A police car sounding a siren with a frequency of 1540 Hz is traveling at 130 km

Question

A police car sounding a siren with a frequency of 1540 Hz is traveling at 130 km/h . A)

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

Express your answers using three significant figures separated by a comma. 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?

Express your answers using three significant figures separated by a comma. 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?

Explanation / Answer

In classical physics, where the speeds of source and the receiver relative to the medium are lower than the velocity of waves in the medium, the relationship between observed frequency f and emitted frequency fo is given by:
f = [(V+Vr)/(V+Vs)] x fo
Where
V is the velocity of waves in the medium
Vr is the velocity of the receiver relative to the medium; positive if the receiver is moving towards the source.
Vs is the velocity of the source relative to the medium; positive if the source is moving away from the receiver.
The frequency is decreased if either is moving away from the other.
1)Given Vs = 130 km/hr = 130 x 1000/3600 = 36.11 m/s
=>f(approach) = [343/(343-36.11)] x 1540 = 1721.203 Hz
=>f(receding) = [343/(343+36.11)] x 1540 = 1393.315 Hz
2)given Vr = 890 km/hr = 90 x 1000/3600 = 25 m/s
=>f(approach) = [(343+25)/(343-36.11)] x 1540 = 1846.655 Hz
=>f(receding) = [(343-25)/(343 + 36.11)] x 1540 = 1291.762 Hz
3) given Vr = 80 km/hr = 80 x 1000/3600 = 22.22 m/s
=>f(approach) = [(343-22.22)/(343-36.11)] x 1540 = 1609.701 Hz
=>f(receding) = [(343+22.22)/(343 + 36.11)] x 1540 = 1483.576 Hz

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