Question

A police car sounding a siren with a frequency of 1600 Hz is traveling at 115 km/h . What frequencies does an observer standing next to the road hear as the car approaches and as it recedes? What frequencies are heard in a car traveling at 90.0 km/h in the opposite direction before and after passing the police car? The police car passes a car traveling in the same direction at 80.0 km/h. What two frequencies are heard in this car?

Answer 1

Given,

fo = 1600 Hz and V = 115 km/hr = 31.94 m/s

We know that the observed frequency and the emitted frequency are related as:

f = [ (V + Vr)/(V + Vs) ]*fo

where, V is the velocity of sound, Vr is the that of reciever and Vs is that of source ;

(1)

since the observer is standing, Vr = 0

f_approach = ( 343 / (343 - 31.94) ) *1600 = 1764.28 Hz

f_reced = (343/ (343 +31.94) )*1600 = 1463.70 Hz

(2)

Now Vr = 90 km/h = 25 m/s

f_approach = ( 343 + 25 / (343 -31.94) ) * 1600 = 1892.88 Hz

f_reced  = (343 - 25 / (343 + 31.94 ) )*1600 = 1356.87 Hz

(3)

Now Vr = 80 km/h = 22.22 m/s

f_approach = ( 343 - 22.22 / (343 -31.94) ) * 1600 = 1649.99 Hz

f_reced  = (343 +22.22 / (343 + 31.94 ) )*1600 = 1558.52 Hz