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Homework Help: Satisfying wave equation

  1. Jan 20, 2008 #1
    [SOLVED] Satisfying wave equation

    1. The problem statement, all variables and given/known data
    Confirm that the following wave satisfies the wave equation and obtain an expression for the velocity of a wave


    2. Relevant equations

    the wave equation is


    3. The attempt at a solution

    I assumed that I had to differentiate Y with respect to 't' twice and the differentiate Y with respect to 'x' twice and then substitute these into the equation.

    This left me with


    but this doesnt really prove that the wave satisfies the equation. Does it?

    I can then rearrange to get V the wave velocity. Am I on the right track?
  2. jcsd
  3. Jan 20, 2008 #2
    Is A constant or is it A(x)? Because with A constant, your function [tex]y(x,t)[/tex], does not satisfy the wave equation.
  4. Jan 20, 2008 #3


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    Staff Emeritus
    Science Advisor

    One would have to demonstrate that both sides of the wave equation are equal when using the proposed solution.

    The general wave equation is
    [tex]\frac{\partial^2 u} {\partial t^2} = c^2 \nabla^2 u[/tex], where c is the wave velocity. That constant, c, would be found in the solution.

    So then, what is the value of V based on the given function?

    I would expect A is a constant coefficient of amplitude.
    Last edited: Jan 20, 2008
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