A train moving at a constant speed is passing a stationary observer on a platform. On one of the train cars, a flute player is continually playing the note known as concert A (f = 440 Hz). After the flute has passed, the observer hears the sound with a frequency of 415 Hz. What is the speed of the train? The speed of sound in air is 343 m/s.
A)7.3 m/s
B)12 m/s
C)21 m/s
D)37 m/s
E)42 m/s

Question

Quizplus · Accepted Answer

This is an application of the Doppler effect formula:
observed frequency = emitted frequency x (speed of sound + observer's velocity relative to the medium) / (speed of sound + source's velocity relative to the medium)
Let v be the speed of the train, then the velocity of the observer relative to the medium (air) is 0 m/s, and the velocity of the source (flute player) relative to the medium is v m/s. We plug in the known values:
415 Hz = 440 Hz x (343 m/s + 0 m/s) / (343 m/s + v m/s)
415 Hz / 440 Hz = 343 m/s / (343 m/s + v m/s)
0.9432 = 343 m/s / (343 m/s + v m/s)
v m/s = 21 m/s. Therefore the answer is choice C.

A Train Moving at a Constant Speed Is Passing a Stationary