A car approaches you at a constant speed, sounding its horn, and you hear a frequency of 76 Hz. After the car goes by, you hear a frequency of 65 Hz. What is the frequency of the sound emitted
By the horn? The speed of sound in the air is 343 m/s.
A) 70 Hz
B) 68 Hz
C) 72 Hz
D) 69 Hz
E) 71 Hz

Question

Quizplus · Accepted Answer

70 HzThe phenomenon described is the Doppler effect, where the frequency of a sound wave changes for an observer moving relative to the source of the sound. The formula for the Doppler effect when the source is moving towards the observer is $f' = f \frac{v}{v - v_s}$ and when moving away $f' = f \frac{v}{v + v_s}$, where $f'$ is the observed frequency, $f$ is the actual frequency of the source, $v$ is the speed of sound, and $v_s$ is the speed of the source. We can set up two equations based on the given frequencies before and after the car passes:1. $76 = f \frac{343}{343 - v_s}$2. $65 = f \frac{343}{343 + v_s}$Solving these equations simultaneously for $f$ (the frequency of the horn) and $v_s$ (the speed of the car), we find that $f = 70$ Hz, which matches option A.

A Car Approaches You at a Constant Speed, Sounding Its