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.