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?

Question

Quizplus · Accepted Answer

The observer perceives a change in frequency due to the Doppler Effect, which is given by:

Δf/f = v/c

where Δf is the change in frequency, f is the original frequency, v is the velocity of the source (or observer) relative to the medium, and c is the speed of sound in the medium.

In this case, the observer is stationary relative to the medium, so v = 35.0 m/s (the velocity of the source). Therefore:

Δf/f = v/c = 35.0/340 = 0.103

This means the observer perceives a frequency that is 10.3% higher than the original frequency of 800 Hz.

Δf = 0.103f = 0.103 x 800 = 82.4 Hz

The answer is closest to choice C: 166 Hz, which is double the calculated Δf. However, this is not a valid answer because it is much larger than the original frequency of the siren (800 Hz). Therefore, the best choice is B: 82 Hz, which is closest to the calculated Δf of 82.4 Hz.

A Police Car Has an 800-Hz Siren