Something I noticed years ago but never paid much attention to, until recently when I happened to experience the phenomenon seemingly often; usually when a (passenger) jet aircraft enters earshot in the skies above, it starts with a low rumble and builds to a higher whine of the jets. However sometimes, the aircraft enters with a way high pitch which then descends to the regular jet whine. What gives?
Without having your ears on my head, I can’t tell for sure, but I’d guess you’re mixing up pitch and volume. As it approaches you, the pitch sounds high and gets louder. As it leaves you, the pitch flips to low and gets quieter. Add in the fact that over great (and sometimes not so great) distances, low-frequency waves travel much farther. Ever hear some jackass thumping his bass in the car, but not the treble? Same thing.
ETA: I’m not sure that what I’m describing is what you’re hearing. I’ve never heard a jet that sounds like it starts “way high” and goes to regular.
My WAG is that this is a manifestation of the Doppler effect.
Higher frequencies are more quickly attenuated than lower ones in air. At first, you’re hearing the jet noise with the higher tones filtered out, with the amount of the filtering decreasing as pitch decreases. As the plane gets nearer, you can hear more of the higher tones.
If, though, there is a strong enough tone at a higher pitch (typically from the frequency of fan blades passing their stator vanes), you can hear that tone clearly from a distance even despite its attenuation. A “pure” tone will be more noticeable than a broad-band sound spectrum, too.
This also causes the propagation of higher frequency waves to be more directional than the lower frequency waves. In other words, the orientation of the emitting surfaces with respect to the listener, matters more for high frequencies than low. As the plane changes angle with respect to a listener, you’ll hear a change in the balance of tones, even without invoking Doppler shift.