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PDE Question

  1. Mar 8, 2012 #1
    1. The problem statement, all variables and given/known data
    I'm just trying to get an understanding of answering PDEs, so wanted to ask what you thought of my answer to this question.

    The one-dimensional wave equation is given by the first equation shown in this link;

    http://mathworld.wolfram.com/WaveEquation1-Dimensional.html

    where Ψ = f(x, t)

    Is f(x, t) = exp(x-ivt) a possible solution?



    2. Relevant equations



    3. The attempt at a solution

    ∂^2 f/∂x^2 = exp(x-ivt)

    and

    ∂f/∂t = -iv exp(x-ivt)

    Possible if v = -i
     
    Last edited: Mar 8, 2012
  2. jcsd
  3. Mar 8, 2012 #2

    Ray Vickson

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    You need to compute [itex] \partial^2 f/\partial t^2, \text{ not just } \partial f/\partial t.[/itex] Anyway: what is "c"? The PDE does not have "c" in it, nor does your f.

    RGV
     
  4. Mar 8, 2012 #3
    Sorry, c should have been v. I've corrected it now.
     
  5. Mar 8, 2012 #4
    So when I obtain the 2nd partial differentiation for 't' I obtain;

    -v^2 exp(x-ivt)

    So I assume this is not a possible solution since

    exp(x-ivt) ≠ -exp(x-ivt)
     
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