A train traveling at 90 km/h is blowing its whistle at 440 Hz as it crosses a level crossing.You are waiting at the crossing and hear the pitch of the whistle change as the train passes you.The sound you hear changes from a frequency of _____ to a frequency of _____.(Take the speed of sound to be 340 m/s.)
A)475 Hz; 410 Hz
B)410 Hz; 475 Hz
C)408 Hz; 472 Hz
D)472 Hz; 408 Hz
E)598 Hz; 348 Hz

Question

Quizplus · Accepted Answer

The change in frequency is due to the Doppler effect. As the train approaches, the frequency increases, and as it moves away, the frequency decreases. The formula for the Doppler effect when the source is moving towards the observer is $f' = f \left(\frac{v + v_o}{v - v_s}\right)$, and when moving away, it is $f' = f \left(\frac{v - v_o}{v + v_s}\right)$, where $f'$ is the observed frequency, $f$ is the source frequency, $v$ is the speed of sound, $v_o$ is the observer's speed (0 in this case), and $v_s$ is the source's speed. Plugging in the given values (with $v_s = 90 \, \text{km/h} = 25 \, \text{m/s}$), for the approach, the observed frequency increases, and for the departure, it decreases, matching option A's frequencies.

A Train Traveling at 90 Km/h Is Blowing Its Whistle