# Dalamber equation

1. Sep 18, 2010

### Petar Mali

$$\Delta\psi(\vec{r},t)-\frac{1}{\upsilon^2}\frac{\partial^2\psi(\vec{r},t)}{\partial t^2}=-g(\vec{r},t)$$

How to get solution

$$\psi(\vec{r},t)=\frac{1}{r}F_1(t-\frac{r}{\upsilon})$$

where $$F_1$$ is any function of argument $$t-\frac{r}{\upsilon}$$.

2. Sep 19, 2010

### Petr Mugver

Write the laplacian in spherical coordinates, and use separation of variables.

3. Sep 19, 2010

Your $$\psi$$ can not be a solution for a nontrivial $$g(r,t)$$ on the rhs.

4. Sep 19, 2010

### HallsofIvy

Well, not for a general g(r,t) but there are solutions for some specific, non-trivial functions.

5. Sep 19, 2010