Basically the plane is making the same sound in every direction. If you think of the sound waves being emitted as pulses, the plane essentially closes the gap between sound pulses in front of it and distances itself from the pulses it makes behind it. The closer the sound pulses, the higher the pitch. The farther apart, the lower the pitch. If your relative position stays consistent, there won’t be a change in pitch. So when a plane passes overhead, you get the higher pitched sound as it gets closer and lower pitch immediately as it passes.
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