Question

A galloping pony speeds past you at 5 m/s. The frequency of the sound produced by the hooves on the dirt is 221 Hz. Assume the speed of sound to be 342 m/s. What is the observed frequency of the hooves after the pony has passed your position?

1. 218 Hz
2. 226 Hz
3. 216 Hz
4. 224 Hz

Answer 1

The answer is A) 218 Hz

Answer 2

Given:
speed of passing pony 5 m/s
frequency of the sound produced: 221 Hz
speed of sound 342 m/s

Let us use the Doppler Shift Formula:
Where the source is moving away from the observer at rest

f' = (v / v+vs) f
Where, vs = Velocity of the Source,
v = Velocity of sound or light in medium,
f = Real frequency,
f' = Apparent frequency.

f'= [342 m/s / (342 m/s+5m/s)] * 221 Hz
f' = 0.9856 * 221Hz
f' = 217.8176 Hz or 218 Hz

The observed frequency of the hooves after the pony has passed your position is 218 Hz.