Question

A source vibrating at constant frequency generates a sinusoidal wave on a string under constant tension. If the power delivered to the string is doubled, by what factor does the amplitude change?
a. a factor of 4
b. a factor of 2
c. a factor of √2
d. a factor of 0.707
e. cannot be predicted

Answer 1

I think the answer is c. I'm going to use an analogy which I THINK fits this. If I replace the string with an electric current, and the string's amplitude by the amplitude of the current, then Power = Current squared times resistance. So, Current amplitude would be the square root of power divided by resistance. If the power were to be doubled, the current amplitude would be increase by the square root of 2.
I think that 0.707 is the same as 1 over root 2, and I don't think it's the right answer.
Let me know if my analogy and analysis are right ... please.
Bon voyage, et bon chance
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Answer 2

Thank you for your reply. If I found the the right answer. I will reply to you.
Thank you so much.

Answer 3

Why not just take a peek at the formula for power carried by a sinusoidal wave? It's basically kinetic energy per wavelength divided by period. You get:

$$P = \frac{1}{2}\mu\omega^2A^2v\\
A = \sqrt{\frac{2P}{\mu\omega^2v}}$$
so by doubling the P we get:
$$A_1 = \sqrt{\frac{2*2P}{\mu\omega^2v}}
A_1 = \sqrt{2} \sqrt{\frac{2P}{\mu\omega^2v}}\\
A_1 = \sqrt{2} A$$

Answer 4

in the last formulas I forgot the newline characters:
$$A_1 = \sqrt{\frac{2*2P}{\mu\omega^2v}}\\
A_1 = \sqrt{2} \sqrt{\frac{2P}{\mu\omega^2v}}\\
A_1 = \sqrt{2} A$$