Question

A police car sounding a siren with a frequency of 1280Hz is traveling at 120.0km/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 90.0km/h in the opposite direc­ tion before and after passing the p

Answer 1

Answer:

a) 1417 Hz

b) 1314 Hz

Explanation:

The euqation for the Doppler effect frequency shift is:

$f = (\frac{c + vr}{c + vs})$

Where:

c: speed of sound (343 m/s in normal atmospheric conditions at sea level)

vr: speed of the receiver (negative if moving away from source, positive otherwise)

vs: speed of the source (positive if moving away from receiver, negative otherwise)

For the case of a standing observer:

120 km/h = 33.3 m/s

$f = (\frac{343 + 0}{343 - 33.3}) = 1417 Hz$

For the case of the car travelling at 90 km/h:

90 km/h = 25 m/s

$f = (\frac{343 - 25}{343 - 33.3}) = 1314 Hz$