Question

A police car sounding a siren with a frequency of 1550 Hz is traveling at 130 km/h .

What frequencies does an observer standing next to the road hear as the car approaches? 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? For both approaching and receding

The police car passes a car traveling in the same direction at 80.0 km/h. What two frequencies are heard in this car? For both approaching and receding

Answer 1

This is the doppler shift effect for sound.

The formula for the shift is given as:

where v is the velocity of sound in medium (air: 340 m/s or 1224 kmph)

v_s is the source's velocity w.r.t an observer at rest.

Applying this , we get:

As it recedes, the formula changes to:

Now, if the observer starts moving, the formula becomes:

where v_o is the speed with which the observer is moving away from the source. Plugging in the numbers, we get:

for car travelling towards police car(appraoaching)

for car travelling away from police car (receding)

Thirdly:

for approach

during recession