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Homework Help: Sketch the displacement of the string

  1. May 25, 2010 #1

    bon

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    1. The problem statement, all variables and given/known data

    2. At time t = 0, the displacement of an infinitely long string is:
    y(x, t) = sin(pix/a) for −a ≤ x ≤ a

    The string is initially at rest. Using d’Alembert’s solution for speed c, sketch the displacement of the string at t = 0, t = a/2c, and t = a/c.



    2. Relevant equations



    3. The attempt at a solution

    So I see how to do this...my only problem is as follows:

    D'Alembert solutions says y = f(x-ct) + g(x+ct)..

    but we don't know if the wave goes left or right..so how do i know whether to sub in x-ct for x or x+ct for x? thanks!
     
  2. jcsd
  3. May 25, 2010 #2

    ehild

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    Re: waves

    Is the initial displacement zero outside the interval [-a,a]?

    You had a very similar problem not long ago.

    ehild
     
  4. May 26, 2010 #3

    bon

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    Re: waves

    yes it is similar outside the interval..

    I know that this is similar to the one before - my problem is just knowing what to substitute instead of x -- should it be x-ct or x+ct?...

    Thanks!
     
  5. May 26, 2010 #4

    ehild

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    Re: waves

    Why do you think that the wave goes either left or right and not in both direction? Apply D'Alembert solution y = f(x-ct) + g(x+ct).

    ehild
     
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