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.