Question

Bill is making waves on a rope with one end attached to a wall. When he starts moving the rope quickly, the frequency of the waves created on the rope doubles. What happens to the energy that is transferred to the wall when the frequency of the waves doubles?

A.
The energy transferred to the wall is quadrupled.
B.
The energy transferred to the wall is tripled.
C.
The energy transferred to the wall is doubled.
D.
The energy transferred to the wall is halved.

Answer 1

The energy transferred by a wave is proportional to the square of its amplitude and the square of its frequency. When Bill starts moving the rope quickly, the frequency of the waves doubles, which means that the energy transferred by each wave is quadrupled (2^2 = 4).

However, the total energy transferred to the wall depends on the number of waves that reach the wall, which is proportional to the wavelength of the waves. The wavelength of the waves is inversely proportional to their frequency, so when the frequency of the waves doubles, their wavelength is halved. This means that twice as many waves will fit in the same distance, so the total energy transferred to the wall is doubled.

Therefore, the correct answer is: C. The energy transferred to the wall is doubled.