengthobserved,multiplyby2 .354m*2=.708m (.708m.686m)/.686m*100%=3.21% 5PulsedExperiments 5.1SpeedofSound X=.55m(Distancefrompistontospeaker) t=.0015sec.(pulsetime) V=X/t=.55/.0015=366m/s(velocityofsound) 366343/343*100%=5.83% 5.2BoundaryConditions .2cmneededtochangereflectedpulse ErrorAnalysis: Therewasverylittleerrorpresentduringtheexperimentwhenwecalculatedthewavelength,all ofwhichhadapercentoferror3.21percentorless.Thesmallerrorthatwasencounteredcould beattributedtohumanerror,insuchacasethatthedistancewasfalselyread,orthatthegraph wasnotzoomedinenoughtoseeexactlywherethemaximumintensityoccurred.Thepercent errordecreasedastheamountofdatapointswewereabletotakewentup,suggestingthatif moredatapointswereavailable,thepercenterrorwouldbeless.Intheexperimentwherewe foundthespeedofsoundapossibleerrormayhavearisenduetothemikenotbeingfullyerect towardstheothersideofthetube,potentiallycreatingfalseresonance/pulse.Anotherfactorthat mayhavecausederroristhattheendofthetubewasnotcompletelysealed,whichmeanssound wavescouldstreamoutorin,diminishingorincreasingthefrequency. Conclusion: MeasuringWavelengths Forafrequencyof500Hzthespeakerisaboutaquarterofawavelengthawayfromaminimumor maximum.Comparisontothestringexperiment...Thewavelengthschangewithfrequencyinthe wayIexpectthatasthefrequencyincreases,thewavelengthdecreasesallowingformoredata pointstobedetectedinthetube.Thisexperimentadequatelydemonstratedhowtocalculatethe wavelengthusingpointsofmaximumintensityoftheSWSsoftware. SpeedofSound Williams 5 Thereflectedpulseinthisexperimentwasinverted.Whilemovingthepistonslowlytowardthe mikewiththescoperunningitisseenthatthereflectedpulsehadaloweramplitudethanthatof theoriginalpulse.Thisexperimentallowedforthecalculationofthespeedofsound.Thisdata figuredisoffoftheexpectedvalue,butitisclosetotheexpectedvalue,showingthatifabetter pointwouldhavebeenchosen,theresultwouldhavebeenbetterthantheresultsthatwere attained. BoundaryCondition Thetubemustbecracked.2cmtochangethereflectedpulse.Itallowsenoughofthepulseto escapeallowingforachangeintheamplitude. Questions: 1.open/openFN=NV/2LF1=V/2L open/closedFN=NV/4LF1=V/4L 2.V=F=V/F F=V/2L=V*2L/V=2L=2L 3.V=( P/) PV=NRT,P=NRT/V =M/V V=(NRTV/VM)<N=1> V=( RT/M) Williams 6 ...
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This note was uploaded on 05/08/2010 for the course PHYS v12 taught by Professor Adler during the Spring '10 term at NYU.

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