A stationary source emits a sound wave of frequency f.If it were possible for a man to travel toward the source at the speed of sound, he would observe the emitted sound to have a frequency of:
A)0
B)f/2
C)2f/3
D)2f
E)infinity

Question

Quizplus · Accepted Answer

This is an application of the Doppler effect. When an observer moves towards a stationary source, the effective frequency of the wave increases. In this case, the observer is moving towards the source at the speed of sound, so the relative velocity between the observer and the source is the speed of sound. The formula for the Doppler effect in this case is:

f' = f (v_sound + v_observer) / (v_sound + v_source)

where f is the frequency of the wave emitted by the source, f' is the frequency observed by the observer, v_sound is the velocity of sound, and v_observer and v_source are the velocities of the observer and the source, respectively.

Since the observer is moving towards the source at the speed of sound, v_observer = v_sound. Therefore:

f' = f (v_sound + v_sound) / (v_sound + v_source) = 2f(v_sound) / (v_sound + v_source)

As the observer approaches the source, v_source becomes less than v_sound, so the denominator of this fraction decreases, and the effective frequency observed by the observer increases. When v_source = 0 (i.e. the source is stationary), we get:

f' = 2f(v_sound) / (v_sound + 0) = 2f

Therefore, the observed frequency would be twice the emitted frequency. The correct choice is D.

A Stationary Source Emits a Sound Wave of Frequency F