Question

Assume that the porsche's maximum speed is 78.0 m/s and the police car's is 58.0 m/s. at the moment both cars reach their maximum speed, what frequency will the porsche driver hear if the frequency of the police car's siren is 440 hz? take the speed of sound in air to be 340 m/s.

Answer 1

The police's car is chasing the porsche with a speed 58.0 m/s. The porsche is moving with speed 78.0 m/s: this means that the porsche is moving away from the police's car by (78.0 - 58.0) m/s = 20.0 m/s.

Because the porsche is moving away from the source of the siren (the police's car), the frequency the porsche's driver hear will be shifted according to (Doppler effect):

`f' = ( (c)/(c+v_s) )f`
where c=340 m/s is the speed of sound, f=440 Hz is the original frequency of the sound, and vs=20 m/s is the relative speed of the porsche with respect to the police's car. Substituting, we find the frequency f' at which the porsche's driver will hear the siren:

`f' = ( (c)/(c+v_s) )f=( (340 m/s)/(340 m/s+20 m/s) )(440 Hz)=415.6 Hz`