Velocity of propagation of an EM field in vacuum

[It's me]

Homework Statement

In a region of empty space, the magnetic field is described by ##\vec{B} = B_0e^{ax}\sin{(ky-\omega t)} \hat{z}##. Find the speed of propagation ##\vec{v}## of this field.

Homework Equations

##\Delta \vec{B} = \frac{1}{v^2}\frac{d^2\vec{B}}{dt^2}## , ##k=\frac{\omega }{ v}##

The Attempt at a Solution

I'm not sure of a way to calculate the velocity. Do I have to take into account the equation, or because the wave is propagating in empty space can I simply say ##v=c##? And I know the direction of propagation would be ##\hat{y}## if the term ##e^{ax}## didn't exist, but is it still ##\hat{y}## with it? I really don't understand how that term affects the velocity of propagation.

 

[phyzguy]

Try plugging your expression for B into Maxwell's equations.

 

[It's me]

I did that and got #\vec{E}#, but I still don't understand what equation to use to get the velocity.