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Wave equation and graph

  1. Jul 14, 2014 #1
    1. The problem statement, all variables and given/known data



    set [tex]\phi = f(x-t)+g(x+t)[/TEX]

    a) prove that [tex]\phi[/tex]satisfies the wave equation : [tex]\frac{\partial^2 \phi}{\partial t^2} = \frac{\partial^2 \phi}{\partial x^2}[/tex]

    b) sketch the graph of [tex]\phi[/tex] against [tex]t[/tex] and [tex]x[/tex] if [tex]f(x)=x^2[/tex] and [tex]g(x)=0[/tex]





    3. The attempt at a solution
    part a, I have already gotten the answer to; just posting that so that the second part makes some sense.

    I don't really know how to do part b, the two functions given don't have a t, so not sure how I graph phi against x and t
     
  2. jcsd
  3. Jul 14, 2014 #2

    LCKurtz

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    If ##f(x) = x^2## and ##g(x) = 0##, then ##\phi(x,t) = (x-t)^2##. Plot that as a 3D surface with ##\phi## in the ##z## direction and ##x## and ##t## as the two independent variables.
     
  4. Jul 14, 2014 #3
    so its a parabolic cylinder?
     
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