Sketch the displacement of the string

[bon]

Homework Statement

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.

Homework Equations

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!

 

[ehild]

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

You had a very similar problem not long ago.

ehild

 

[bon]

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

You had a very similar problem not long ago.

ehild

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!

 

[ehild]

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