Doppler head-wind of 15 m/s

Question

10. A man drives a car at a speed of 108 km/hr while there is a head-wind of 15 m/s. He honks the horn (that has a frequency of 530 Hz) when he sees a speeding car approaching him from in front, driving at a speed of 162 km/hr.

At what frequency will the speeding car hear the horn?

Assume the speed of sound in air to be 330 m/s. All speeds are ground speeds.

Answer 1

Considering the head-wind to be a movement of air in the opposite direction of the Car1.  To make easier the calculations below I consider as if the sound could travel in different speeds (it does not) for the same frequency.

Car 1 speed = 108km/h = 30m/s, sound wave travels forward at 360m/s

Head-wind of 15m/s, sound wave travels forward at 345m/s

Car 2 speed = 162km/h = 45m/s, sound wave hit Car 2 at 390m/s

If Car 1 send a pressure wave of 554Hz at 330m/s, it will hit Car2 as;

Frequency * (SpeedOfSound + Car1Speed - HeadwindSpeed + Car2Speed) / SpeedOfSound

554 * (330 + 30 - 15 + 45) / 330 = 654.727272Hz.