Solving Wave Equation with D'Alembert: Step by Step

[bon]

Homework Statement

Ok so hope someone will be able to help...

I've used the D'Alembert method to solve the wave equation and have got that the general form should be

y(x,t) = f(x+ct) + g(x-ct)

Now I am also told that the time dependence at x=0 is sinusoidal..

that is, y(x,0) = sin(wt)...

How can i deduce that the full x,t dependence is given by:

y(x,t) = Asin(kx+wt) + Bsin(kx-wt)

where k = w/c?

Thank you

Homework Equations

The Attempt at a Solution

Not sure where to go..

It seems the conditions tell me that f(x) + g(x) = sinwt..cant see how that helps :S

 

[bon]

anyone :S?