# Wave equation under a Galilean transform.

1. Jan 23, 2010

### Johnny Blade

1. The problem statement, all variables and given/known data

Show that the wave equation becomes
$$\left(1-\frac{V^{2}}{c^{2}}\right)\frac{\partial^{2}\psi'}{\partial x'^{2}}-\frac{1}{c^{2}}\frac{\partial^{2}\psi'}{\partial t'^{2}}+\frac{2V}{c^{2}}\frac{\partial^{2}\psi'}{\partial t' \partial x'} = 0$$

under a Galilean transform if the referential R' moves at constant speed V along the x axis.

2. Relevant equations

3. The attempt at a solution

Frankly I don't really know how to do that. I tried using a general solution with x = x' + Vt' and using it in the normal wave equation, but gave me nothing good. Now I don't even know what else I could do.

2. Jan 24, 2010

### Johnny Blade

Bump.

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