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PDE Wave equation with phi(x) as initial boundaries

  1. Jul 16, 2013 #1
    Homework problem:

    For the wave equation:

    Utt-Uxx=0, t>0, xER


    1, |x|<1

    0, |x|>1

    sketch the solution u as a function of x at t= 1/2, 1, 2, and 3

    I am able to use d'Alemberts and solve for u however the boundaries and the odd/even reflections are throwing me off and I don't know how to do this. Any help would be great thank you.
  2. jcsd
  3. Jul 17, 2013 #2


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    What boundaries? This is an infinite string with ##x## domain ##(-\infty,\infty)##. You have given an initial displacement but the d'Alembert solution also requires an initial velocity ##u_t(x,0)##. Did you leave that out? Is it ##0##? If so, just plot the traveling waves.
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