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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)