As you stand by the side of the road, 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 speed of the car? The speed of sound in the air is 343 m/s.
A) 29 m/s
B) 27 m/s
C) 30 m/s
D) 26 m/s
E) 28 m/s

Question

Quizplus · Accepted Answer

The Doppler effect formula for sound can be used to find the speed of the car. When the car is approaching, the observed frequency $f'$ is higher, and when it's moving away, $f'$ is lower. The formula when the source is moving towards the observer is $f' = f \left(\frac{v + v_o}{v - v_s}\right)$ and when moving away $f' = f \left(\frac{v - v_o}{v + v_s}\right)$, where $v$ is the speed of sound, $v_o$ is the observer's speed (which is 0 in this case), and $v_s$ is the source's speed. We can set up two equations based on the given frequencies before and after the car passes and solve for $v_s$, the speed of the car. Given $f_{approach} = 76 Hz$, $f_{away} = 65 Hz$, and $v = 343 m/s$, we can solve for $v_s$. Rearranging and solving the equations gives us $v_s \approx 27 m/s$.

As You Stand by the Side of the Road, a Car