01quiz_08

01quiz_08 - Physics 9B-C Quiz #1 Name: key 10/3/08 Last 4...

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Unformatted text preview: Physics 9B-C Quiz #1 Name: key 10/3/08 Last 4 of ID: Showthatthegeneralequation y=y(kx+t) ,i.e., y isafunctionof( kx+t) andisasolutionto thesecondorderwaveequation.Thefunction y ()isunknown,but y &itsderivativesexistand arewell-behavedandsingle-valued.Thewavehasaphasevelocitygivenby v =/ k . Explicitlywriteoutallderivativessuchas dy du .Donotusethe y' notationforderivatives. Method1: Startbyapplyingthederivativesandusingthechainrule.Let u = kx + t: y x = dy du u x = k dy du sothat 2 y x 2 = d du y x u x = k 2 d 2 y du 2 (3pts) Similarlyfor dt, y t = dy du u t = +...
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