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?

Question

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?

anonymous · Answer

We can use the Doppler Effect formula $$f = (\frac{ c + v _{o} }{ c + v _{s} })*f _{o}$$, where c is the speed of sound, v_0 is your speed, which is zero, f_o is the emitted frequency, and v_s is the speed we wish to find. Now we have $$v _{s} = \frac{ f _{0}*c }{ f } + c$$, which will yield your answer.