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

The frequency of the horn is 83.87 Hz

Step-by-step 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(v_(s)-v_(o) )/(v_(s)-v ) \\f_(ap)=f(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

Step-by-step 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