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Homework Help: Solving the Wave Equation

  1. May 20, 2010 #1
    1. The problem statement, all variables and given/known data

    [PLAIN]http://img33.imageshack.us/img33/8236/waveeq.jpg [Broken]



    3. The attempt at a solution

    We calculate second differential with respect to x, and t, substitute into the wave equation.

    We then equate the coefficients: [A''(x) + (w/v)^2A(x)]sin(wt)=0

    We know from SHM equation that: A''(x) = -(w/v)^2A(x), and hence A''(x) = -k^2 A(x)

    But where do we go from here? Any hints?

    Also, what about part b?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. May 20, 2010 #2
    From A''(x) = -k^2 A(x), we seek a solution of the form A(x) = Csin(kx + psi)

    Apply our boundary conditions of y(0,t) and y(L,t) both = 0.

    We end up with sin(kL) = 0, where kL varies from 0 to 2PI, this implies that kL=nPI where n=1,2,3...

    Because it's quantised, we can say k(n) = nPI/L, where n=1,2,3...

    Since k = w/v, w(n) =nPI/L . v


    Where w(n) are the normal mode frequencies.

    Could someone verify this is correct?
     
  4. May 20, 2010 #3
    Also, any clues for b)?
     
  5. May 20, 2010 #4

    Redbelly98

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    Looks good for part (a).
    For (b), I'm not quite sure what they are getting at. In a sense, you already showed this in your derivation for part (a). Maybe they want you to think in terms of the wavelength λ and how it relates to the string length L.
     
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