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

The answer is A) 218 Hz

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.