Sonic booms

Many people have heard of the sonic boom, a loud noise that happens when something (an airplane, a bullet, the tip of a bull whip) starts moving faster than the speed of sound. What a lot of people don't realize, though, is that it's not just a single boom - it keeps going for as long as the object is moving faster than Mach 1 (1 times the speed of sound). In the case of an airplane, it will pass overhead, and the shock wave that is the sonic boom will travel outward to you, the observer, at the speed of sound. That is, slower than the airplane is moving. As a result, you end up hearing the sonic boom fairly substantially after the object actually passes over you. It expands in what looks like a cone shape, like this:

The red object, moving from left to right at Mach 1.5, leaves behind a sonic boom cone. When the edge of the cone reaches an observer on the ground, they hear the boom.

 

Where does this shock wave come from, anyway? An airplane in normal flight sends out vibrational waves (some in the form of sound, others at frequencies we can't hear) in all directions. These vibrations progress outwards at, you guessed it, the speed of sound.* But what happens when an object starts moving at the speed of sound? All the vibrations it's been beaming forward suddenly can't leave the vicinity of the object, so they just pile up in approximately one place, right along the object itself!

The red object, (still) moving from left to right, now at Mach 1, appears to create a massive shock wave, thanks to many many waves piling on top of each other at the object's location. This is the Prandtl-Glauert singularity.

This hypothesis, the Prandtl-Glauert singularity (which also suggests infinite pressure at Mach 1), turns out to be not entirely true, because other effects, like turbulence and viscosity, start to assert themselves, and compressible fluids under extreme conditions are hard to describe in a precise mathematical way. In other words, physics is awesome.

* This, by the way, is the origin of the Doppler effect: when an object is moving towards you, you hear a higher-pitched sound than when it passes you and starts moving away, because the sound waves are compressed in front. That compression lessens the time between peaks of the sound's oscillation, which manifests itself as a higher-pitch noise. Conversely, once the object is past you, the wave peaks grow further apart in time, so you hear it as a lower-pitch sound.

An object traveling from left to right at Mach 0.7 emits sound (and other vibrations) in all directions. But it's catching up to the waves it sends forwards, and is running away from the waves it sends behind it. The Doppler effect is the result.