A police car is approaching you with its siren sounding apparently at 330 Hz. When it reaches you, the police car stops and the frequency of the siren is now 300 Hz. If the air temperature is 20 0C, how fast was the police car travelling when it was approaching you?

The change in frequency is called the Doppler effect. The speed of the car can be calculated by the formula for the Doppler effect for when the observer is standing still and the source of the sound is moving towards him:

f¹={V / (V-Vs) }*f,

where f¹ is the frequency of the car while moving towards the observer, V=343 m/s is the speed of sound, Vs is the speed of the car and f is the frequency of the car while standing still.

We need to solve the equation for the Vs:

f¹/f=V / (V-Vs)

V-Vs=V / (f/f¹)

-Vs=V / (f/f¹) - V

Vs=-V / (f/f¹) + V = - 343 / (300/330) + 343=-343*0.91+343=-312.1+343=30.9 m/s

So the speed of the moving police car is Vs=30.9 m/s.