Electromagnetic wave equation not invariant under galilean trans.

[bfusco]

Homework Statement

Prove that the electromagnetic wave equation: 
(d^2ψ)/(dx^2) + (d^2ψ)/dy^2) + (d^2ψ)/(dz^2) − (1/c^2) * [(d^2ψ)/(dt^2)]= 0 is NOT invariant under Galilean transformation. (i.e., the equation does NOT have the same form for a moving observer moving at speed of, say, v in the x direction).

*note: all the "d"s in this equation are the partial derivatives.

Homework Equations

galilean transformation:
t'=t, x'=x-vt, y'=y, z'=z

The Attempt at a Solution

-from what i understand to solve this involves the chain rule for partial derivatives.
-looking at the equation i can't help but jump to something with the gradient of ∇ψ, but i don't know where to go from there.

 

[mfb]

The y,z,t components in the equation just stay the same, you can ignore them. You just have to change the x-component.
Hint: It will get an additional t-component afterwards.

 

[bfusco]

d/dx(dψ/dx' * dx'/dt + dψ/dt' * dt'/d(something)) ?

 

[bfusco]

d/dx(dψ/dx' * dx'/dt + dψ/dt' * dt'/d(something)) ?

wait is it d/dx(dψ/dx' * dx'/dx + dψ/dt' * dt'/dx), which equals d/dx(dψ/dx' * 1 + dψ/dt' * 0)?