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Power of a wave at a specific point

  1. Nov 19, 2006 #1
    Q: A wave pulse traveling along a string of linear mass density 0.0026 kg/m is described by the relationship [tex]y = A_0 e^{-bx}\sin(kx - \omega t)[/tex] where [tex]A_0 = 0.0097 m, b = 0.9 m^{-1}, k = .88 m^{-1} and \oemga = 56 s^{-1}[/tex]. What is the power carried by this wave at the point [tex]x = 2.6 m[/tex]?

    My book has: [tex]\wp = \frac{1}{2} \mu \omega^2 A^2 v[/tex] which is the "power associated with the wave" but yet we're to show "the power carried by this wave at the point x = 2.6 m". Plus the equation given isn't a normal wave function - I guess - since it has the coefficient [tex]e^{-bx}[/tex].

    The book also has [tex]\wp = \frac{E_\lambda}{\Delta t}[/tex] so if I had a [tex]\Delta x[/tex] I could so something similar as before, that is [tex]\wp_{\Delta x} = \frac{E_{\Delta x}}{\Delta t}[/tex] but this isn't the same thing?

    How should I proceed? thanks.

    I guess I could take as A the whole [tex]A_0 e^{-bx}[/tex] and plug it into the equation (using the given values)?
    Last edited: Nov 19, 2006
  2. jcsd
  3. Nov 19, 2006 #2


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    That should do it. A is a time-decaying amplitude in this case.
  4. Nov 19, 2006 #3
    fantastic! thanks!! :-)
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