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Homework Help: Speed of wave.

  1. Feb 16, 2008 #1
    1. The problem statement, all variables and given/known data
    What's the speed and direction of the following wave(A,B and C are constants)
    [tex]y(x,t)=Ae^{Bx^2+BC^2t^2-2BCxt}[/tex]


    3. The attempt at a solution
    [tex]y(x,t)=Ae^{B(x-Ct)^2}[/tex]

    from (x-Ct)

    v=C in the +x direction
     
  2. jcsd
  3. Feb 16, 2008 #2
    Are you missing the imaginary constant in your exponential? If so, then you are correct. If not, you have a diverging or decaying exponential rather than a plane wave.
     
  4. Feb 16, 2008 #3
    No,it's original question.There's no imaginary constant.
    So my solution is true.Thanks for checking.
     
  5. Feb 16, 2008 #4
    No, there has to be an imaginary constant. You need to have something of the form

    [tex]Ae^{i(x-vt)}[/tex]

    Regular exponentials don't satisfy the wave equation. The wave equation says that two derivatives in time equal two derivatives in space divided by the velocity squared.
     
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