what values of a and b satisfy the following wave equation?

[s_gunn]

1. The problem statement, all variables and given/known data

For which values of the constants a and b does u(x,t) = sin(ax)sin(bt) satisfy the wave equation Utt = C2uxx?

2. Relevant equations


3. The attempt at a solution

I've taken the partial differentials:
Ux = acos(ax)sin(bt)
Uxx = -a2sin(ax)sin(bt)
Ut = bcos(bt)sin(ax)
Utt = -b2sin(bt)sin(ax)

and subbed them into the equation to get:
-b2sin(bt)sin(ax)+c2a2sin(ax)sin(bt)=0
so:
(-b2+c2a2)(sin(bt)sin(ax)) = 0

But then I'm lost!!

I have a feeling that I may have gone in completely the wrong direction so any help would be greatly appreciated!!!
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

[Gokul43201]

You have not gone in the wrong direction.

If p*q=0, what can you say about p and q?

[s_gunn]

I know that each of them must equal zero making
b = ca and a = b/c
but is rearranging them to make a the subject really all their asking for?! Am i missing something!!?

[Gokul43201]

I know that each of them must equal zero making
b = ca This is correct, but you skipped a step, and in the process lost one of the solutions.

But once have the other solution, that's basically all you are asked to do.

[s_gunn]

Thanks Gokul43201, sometimes you just need a nudge in the right direction!!