An ambulance has picked up an injured rock climber and is heading directly away

Question

An ambulance has picked up an injured rock climber and is heading directly away from the canyon wall (where the climber was injured) at a speed of 31.3 m/s as seen in Figure. The ambulance’s siren has a frequency of 400.0 Hz. After the ambulance turns off its siren, the injured rock climber can hear the reflected sound from the canyon wall for a few seconds. The velocity of sound in air is vsound = 343 m/s. What is the frequency of the reflected sound from the ambulance’s siren as heard by the injured rock climber in the ambulance?

Explanation / Answer

This is a case of doppler's effect:

first the ambulance is source and wall is observer

frequency received by the wall = 400*(343/(343+31.3)) = 366.55 Hz

now the wall is source and injured climber is observer

frequency heard by the rock climber = 366.55*((343-31.3)/343)

=333.1 Hz

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