I always assumed that the recognisable ‘whoosh’ sound a plane makes when passing overhead simply comes from the famous Doppler effect. But when you listen closely, this explanation doesn’t make complete sense.

(Audio clipped from freesound)

A classic example of the Doppler effect is the sound of a passing ambulance constantly descending in pitch. When a plane flies overhead the roar of the engine sometimes does that as well. But you can also hear a wider, breathier noise that does something different: it’s like the pitch goes down at first, but when the plane has passed us, the pitch goes up again. That’s not how Doppler works! What’s going on there?

Comb filtering.

Let’s shed light on the mystery by taking a look at the sound in a time-frequency spectrogram. Here, time runs from top to bottom, frequencies from left (low) to right (high).

We can clearly see one part of the sound sweeping from right to left, or from high to low frequencies; this should be the Doppler effect. But there’s something else happening on the left side.

The sound’s frequency distribution seems to form a series of moving peaks and valleys. This resembles what audio engineers would call ‘comb filtering’, due to its appearance in the spectrogram. When the peaks and valleys move about it causes a ‘whoosh’ sound; this is the same principle as in the flanger effect used in music production. But these are just jargon for the electronically created version. We can call the acoustic phenomenon the whoosh.

The comb pattern is caused by two copies of the same exact sound arriving at a slightly different times, close enough that they form an interference pattern. It’s closely related to what happens to light in the double slit experiment. In recordings this often means that the sound was captured by two microphones and then mixed together; you can sometimes hear this happen unintentionally in podcasts and radio shows. So my thought process is, are we hearing two copies of the plane’s sound? How much later is the other one arriving, and why? And why does the ‘whoosh’ appear to go down in pitch at first, then up again?

Into the cepstral domain.

The cepstrum, which is the inverse Fourier transform of the estimated log spectrum, is a fascinating plot for looki