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):
[tex]f' = ( \frac{c}{c+v_s} )f
[/tex]
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:
[tex]f' = ( \frac{c}{c+v_s} )f=( \frac{340 m/s}{340 m/s+20 m/s} )(440 Hz)=415.6 Hz[/tex]
