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Homework Help: Finding the real component of a two dimensional wave

  1. Oct 4, 2014 #1
    1. The problem statement, all variables and given/known data
    Show that if the displacement of the waves on a membrane of width b is given by the superposition

    [itex]z=A_1\exp^{i(\omega t-(k_1x+k_2y))}+A_2\exp^{i(\omega t-(k_1x-k_2y))}[/itex]

    with [itex]z=0[/itex] when [itex]y=0[/itex] and [itex]y=b[/itex] then the real part of z is

    [itex]z=2A_1sin(k_2)sin(\omega t-k_1x)[/itex] where [itex]k_2=\frac{n\pi}{b}[/itex]

    2. Relevant equations

    3. The attempt at a solution

    So I've found that [itex]A_1=-A_2[/itex] and [itex]k_2=\frac{n\pi}{b}[/itex], but I don't quite see how I can show that the real part of z is [itex]z=2A_1sin(k_2)sin(\omega t-k_1x)[/itex]. Can someone please provide some guidance?
  2. jcsd
  3. Oct 5, 2014 #2


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    How do you find the real part of a complex ##z## ?
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