Question

A sinusoidal wave with amplitude y is travelling with speed $v$ on a string with linear density $\rho $ . The angular frequency of the wave is $\omega $ . The following conclusions are drawn. Mark the one which is correct. (in particular option, if we are changing one quantity, assume others are kept constant)

• A. Doubling the frequency doubles the rate at which energy is carried along the string
• B. If the amplitude were doubled, the rate at which energy is carried would be halved
• C. If the amplitude were doubled, the rate at which energy is carried would be doubled
• D. The rate at which energy is carried is directly proportional to the velocity of the wave

Answer 1

Answer: (D)

$P_{\text{ar}}=\frac{1}{2}\mu v\omega ^{2}A^{2}$
So $P \propto v$
$ \propto \omega ^{2}$
$ \propto \text{A}^{2}$
So if frequency or amplitude is doubled power will be quadrupled, but if velocity is doubled power will also be doubled.