A source vibrating at constant frequency generates a sinusoidal wave on a string under constant tension. If the power delivered to the string is quadrupled, by what factor does the amplitude change? 16

Amplitude changes by factor of 2 means double.

Explanation:

Given:

If the power delivered to the string is quadrupled.

From the formula of power transmitted by a sinusoidal wave on a stretched string is,

Where mass per unit length, angular speed, amplitude, wave speed, power delivered.

Here we need only two terms power and amplitude.

       ∝

All other quantities are constant for our problem,

Where constant

Here Power become quadruple means four times,

So amplitude changes by factor of 2 means double

wind moving at higher speeds will transfer more energy to the water, resulting in stronger waves.