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Homework Help: Waves, frequency, and power

  1. Dec 28, 2008 #1
    1. The problem statement, all variables and given/known data

    Two identical but separate strings, with the same tension, carry sinusoidal waves with the same amplitude. Wave A has a frequency that is twice that of wave B and transmits energy at a rate that is ____ that of wave B.
    A) half
    B) twice
    C) one fourth
    D) four times
    E) eight times

    2. Relevant equations

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

    3. The attempt at a solution

    [tex]V_{B} = \lambda[/tex][tex]f_{B}[/tex]
    [tex]V_{A} = \lambda[/tex][tex](2f_{B})[/tex] = [tex]2V_{B}[/tex]
    [tex]P_{B} = \frac{1}{2}\mu\omega^{2}A^{2}v_{B}[/tex]
    [tex]P_{A} = \frac{1}{2}\mu\omega^{2}A^{2}2v_{B}[/tex] = [tex]2P_{B}[/tex]

    Thus my answer is B.

    However, the answer key says D. What did I do wrong?
  2. jcsd
  3. Dec 28, 2008 #2


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    Science Advisor
    Homework Helper

    If the strings are identical (same mu) and have the same tension, the velocity v is also identical. You can't assume lambda is the same, it can't be. What changes in your power formula is omega. How much does it change?
  4. Dec 28, 2008 #3
    Ah okay, so w = 2pi / f.
    Therefore the Pa = 4Pb.
    Thank you, that makes sense.
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