A police car has an 800-Hz siren. It is traveling at 35.0 m/s on a day when the speed of sound through air is 340 m/s. The car approaches and passes an observer who is standing along the
Roadside. What change of frequency does the observer hear?
A) 166 Hz
B) 249 Hz
C) 82 HZ
D) 0 Hz

Question

Quizplus · Accepted Answer

The change in frequency observed is due to the Doppler effect, which describes the change in frequency of a wave in relation to an observer moving relative to the source of the wave. When the police car is approaching the observer, the observed frequency increases, and when it moves away, the observed frequency decreases. The total change observed as the car approaches and then recedes can be calculated using the Doppler effect formula for moving source and stationary observer. The observed frequency when the car is approaching is given by $f' = f \frac{v + v_o}{v - v_s}$, where $f$ is the source frequency (800 Hz), $v$ is the speed of sound (340 m/s), $v_o$ is the observer's speed (0 m/s, since the observer is stationary), and $v_s$ is the speed of the source (35.0 m/s). When the car is moving away, the observed frequency is given by $f' = f \frac{v - v_o}{v + v_s}$. The change in frequency is the difference between the frequencies observed as the car approaches and recedes. The correct calculation shows that the change in frequency is 166 Hz, which is significant as it demonstrates how the Doppler effect can alter the perception of sound based on the relative motion of the source and the observer.

A Police Car Has an 800-Hz Siren