(adsbygoogle = window.adsbygoogle || []).push({}); 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 U_{tt}= C^{2}u_{xx}?

2. Relevant equations

3. The attempt at a solution

I've taken the partial differentials:

U_{x}= acos(ax)sin(bt)

U_{xx}= -a^{2}sin(ax)sin(bt)

U_{t}= bcos(bt)sin(ax)

U_{tt}= -b^{2}sin(bt)sin(ax)

and subbed them into the equation to get:

-b^{2}sin(bt)sin(ax)+c^{2}a^{2}sin(ax)sin(bt)=0

so:

(-b^{2}+c^{2}a^{2})(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

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# Homework Help: What values of a and b satisfy the following wave equation?

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