Traveling Wave with Unknown Speed and Direction

[patm95]

Homework Statement

Is this a traveling wave? If so, find the speed and direction.

e^-(a^2y^2+b^2t^2-2abty)

Homework Equations

Probably relevant to know the differential wave equation.

The Attempt at a Solution

I have a feeling that this is a traveling wave as it is twice differentiable and appears to be a solution of the differential wave equation.

I first rearrange the equation to:

e^-(ay-bt)^2

So would this be a wave traveling right at speed b? I am unsure if it matters that I am keeping the sqaure in there?

 

[BigJDubs]

If it does, then I would think that the speed and direction can't be determined. Thanks for any help!