# Wave equation with nonhomogenous neumann BC

1. Jul 2, 2012

### Mugged

I've been searching online for the past week but can't seem to find what im looking for.

I need the analytic solution to the wave equation: utt - c^2*uxx = 0

with neumann boundary conditions that are not homogeneous, i.e. ux(0,t) = A, for nonzero A.

also, the domain i require the solution to be in is a bounded domain (0 to L) or better yet the semi-infinite domain (0 to ∞)

can anyone refer me to a source?

Thank you

2. Jul 3, 2012

### lpetrich

So it's utt - c2uxx = 0
([noparse]utt - c2uxx = 0[/noparse])

The general solution is easy: u = u1(x - c*t) + u2(x + c*t)
for arbitrary functions u1 and u2.
One can find it by changing variables to w1 = x - c*t and w2 = x + c*t

One can see from that solution that a single boundary condition won't be enough to fix u1 and u2. One will need two boundary conditions for that.

3. Jul 3, 2012

### Mugged

I need more than the general solution

4. Jul 3, 2012

### Mute

Have you tried solving it yourself?