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Power transmitted through string

  1. Jan 22, 2008 #1
    1. The problem statement, all variables and given/known data

    A horizontal string can transmit a maximum power (without breaking) if a wave with amplitude A and angular frequency is travelling along it. To increase this maximum power, a student folds the string and uses this "double string" as a medium. Determine the maximum power that can be transmitted along the "double string" assuming that the tension is constant.


    2. Relevant equations

    [tex]\wp[/tex] = [tex]\frac{1}{2}[/tex] [tex]\mu[/tex] [tex]\omega[/tex] [tex]^{2}[/tex]A[tex]^{2}[/tex]v

    omega squared...for some reason the greek letter like to be superscript?

    Also, I have

    v = [tex]\lambda[/tex]f

    v = [tex]\frac{\lambda}{T}[/tex]

    v = [tex]\sqrt{\frac{T}{\mu}}[/tex]


    3. The attempt at a solution - Well, in a way...

    So I'm not quite sure what to do in terms of the math, but I've been thinking.

    Say you fold the string in two. You essentially get two new strings that are half the length of the original. Now, wouldn't the total power output be exactly the same as the original full-length string? Follow my logic?

    I also tried subbing in v = [tex]\sqrt{\frac{T}{\mu}}[/tex] but that brought me nowhere.

    On another path, I know that if the length of the string shortens, and tension remains constant, then [tex]\mu[/tex] and [tex]\omega[/tex] would change, would they not? If
    so, how do I incorporate this into the solution?

    Any help is appreciated, thanks in advance!
     
  2. jcsd
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