# Sketch the displacement of the string

1. May 25, 2010

### bon

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

2. At time t = 0, the displacement of an inﬁnitely long string is:
y(x, t) = sin(pix/a) for −a ≤ x ≤ a

The string is initially at rest. Using d’Alembert’s solution for speed c, sketch the displacement of the string at t = 0, t = a/2c, and t = a/c.

2. Relevant equations

3. The attempt at a solution

So I see how to do this...my only problem is as follows:

D'Alembert solutions says y = f(x-ct) + g(x+ct)..

but we don't know if the wave goes left or right..so how do i know whether to sub in x-ct for x or x+ct for x? thanks!

2. May 25, 2010

### ehild

Re: waves

Is the initial displacement zero outside the interval [-a,a]?

You had a very similar problem not long ago.

ehild

3. May 26, 2010

### bon

Re: waves

yes it is similar outside the interval..

I know that this is similar to the one before - my problem is just knowing what to substitute instead of x -- should it be x-ct or x+ct?...

Thanks!

4. May 26, 2010

### ehild

Re: waves

Why do you think that the wave goes either left or right and not in both direction? Apply D'Alembert solution y = f(x-ct) + g(x+ct).

ehild