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Math Help - Determine whether the given function satisfies the wave equation

  1. #1
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    Determine whether the given function satisfies the wave equation

    w(x,t)=e^{x-ct}

    Thank you for the help on the last problem, but for this one I'm still stumped as to what I need to do, even after reading a bit on wikipedia. Any help would be much appreciated.

    Wikipedia has:

    \frac{\partial u^{2}}{\partial t^{2}}=c^{2}\nabla^{2}u

    But, I don't know what u and \nabla are.
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  2. #2
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    Quote Originally Posted by downthesun01 View Post
    w(x,t)=e^{x-ct}

    Thank you for the help on the last problem, but for this one I'm still stumped as to what I need to do, even after reading a bit on wikipedia. Any help would be much appreciated.

    Wikipedia has:

    \frac{\partial u^{2}}{\partial t^{2}}=c^{2}\nabla^{2}u

    But, I don't know what u and \nabla are.
    u is the function that satisfies the wave equation. In your case, you're asked to show that u = w(x, t) is a solution.

    \nabla^2 is the Laplace operator.
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  3. #3
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    In Cartesian coordinates in three dimensions, \nabla^2 f= \frac{\partial^2 f}{\partial x^2}+ \frac{\partial^2 f}{\partial y^2}+ \frac{\partial^2 f}{\partial z^2}.

    Here, you don't have any dependence on y or z so your equation reduces to
    \frac{\partial^2 u}{\partial t^2}= c^2\frac{\partial^2 u}{\partial x^2}.

    "u" is function. You are asked to replace u by e^{x- ct} in that equation and see if it is true.

    But what course did you see this in? I cannot imagine you being asked to do a problem like this if you were not already expected to know what \nabla^2 was!
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