- #1

s_gunn

- 34

- 0

## Homework Statement

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}?

## Homework Equations

## 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!