Physics

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I have the following exercise:

Verify that Ex=f(z-ct)+g(z+ct) is a solution of the one dimensional wave equation.

But I don't get what I should do, I mean, isn't Ex the formula of the one dimensional wave equation itself? U.U

How can I verify it?

Thank you.

  • Physics -

    review section 5.2 of this: https://web.stanford.edu/class/math220a/handouts/waveequation1.pdf

  • Physics -

    Bobpursley coudl I get an email from you? I need to ask you something.

  • Physics -

    No emails. Our web safety issues don't allow that.

  • Physics -

    :( I could really use some assistance better than the provided from a input field of HTML xD, and my questions usually have symbols that require more precision in order for me to understand them.

    Is there nothing we can do?

  • Physics -

    Not now, we are working on a more flexible input field. Or a white board.

  • Physics -

    The equation is:
    d^2y/dx^2 = (1/c^2 )[d^2y/dt^2]

    here:
    d^2x/dz^2 = (1/c^2 )[d^2x/dt^2] with the strange letters for displacements
    I will just do the half that is moving right (z+ct)= constant or f(z-ct)

    write as f(w) where w = z-ct
    df/dz = df/dw * dw/dz = df/dw
    d^2f/dz^2 = d^2f/dw^2 dw/dz = d^2f/dw^2
    and then
    df/dt = df/dw * dw/dt = df/dw (-c) ah hah !
    d^2f/dt^2 =d^2f/dw^2 (-c)(-c) = c^2 d^2f/dw^2

    so in the end
    d^2f/dt^2 /c^2 = d^2f/dw^2 = d^2f/dz^2
    which is what we had to show.
    note that due to the (-c)(-c) = c*c
    it will come out the same for x+ct as for x-ct

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