A sinusoidal wave on a given stretched string has amplitude A, frequency f and average power P̄. The amplitude is doubled while the frequency is reduced to one-half. The string tension and linear density remain unchanged. What is the new average power?
Options

Question

A sinusoidal wave on a given stretched string has amplitude A, frequency f and average power P̄. The amplitude is doubled while the frequency is reduced to one-half. The string tension and linear density remain unchanged. What is the new average power?

Options

G1 Physics · Accepted Answer

For the same string, P̄ ∝ A²ω² and therefore P̄ ∝ A²f². New amplitude factor: (2)² = 4. New frequency factor: (1/2)² = 1/4. Thus, P̄(new)/P̄(old) = 4×1/4 = 1. Therefore the average power remains unchanged. Correct option: B.