(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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**