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Finding the solution of the wave equation that satisfies the boundary conditions

  1. Mar 2, 2009 #1
    1. The problem statement, all variables and given/known data

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    2. Relevant equations

    N/A

    3. The attempt at a solution


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    Really stuck with this, i can't work out how to apply the boundary conditions to generate the simultaneous equations to find the specific solution. Can't find any similar examples either.
    Help appreciated.
     
  2. jcsd
  3. Mar 2, 2009 #2

    Tom Mattson

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    Do you know D'Alambert's formula? It will give you the solution almost immediately!
     
  4. Mar 2, 2009 #3
    Just looked it up on wikipedia but it confuses me, it doesn't explain it very well.
     
  5. Mar 2, 2009 #4

    Tom Mattson

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    You need to translate their notation to yours. They put it thusly.

    [tex]u_{tt}-c^2u_{xx}=0[/tex]

    The subscripts indicate partial differentiation, ie [itex]u_{tt}=\frac{\partial^2u}{\partial t^2}[/itex]. So their [itex]g(x)[/itex] equals your [itex]e^{-x^2}[/itex] and their [itex]h(x)[/itex] equals your [itex]2cxe^{-x^2}[/itex]. It's just plug and chug from there.
     
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