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Dalamber equation

  1. Sep 18, 2010 #1
    [tex]\Delta\psi(\vec{r},t)-\frac{1}{\upsilon^2}\frac{\partial^2\psi(\vec{r},t)}{\partial t^2}=-g(\vec{r},t)[/tex]

    How to get solution

    [tex]\psi(\vec{r},t)=\frac{1}{r}F_1(t-\frac{r}{\upsilon})[/tex]

    where [tex]F_1[/tex] is any function of argument [tex]t-\frac{r}{\upsilon}[/tex].
     
  2. jcsd
  3. Sep 19, 2010 #2
    Write the laplacian in spherical coordinates, and use separation of variables.
     
  4. Sep 19, 2010 #3
    Your [tex]\psi[/tex] can not be a solution for a nontrivial [tex]g(r,t)[/tex] on the rhs.
     
  5. Sep 19, 2010 #4

    HallsofIvy

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    Well, not for a general g(r,t) but there are solutions for some specific, non-trivial functions.
     
  6. Sep 19, 2010 #5
    For instance for g(r,t)=0. Where did you get the idea that your formula is a solution for a non-zero g?
     
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