Doppler effect: 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 80.0 Hz. After the car goes by, you hear a frequency of 60.0 Hz. What is the speed of the car? The speed of sound in the air is 343 m/s.
A) 64.0 m/s
B) 49.0 m/s
C) 16.0 m/s
D) 36.0 m/s
E) 25.0 m/s

Question

Quizplus · Accepted Answer

The Doppler effect formula for sound is given by $f' = f \frac{v + v_o}{v - v_s}$, where $f'$ is the observed frequency, $f$ is the source frequency, $v$ is the speed of sound, $v_o$ is the speed of the observer (which is 0 in this case since the observer is stationary), and $v_s$ is the speed of the source. We can set up two equations, one for when the car is approaching ($f' = 80.0 \, \text{Hz}$) and one for when it is receding ($f' = 60.0 \, \text{Hz}$), and solve for $v_s$.When the car is approaching, the formula becomes $80 = f \frac{343}{343 - v_s}$. When the car is receding, it becomes $60 = f \frac{343}{343 + v_s}$. Dividing these two equations to eliminate $f$ gives us $\frac{80}{60} = \frac{343 + v_s}{343 - v_s}$, which simplifies to $\frac{4}{3} = \frac{343 + v_s}{343 - v_s}$.Solving for $v_s$ gives $v_s = 49.0 \, \text{m/s}$, which matches choice B.

Doppler Effect: as You Stand by the Side of the Road