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Homework Help: Speed and direction of a travelling wave

  1. Sep 20, 2015 #1
    1. The problem statement, all variables and given/known data
    [tex]\Psi(y,t)=A\cos^22\pi(t-y) [/tex]
    Show that this is a travelling wave. Use the general form of a travelling wave to determine its speed and direction.
    Verify your answer using [tex]\frac{-\partial \Psi / \partial t}{\partial \Psi / \partial x}[/tex]

    2. Relevant equations
    The general form of a travelling wave from class is [tex]\Psi(x,t)=f(x-vt)[/tex].

    3. The attempt at a solution
    So I tried to just use the form of the travelling wave, but the thing that confused me was whether or not I had to switch around the order of (t-y) in the equation to (-y+t)? If I leave it as is I get that the speed (v) is -1, but if I change the equation to read (-y+t) the speed becomes 1 instead. Either way using the partial derivative equation verifies my answer. I can post my handwritten work if neccesary for proof that I attempted it.

  2. jcsd
  3. Sep 20, 2015 #2


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    2017 Award

    Staff: Mentor

    Please show your work (ideally typed here, that is easier to read. You can also use LaTeX). That should not happen as t-y is exactly the same as -y+t.
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