Question

A driver sitting at a railroad crossing perceives that the train's whistle has a

frequency of 159 Hz after it passes by. If the people on the train hear a frequency of
184 Hz, how fast is the train moving? Use 337 m/s for the speed of sound.

Answer 1

This is an example of the Doppler effect, where the perceived frequency of a sound wave changes due to the relative motion between the source of the sound wave and the observer.

The formula for the Doppler effect is:

f' = f * (v + u) / (v - us)

where:
f' is the perceived frequency of the sound wave by the observer
f is the actual frequency of the sound wave emitted by the source
v is the speed of sound in air (337 m/s)
u is the speed of the observer relative to the medium (in this case, the air)
s is the speed of the source relative to the medium (in this case, the air)

In this problem, we can assume that the speed of sound is constant and that the driver is stationary, so u = 0. We want to solve for s, the speed of the train.

Let's plug in the given values and solve for s:

f' = 159 Hz
f = 184 Hz
v = 337 m/s
u = 0 m/s
s = ?

159 = 184 * (337 + 0) / (337 - s)
159(337 - s) = 184(337)
53733 - 159s = 62728
159s = 8985
s = 56.5 m/s (rounded to one decimal place)

Therefore, the speed of the train is approximately 56.5 m/s.