Wave equation under a Galilean transform.

[Johnny Blade]

Homework Statement

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.

Homework Equations

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.

 

[Johnny Blade]

Bump.