You would measure the increase in pitch or freq. then translate back to RPM.
The only problem is that there is no way to measure the pitch of an air-born eng. from the ground. The 'Doppler Effect' shifts the pitch higher as it comes toward, lower as it recedes. It would only be accurate flying at a constant diameter circle around the microphone.

Ever notice on TV lately how the RPM of top fuel drag cars appears to hold constant or even drop as it goes down the line.
When the mic is at the line, the car accelerates away from the mic faster than the increase in RPM!!! AMAZING!!!!

Kirk