A car moving at 35 m/s approaches a stationary whistle that emits a 220 Hz sound. The speed of sound is 343 m/s. What is the frequency of sound heard by the driver of the car?
A)198 Hz
B)220 Hz
C)245 Hz
D)282 Hz
E)340 Hz

Question

Quizplus · Accepted Answer

When a sound source is moving relative to an observer, the frequency of the sound heard by the observer changes. This is known as the Doppler effect. The frequency heard by the observer moving towards the source is higher than the frequency emitted by the source, and the frequency heard by the observer moving away from the source is lower than the frequency emitted by the source.

In this case, the car is moving towards the stationary whistle. So, the frequency heard by the driver of the car will be higher than the frequency emitted by the whistle. We can use the following formula to calculate the frequency heard:

f' = f (v + u) / (v + s)

where, 
f = frequency emitted by the source (220 Hz in this case)
v = speed of sound (343 m/s)
u = speed of the observer (speed of the car = 35 m/s in this case)
s = speed of the source (0 m/s in this case, as the whistle is stationary)

Substituting the values, we get:

f' = 220 (343 + 35) / (343 + 0) = 245 Hz

Therefore, the frequency of sound heard by the driver of the car is 245 Hz, which is closest to choice C (245 Hz).

A Car Moving at 35 M/s Approaches a Stationary Whistle