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Homework Help: Wave function

  1. Feb 3, 2006 #1
    I have a function defined between 0<x<infinity, and 0<y<b

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

    Given [itex] \frac{\partial \phi}{\partial x} = a cos(\pi y/b)e^{iwt} [/itex] at x=0
    and [itex] \omega ^2 = \pi ^2 v^2 n^2 /b^2 [/itex]
    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

    [itex] \frac {\partial ^2 \phi}{\partial x^2 } + \frac {\partial ^2 \phi}{\partial y^2 } = 1/v^2 \frac {\partial ^2 \phi}{\partial t^2 }[/itex]


    I get, relationship between v and w. No new info.





    I would appreciate any hints,


    THanks,


    Gamma.
     
    Last edited: Feb 3, 2006
  2. jcsd
  3. Feb 3, 2006 #2
    This is a problem in claculus. I should have posted in there.

    Any way,

    I have for w,

    [itex]\frac{w^2}{v^2} =\frac{\pi^2}{b^2} - \lambda ^2[/itex]

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

    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?
     
  4. Feb 3, 2006 #3
    never mind. I think I got it..

    Thanks,
     
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