My search for Doppler shifted sounds has resulted in a number of recordings of aircraft. As I studied those recordings for the Doppler shift, I noticed that there was also another feature in the spectrograms that I didn’t understand. There is a shallow bowl shaped feature centered on the time of closest approach, ie when the aircraft was roughly overhead. The “bowl” seems to be formed by harmonic content in the signal. The frequency increases not only as the aircraft is approaching, as one would expect for a Doppler shift, but also as it moves away. The two spectrograms accompanying this post, for the Air Tractor fixed wing and the Chinook helicopter, show the feature pretty clearly.
I have thought about refraction due to the temperature lapse rate as a function of altitude but the equations don’t show any frequency dependence. I considered source directivity but I see it in two very different aircraft. If you listen carefully to an airplane or helicopter flying over you can hear a frequency component that is increasing as the craft flies away from you…it seems to be a real phenomenon. I am stumped!
Please comment if you know what causes this feature or if you have a suggestion as to what it might be.