A truck moving at 36 m/s passes a police car moving at 45 m/s in the opposite direction. If the frequency of the siren is 500 Hz relative to the police car, what is the frequency heard by an observer in the truck after the police car passes the truck? (The speed of sound in air is 343 m/s.)

Question

Quizplus · Accepted Answer

The frequency heard by the observer in the truck can be calculated using the Doppler effect formula for sound. Since the source (police car) and the observer (truck) are moving towards each other before passing, and then away from each other after passing, we use the formula for the source and observer moving away from each other after the pass. The formula is $f' = f \frac{v}{v + v_s}$, where $f'$ is the observed frequency, $f$ is the source frequency, $v$ is the speed of sound, and $v_s$ is the speed of the source relative to the medium. Here, the relative speed of the police car to the truck after passing is $45 m/s + 36 m/s = 81 m/s$. Plugging in the values, we get $f' = 500 Hz \times \frac{343 m/s}{343 m/s + 81 m/s} = 500 Hz \times \frac{343}{424} \approx 396 Hz$.

A Truck Moving at 36 M/s Passes a Police Car