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ph2a_quiz2

# ph2a_quiz2 - P h002a F all 2 009 Quiz 2 Due 2 7 O ctober 2...

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Ph002a, Fall 2009 Quiz 2 Due: 27 October 2009 sent from position r : [email protected] and time f, : -oo along a A traveling wave is string, as shown: Yt }d'+ c: y=o Before the wave hits the right end, the string displacement is given by (1) where ,4 is the amplitude of the displacement (assumed to be small), and u is the velocity at which the traveling wave propagates. The string is fixed at the right end, which we take to be at tr : tr, as shown above. At time t:0, when the left end of the wave is at r : 0, a clamp is applied at \$ :0 thus fixing the string at tr - 0, as shown: Y,T + k=0 We thus have at time t : 0 a traveling wave on a string of length ,L with ends at r:0 and r:,L fixed. 1. Sketch the string configuration at time I : LlQu)- [1 point] 2. Write down an equation for the displacement y(r,t : 0) at time f : 0' [0.5 point] , .\ (+*, for0<(r-ut)<L18, ul:x.tl- < "t" |.0, otherwise, ,,/

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3. Write down an equation for the vertical string velocity time t : 0. (simply differentiate Eq. (1) with respect to time.) [0.5 point] 4. In class we showed that the most general string motion (if both ends
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ph2a_quiz2 - P h002a F all 2 009 Quiz 2 Due 2 7 O ctober 2...

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