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SuperpositionofwavesonastringName:
GroupMembers:
Date:
TA’sName:
Apparatus:PASCOmechanicalvibrator,PASCOinterface,string,masshanger(50g)andsetofmasses,meterstick,electronicscale,twowireleads,pulleyandtwometalstandswithbrackets.Objectives:
1. Tounderstandsuperpositionoftwosinusoidalwavesmovinginoppositedirections.2. Tostudywavepropagationinastring.3. Tounderstandtheformationofstandingwavesonastring.
Part1:IntroductionInyourtutorialyoustudiedthereflectionandsuperpositionofpulsesmovinginaslinkyandinastring.Hereinthisexperimentyouaregoingtoinvestigatethesuperpositionoftwooppositelymovingsinusoidalwavesmovinginatightstring.Whentwosinusoidalwavesofthesamefrequencyaremovinginoppositedirectionsinthesamemedium,astandingwaveistheresult.Thisoftenoccurswhenawaveistravelinginamediumwherethereisareflectionatoneorbothends.Figure1showsastandingwavepatternresultingfromperiodicwavesofwavelengthλtravelingtotherightandtotheleftinthestring.Inastandingwave,therearepointsinthemediumwithzerodisplacementcalled“nodes”wherethetwowavesarealwaysindestructiveinterference.Therearealsopointswithmaximumdisplacementcalled“antinodes”wherethetwowavesarealwaysinconstructiveinterference.Thethreelinesshowninthestandingwavepatternindicatethepositionofthestringatthreedifferenttimesinthemotion;onewhentheentirestringisattheequilibriumposition(flatline),onewhentheantinodeshaveamaximumdisplacementfromequilibrium,andonewhentheantinodeshaveamaximumdisplacementintheoppositedirectionfromequilibrium.
1. Identifyallnodesbymarkingthemwiththeletter“N”andallantinodesbymarkingthemwiththeletter“A”inthestandingwavepatternshownbelow.
Wavelengthλ
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Part2:Fixedfrequencywithdifferenttensions2. Inthelastexperiment,youinvestigatedtherelationshipofwavespeedwithtension.Whatdid
youconcludefromthatexperiment?
Fixthestringvibratortoametalstand.Thentakethestringandattachoneendtothestringvibrator.ConnectthePASCOinterfacetothevibratorusingtwowireleads.ConnectthePASCOinterfacetothecomputerifitisnotalreadyconnected.Openupatemplate.Selectthesignalgeneratorinthemenulocatetotheleft.Thenclickopencontrolsofthesignalgeneratorandselectthefrequencytobe60HZandamplitudetobe6V.Switchonthesignalgeneratorusingtheon/offbutton.Holdthefreeendofthestringasshowninthefigurebelowandslowlyincreasethetensionbypullingitaway.Observethestandingwavepatternsthatoccurasyoustretchthestring.PASCOvibrator
PASCO
3. Whathappenstothenumberofantinodesasyouincreasethetension?Wireleadsinterface
4. Whathappenstothewavelengthasyouincreasethetension?Referbacktothefigureonthefirstpagetoseehowwavelengthisrelatedtonodesandantinodes.
5. Doesthefrequencyofthestandingwavechangeasyouincreasethetension?
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6. Whatisthejustificationtoyouranswerin#5?
7. Adjustthetensionuntilthestringvibrateswith4segments.Thenadjustthetensionslightly(finetune)sothatyougetagoodnodeattheblade.
GoodnodeatthevibratorendBadnodeatthevibratorend
Experimentallyverifythatthedisplacementofthemedium(string)iszeroatnodes.Brieflyexplainwhatyoudidtoverifythatthereisnodisplacementatthenodes.
8. Measureandrecordthelengthofasegmentorbetweentwoadjacentnodesusingmeterstick.
Lengthofasegment:
9. Determinethewavelengthofthestandingwaveusingameterstick.
Wavelength=______________________________
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Part3:FixedtensionwithdifferentfrequenciesYoujustexperimentallyverifiedtheexistenceofstandingwaveswithnodesandantinodes.Youalsoobservedthatforafixedlengthofastringthewavelengthofastandingwavevarieswithtensioninthestring.Nowyouaregoingtoinvestigatetheformationofstandingwavesinthestringwithdifferentfrequenciesatafixedtension.Nowsetuptheapparatusasshownbelow.Makesurethatthestringishorizontal.Place100ginthemasshangersothatthetotalmassattachedis150g.Adjustthelengthbetweenthepulleyandthevibratortobemorethan1.00m.Connectthefrequencygeneratortothestringvibrator.Thesignalgeneratorgeneratessinusoidalwavesandthatsignalisfedtothevibrator.Thereforethevibratorvibrateswithsimpleharmonicoscillations.StringStringVibratorWireleadsPASCOInterfacePulleyMetalstandTableMassandhanger
10. NowslowlyincreasethefrequencyofthesignalgeneratorusingPASCOinterfacecomputercontrolsusedabovestartingat0Hzandcarefullyobservetheformationofstandingwaveswhichhaveagoodnodeatthevibratorend.Onceyoureachsuchafrequency,finetuneitwithfinefrequencyadjustment.Completetheobservation/measurementchartbelow.
Sketchofthestandingwavepattern #ofantinodes f(Hz) λ(m) fλ
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11. Thelastcolumnistheproductoffrequencytimeswavelength,fλ.WhatSIunitsdoesthisquantity
have?
12. Whatkindsofquantitieshavethesameunitsasdoesthefrequencytimeswavelength?
13. Isthequantityfλapproximatelythesameforallthesestandingwaves?
14. Basedonthevaluesinthelastcolumncalculatetheaveragespeedofthewavesinthestring?
15. Lookatthefrequenciesyoufoundthatgivegoodstandingwaves.Doyouseeapatternforthesevalues?Whatrelationshipdoyoufindbetweenfrequencyandthenumberofantinodes?
16. Lookatthewavelengthsyoufoundthatgivegoodstandingwaves.Doyouseeapatternforthese
values?Expressthewavelengthintermsofthelengthofthestringandthenumberofantinodes.
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Part4:Samestandingwavepatternwithdifferenttension17. Transferyourdataforstandingwavewith3antinodesusing150ghangingmasstothetable
below.Thenrepeat#10withdifferenttensionsusing250gand350gtotalhangingmassestofindthefrequencywhichresultsinagoodstandingwavewith3antinodes.Completethetablebelow.
#of
antinodesmass=150g mass=250g mass=350g
f(Hz) λ(m) fλ f(Hz) λ(m) fλ f(Hz) λ(m) fλ3
18. Whatcanyouconcludeabouthowtensionaffectsthewavespeed?Isthisconsistentwithwhatyoufoundinthepreviousexperiment?
19. Whenthewavespeedincreases,willthewavelengthneedtoincrease,decreaseorstaythesametogetthesamestandingwavepattern(suchastheonewith3antinodes)?
20. Whenthewavespeedincreases,willthefrequencyneedtoincrease,decreaseorstaythesametogetthesamestandingwavepattern(suchastheonewith3antinodes)?
Part5:Application21. Basedonyourexperienceinthisexperimentexplaintuningaguitar(oranyotherstringed
instrument)bychangingthetensionofthestring.(Youexplanationmustbebasedonfrequency,wavelength,andspeedofthewave)
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