A siren emits a sound of frequency 1200 kHz. With which frequency is it received by a car moving at a speed of 20 m/s.

a) Away from the siren?
b) Towards the siren?

look up Doppler shift formula

A siren emits a sound of frequency 1200 kHz. With which frequency is it received by a car moving at a speed of 20 m/s.

a) Away from the siren?
b) Towards the siren?
The solution please

To determine the frequencies received by a car moving with respect to a stationary siren, we need to apply the Doppler effect formula. The Doppler effect describes how the perceived frequency of a sound changes when there is relative motion between the source of the sound and the observer.

The formula to calculate the apparent frequency, f', observed by an observer moving with velocity vO (in this case, the car) when the source (in this case, the siren) emits a frequency f is given by:

f' = f * (v + vO) / (v + vS)

where:
f is the emitted frequency
v is the speed of sound in the medium
vO is the velocity of the observer (car)
vS is the velocity of the source (siren)

Given the provided information, we have:
f = 1200 kHz = 1200 × 10^3 Hz
v = speed of sound in air ≈ 343 m/s
vO = 20 m/s (velocity of the car)

a) When the car is moving away from the siren:
In this scenario, the velocity of the source is negative since it is opposite to the motion of the car. Thus, vS = -vO = -20 m/s.

Plugging the values into the Doppler effect formula, we get:
f' = 1200 × 10^3 Hz * (343 m/s + 20 m/s) / (343 m/s - 20 m/s)

After calculating this expression, we can determine the apparent frequency received by the car.

b) When the car is moving towards the siren:
In this scenario, the velocity of the source and the car are in the same direction, so vS = vO = 20 m/s.

Using the same Doppler effect formula and plugging in the values, we can determine the apparent frequency received by the car.

By following these steps and applying the Doppler effect formula, you should be able to calculate the frequencies for scenarios a) and b) accordingly.