Question

Two automobiles are equipped with the same single frequency horn. When one is at rest and the other is moving toward the first at 18 m/s, the driver at rest hears a beat frequency of 4.5 Hz. What is the frequency (Hz) the horns emit? Assume T = 20 degrees C

Answer 1

Given that one automobile is at rest and the other is moving towards the first at 18m/s, the driver at rest hears a beat frequency of 4.5 Hz.

Now let the first automobile driver is the observer and the second automobile is the source then by using Doppler effect, we have

F(observed)={v/v-v(source)}×F(source)

Where v is the speed of sound=343m/s

v(source) is the velocity of source=18m/s

F(source) is the frequency of source

F(observed)={343/(343-18)}×4.5

F(observed)=(343/325)×4.5

F(observed)=1.055×4.5

F(observed)=4.75Hz