- #1
clairez93
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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?