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Wave equation

  1. Oct 27, 2007 #1
    when we derive the wave equation for a an o0ne dimensional wave moving at constant speed we assume that the wave move losslessly that is a plot of [tex]\psi(x,t)[/tex] with [tex]x[/tex] at any time [tex]t[/tex] is same to the extent that one can be obtained from the other by translation.
    similarly what are the assumptions when we get the general three dimensional wave equation
    [tex]\Nabla ^{2} \psi=\frac{1}{v^{2}} \frac{\delta^{2} \psi}{\delta t^{2}}[/tex]
     
  2. jcsd
  3. Oct 27, 2007 #2

    OOO

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    Looks like you are referring to a very special derivation of the wave equation. There are lots of derivation, probably the most clear ones are from physical principles (e.g. Maxwell's equations, continuum mechanics, special relativity...). I think there is no such derivation from translation stuff in more than 1 spatial dimension.
     
  4. Oct 28, 2007 #3

    Claude Bile

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    A key assumption is linearity, that the wave behaviour is invariant with respect to wave amplitude.

    Claude.
     
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