Question

A train is traveling away from you at 120 km/h. It blows its whistle, and you hear a tone of 0.400 kHz. Take the speed of sound to be 340 m/s. What frequency does the whistle actually produce

Answer 1

Answer:

The actual frequency produced by the train whistle is 444 Hz.

Explanation:

Given;

speed of the train, Vs = 120 km/h = 33.33 m/s

observed frequency, Fo = 0.4 kHz = 400 Hz

speed of sound in air, V = 340 m/s

Note: as the train moves away, the observed frequency will be smaller than the source frequency. Thus, the source frequency which is frequency of the train whistle will be greater than 400 Hz.

The source frequency is given by Doppler effect formula;

$F_s = F_o [\frac{V}{V-V_s} ]\\\\F_s = 400[\frac{340}{340-33.33} ]\\\\F_s = 400(1.109)\\\\F_s = 443.6 \ Hz$

Fs = 444 Hz

Therefore, the actual frequency produced by the train whistle is 444 Hz.