Question

A police car sounding a siren with a frequency of 1640 Hz is traveling at 110 km/h .

A What frequencies does an observer standing next to the road hear as the car approaches and as it recedes?

B) What frequencies are heard in a car traveling at 90.0 km/h in the opposite direction before and after passing the police car?

C) 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

110 km/h = 30.56 m/s

f'(approaches) = f*1/(1 - Vsiren/V sound)

= 1640*1/(1 - 30.56/343)

= 1800 Hz

f'(recedes) = f*1/(1 + V siren/V sound )

= 1640*1/(1 + 30.56/343)

= 1506 Hz

(b) 90 km/hr = 25 m/s

f'(approaches) = f*(Vsound + V car) /(Vsound - Vsiren)

= 1640*(343 + 25)/(343 - 30.56)

= 1932 Hz

f'(recedes) = f*(Vsound - V car) /(Vsound + Vsiren)

= 1640*(343 - 25)/(343 + 30.56)

= 1396 Hz

(c) 80 km/hr = 22.22 m/s

f'(approaches) = f*(Vsound - Vcar) /(Vsound + Vsiren)

= 1640*(343 - 22.22)/(343 - 30.56)

= 1684 Hz

f'(recedes) = f*(Vsound + V ar) /(Vsound + V siren)

= 1640*(343 + 22.22)/(343 + 30.56)

= 1603 Hz