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 20 m/sm/s , the driver at rest hears a beat frequency of 5.2 HzHz .

Answer 1

Answer:

The frequency of the horn is 83.87 Hz

Explanation:

Given:

v = speed of the second horn = 20 m/s

vs = speed of the sound = 343 m/s

Δf = beat frequency = 5.2 Hz

The apparent frequency is equal to:

$f_{ap} =f\frac{v_{s}-v_{o} }{v_{s}-v } \\f_{ap}=f\frac{343-0}{343-20} \\f_{ap}=1.062f$

The frequency of the horn is equal:

$deltaf=f_{ap} -f\\deltaf=1.062f-f\\5.2=0.062f\\f=83.87Hz$

Answer 2

Explanation:

This is a good example of Doppler effect

Given

Source velocity Vs=20m/s

Apparent frequency Fa= 5.2 Hz

Recall speed of sound V=340m/s

The frequency of the horn Fh=?

But mathematically Fh=(V-Vs/V)*Fa

(340-20)/340*5.2=4.89Hz