You stand on the curb waiting to cross the street.Suddenly you hear the sound of a horn from a car approaching you with a constant speed of 25.0 m/s.You hear a frequency of 100 Hz.After the car passes you by,what is the frequency that you will hear?

Question

Quizplus · Accepted Answer

This is a Doppler Effect problem. As the car approaches, the frequency you hear is higher than the actual frequency of the horn due to the compression of sound waves. As the car passes and moves away from you, the frequency you hear is lower than the actual frequency due to the stretching of sound waves. The formula to calculate the new frequency is: 
f' = f*(v +/- v0)/(v +/- vs)
where f is the actual frequency of the horn (100 Hz), v is the speed of sound (343 m/s), v0 is the speed of the observer (0 m/s), and vs is the speed of the source (25.0 m/s in this case). 
Plugging in the values, we get:
f' = 100*(343 +/- 0)/(343 +/- 25.0)
f' = 100*(343/318) or 100*(343/368)
Solving these two equations gives us f' = 86.4 Hz or f' = 91.0 Hz. Since the car is moving away from you, the minus sign should be used in the formula, giving us f' = 86.4 Hz as the final answer.

You Stand on the Curb Waiting to Cross the Street