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Standing wave energy

  1. Jan 17, 2009 #1
    1. The problem statement, all variables and given/known data

    A standing wave is maintained in a homogenous string of cross-sectional area a and density [tex]\rho[/tex] . It is formed by the superposition of two waves travelling in opposite directions given by the equations

    y1 = Asin(wt-kx)
    y2 = 2Asin(wt +kx)

    Find the total mechanical energy confined between the section corresponding to the adjacent antinodes.

    2. The attempt at a solution

    The wave is given by y = Asin(wt-kx) + 2Asin(wt +kx)

    KE of a small element is 1/2 u dx v^2 , where u = mass per unit length.

    I find v by differentiating y wrt t.

    Then I integrate with proper limits. But the integration looks outrageous looking at the simple answer. Is there any shortcut ? Also using above method we only get the KE, what about the PE?
  2. jcsd
  3. Jan 17, 2009 #2


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    Hi atavistic! :smile:
    Show us! :smile:
  4. Jan 17, 2009 #3
    Well can you tell me what I did is right or not and the thing about PE.
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