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?
A) 364 Hz
B) 444 Hz
C) 439 Hz
D) 361 Hz

Question

Quizplus · Accepted Answer

The frequency heard is lower than the actual frequency produced by the whistle due to the Doppler effect, as the train is moving away. The formula to calculate the actual frequency ($f$) when the source is moving away from the observer is $f = f'\left(\frac{v + v_o}{v - v_s}\right)$, where $f'$ is the frequency heard by the observer, $v$ is the speed of sound, $v_o$ is the observer's speed (0 m/s in this case since the observer is stationary), and $v_s$ is the speed of the source (train). Converting the train's speed to m/s (120 km/h = 33.33 m/s), and substituting the given values: $f = 400 \times \left(\frac{340}{340 - 33.33}\right)$, we find the actual frequency produced by the whistle to be approximately 439 Hz.

A Train Is Traveling Away from You at 120 Km/h