harmonic waves谐波

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1、Physics240:Worksheet24Name:_______________(1)Astringhasamassof1kgandalengthof1000m.Thestringistiedbetweentwotreesandhasatensionof100N.Findthefrequenciesofthemodesofoscillationofthesystem.(2)Astringhasamassof1kgandalengthof10m.Thestringistiedtoamasslessringwhichcanslidefreelyalongafrictionle

2、ssrodandthestringisfixedtoatreeontheotherend.Thestringhasatensionof50N.Findthefrequenciesofthemodesofoscillationofthesystem.(3)Awirehasamassof0.01kgandatotallengthof1.3m.0.3mofthewirehangsoverapulleyasshownandisattachedtoa20kgmasswhiletheotherendofthewireisattachedtoagreyblock.Findthelowest

3、5modesofoscillationinthissystem.(4)CowboyRyaniscontinuingonhisroadtripandhedecidedtoheadoutWest!RightbeforepassingthroughthemountainsofwesternWyoming,hedecidedtocampoutinthegrangeovernight.Duringthenight,withthecampfirebuilt,hepulledouthistrusty6stringguitarandthoughtofaninterestingproblemb

4、ecausehehadbeengonefrommyphysicsclassforsolong.Supposethateachofthestringsonhisguitarhadthesamemass,butthetensiononeachstringwastwicethetensiononthepreviousstring.Findtheratioofthelowestlyingmodesofoscillationonhisguitar.Ifthelowesttensiononthestringswas100N,andthelengthofeachofthestringswa

5、s0.75m,andthemassofeachstringwas0.001kg,findthelowestfrequenciesofeachofthestrings.(5)Ansinusoidaloscillatorproducesanamplitudeof0.05m.Theoscillatorisattachedtoastringwithamassperunitlengthof0.01kg/m.Howmuchpowermusttheoscillatorsupplytothesystemifitistooperateat60Hzunderatensionof50N?Physi

6、cs240:Worksheet24Name:_______________HarmonicwavesAharmonictravelingwaveisdescribedbyYoumayalsoseethesewavesdescribedas:Thewavelengthofthewaveisthelengththatthewavetakesbetweenidenticalamplitudesandvelocitiesforapointasshownabove.Theamplitudeisthemaximumdepartureofapointfromtheequilibriumpo

7、sition.Howdoesthisrelatetoourpreviousworkwithtravelingpulseswherewefoundthatapulsecanbedescribedby?Wellsupposetheparticularfunctionisthis:Then,inthiscontext,itbecomesclearthattheargumentimpliestheresultthat:Foratravelingwaveofwavelengthl,weneedtoworkouta