# Showing a general solution for a wave on a string fixed at one end

#### catpants

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

http://img811.imageshack.us/img811/1989/problem1.png [Broken]

2. Relevant equations

All shown in the above link, AFAIK

3. The attempt at a solution

Not worried about part a.
For part b, when they say "assume the string is initially at rest" I took that to mean:
$$\frac{\delta\Psi(x,0)}{\delta t}=0$$
But I don't know if that is right. It would be used as some sort of initial conditions for solving some diff eq. But I don't understand what that diff eq would be, or how to set it up. I would imagine I solve this diff eq using sep of vars?

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#### HallsofIvy

The wave equation, which I presume you have already seen, since it is not mentioned in the problem is
$$\frac{\partial^2 \psi}{\partial x^2}= \frac{1}{c^2}\frac{\partial^2\psi}{\partial t^2}$$.

Yes, an initial condition is
[tex]\frac{\partial \psi(x, 0)}{\partial t}= 0[/math]

(By the way, use "\partial" to get the $\partial$ in LaTex.)

#### catpants

I think the wave equation is what I was missing. Do I try and solve it using separation of variables? Also, the end of your post got mangled, what were you trying to say?

Thanks!!

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