Why does an aircraft sound quieter after passing overhead?

It's known as the doppler effect.

http://en.wikipedia.org/wiki/Doppler_effect

When something comes towards you, the sound waves from it are squished and intensified. When it moves away from you, the sound waves from it are stretched out and weakened. This is called the Doppler effect, and it produces the change you describe.

The frequency and intensity of the noise you perceive from the airplane are higher than the actual frequency and intensity emitted by the airplane while it is approaching you, but then the frequency and intensity become lower as the airplane moves away from you. So once an aircraft passes over you, the noise it makes drops in pitch and becomes quieter.

The Doppler effect occurs in all sorts of situations, not just with airplanes. Probably the best known Doppler effect is the one you hear when a train passes near you, blowing its horn.

Since I work on Doppler, and have taught classes in it, here's a quick lesson to show you how it works and how movement translates to speed.

Stand 6' away from a wall and bounce a tennis ball against it a few times. Now throw it and walk backwards and catch it. Then, stand 6' from it, throw the ball and walk toward the wall. You'll notice how fast the ball comes at you.

It's the same with sound and RF energy. Sound you can easily detect as you mentioned, RF changes can be measured electronically to calculate speed and direction change.

Ah, good question. The aircraft engines are pushing the sound waves ahead, the direction of travel, which means the waves are closer together. This makes them louder. The waves after passing are further apart - not as intense - and therefore not as loud. Think of it this way. A wave of water coming onto the beach has enough intensity to push you over. But the water momentarily remaining on the beach after the wave has little intensity.

It doesn't, it sounds lower frequency due to the doppler effect. Here's a Sukhoi 27 over Krasnoyarsk in Siberia, you can hear the sound bouncing off the cloud base. Also, turbofan engines make most of their noise from the front, which acts like a loudspeaker projecting it forwards.

http://www.youtube.com/watch?v=Q0ksXVD2YH8

As the pilot sees you appear to disappear beneath the nose of his bird, he reduces power. It's an old pilot trick to make you have to look harder for his plane.

Actually, it's physics. The plane is a sound emitter. The max decibels is produced as it passes beside you. As it passes the level od dbs drops.