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?

Question

Quizplus · Accepted Answer

The observed frequency is lower because the train is moving away, so we use the formula for the Doppler effect for sound when the source is moving away from the observer: $f' = f \times \frac{v}{v + v_s}$, where $f'$ is the observed frequency (400 Hz), $v$ is the speed of sound (340 m/s), $v_s$ is the speed of the source (120 km/h, which is 33.33 m/s), and $f$ is the actual frequency we need to find. Rearranging the formula to solve for $f$, we get $f = f' \times \frac{v + v_s}{v}$. Plugging in the numbers, $f = 400 \times \frac{340 + 33.33}{340}$, which gives approximately 439 Hz.

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