A source travelling to the right at a speed of 5 m/s emits a sound wave which is reflected off a reflector travelling to the left at a speed of 5 m/s.If the frequency of the reflected sound wave detected by a listener back at the source is 100 Hz,what is the frequency of the wave emitted at the source?
A)100 Hz
B)106 Hz
C)103 Hz
D)94.3 Hz
E)97.1 Hz

Question

A source travelling to the right at a speed of 5 m/s emits a sound wave which is reflected off a reflector travelling to the left at a speed of 5 m/s.If the frequency of the reflected sound wave detected by a listener back at the source is 100 Hz,what is the frequency of the wave emitted at the source? 
A)100 Hz 
B)106 Hz 
C)103 Hz 
D)94.3 Hz 
E)97.1 Hz

Quizplus · Accepted Answer

When the sound source is moving towards the reflector, the relative velocity of the wave is the difference of the velocity of sound and the velocity of the source. When the sound is reflected from the reflector, the wave is moving away from the reflector with relative velocity as the sum of the velocity of sound and the velocity of the reflector. Let the frequency of the wave emitted at the source be f. Then, the frequency of the wave detected by the listener back at the source can be calculated as follows:

f' = f(V + Vr)/(V - Vs)

Where 
f' = frequency of the reflected wave detected by the listener
V = velocity of sound
Vs = velocity of the source = 5 m/s (rightwards)
Vr = velocity of the reflector = -5 m/s (leftwards)

Substitute the values to get,

100 = f(340 - 5)/ (340 + 5)

f = 94.3 Hz

Hence, the answer is D)94.3 Hz.

A Source Travelling to the Right at a Speed of 5