Waves, frequency, and power

  • Thread starter clairez93
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  • #1
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Homework Statement



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

Homework Equations



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

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?
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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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?
 
  • #3
114
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Ah okay, so w = 2pi / f.
Therefore the Pa = 4Pb.
Thank you, that makes sense.
 

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