Why a siren drops as it goes past

Sound leaves the source at a fixed speed. If the source is chasing its own waves, they bunch up ahead of it and stretch out behind — so the pitch you hear is higher coming toward you and lower going away. Turn the sound on and stand somewhere.

The rings are the actual wavefronts, each one drawn where it was emitted and growing at the speed of sound. Push the source past 343 m/s and they stop being able to get out in front — that cone is a sonic boom.