Sonic Boom
A point source moves through a medium, emitting spherical wavefronts. Watch the wavefronts compress ahead, pile into a shock front, and finally form a Mach cone as the source goes supersonic.
About this lab
When a sound source moves through air, it emits spherical pressure waves that expand outward at the speed of sound. If the source travels slower than these waves, the wavefronts spread out ahead of it but remain nested concentrically, with the spacing compressed in the forward direction and stretched behind. This is the Doppler effect: an observer in front hears a higher frequency, while one behind hears a lower frequency. The ratio of observed to emitted frequency depends on the Mach number M = v/c, where v is the source speed and c is the wave speed.
At exactly Mach 1, the source keeps pace with its own wavefronts. Each new wavefront is emitted at the same point where the previous one is expanding from, causing all the forward wave energy to pile up into a single, flat shock front perpendicular to the direction of motion. This is the sound barrier — a region of enormously amplified pressure. Aircraft approaching Mach 1 experience dramatically increased drag from this pressure buildup, which historically led engineers to wonder whether supersonic flight was even possible.
Beyond Mach 1, the source outruns its own waves entirely. The wavefronts can no longer get ahead; instead, they accumulate along a cone whose half-angle is given by sin θ = 1/M. This Mach cone is the shock wave, and its intersection with the ground produces the sonic boom — not a single event, but a continuous phenomenon that sweeps along the ground as long as the source is supersonic. The boom was first understood mathematically by Ernst Mach in the 1870s, using precisely this wavefront geometry.
The physics extends far beyond sound. Cherenkov radiation occurs when a charged particle moves through a medium faster than the local speed of light in that medium, producing an electromagnetic Mach cone visible as blue glow in nuclear reactor pools. The wake of a boat on water creates a Kelvin wake pattern governed by similar envelope geometry. Even in astrophysics, relativistic jets from active galactic nuclei can produce apparent superluminal motion through projection effects related to Mach-like cone geometry. The wavefront envelope is one of the most general constructions in wave physics.