Finding A and B Given a Function: Gamma's Quest

[Gamma]

I have a function defined between 0<x<infinity, and 0<y<b

\phi=cos(\pi y/b) e^{iwt}(A e^{\lambda x} + B e^{-\lambda x)}

Given \frac{\partial \phi}{\partial x} = a cos(\pi y/b)e^{iwt} at x=0
and \omega ^2 = \pi ^2 v^2 n^2 /b^2
need to find A and B.

Above condithion gives one equation for A and B.

How do I find a second equation relating A and B.
Given function satisefies the 2D wave equation.

Pluggig in values in

\frac {\partial ^2 \phi}{\partial x^2 } + \frac {\partial ^2 \phi}{\partial y^2 } = 1/v^2 \frac {\partial ^2 \phi}{\partial t^2 }I get, relationship between v and w. No new info.I would appreciate any hints,THanks,Gamma.

 

[Gamma]

This is a problem in claculus. I should have posted in there.

Any way,

I have for w,

\frac{w^2}{v^2} =\frac{\pi^2}{b^2} - \lambda ^2

From the given condition \frac{\partial \phi}{\partial x} = a cos(\pi y/b)e^{iwt}

I have,

a = lambda (A-B) -------------------------(1)

I used the fact that phi(x,y, t) = 0 at x=0, y=0. This boundary condition gives

A = -B ----------------------(2)


A = -B = a /2*lambda -----------------(3)

Does this look right?

 

[Gamma]

never mind. I think I got it..

Thanks,