Macha

Meet Macha, a jet flying faster than her own sound, trailing a cone of piled-up waves.

A moving object sends out sound waves in all directions. Below the speed of sound, they spread ahead of it. Above it, the object outruns its own waves, and they pile up along a cone with the object at its tip. The Mach number M is the object's speed divided by the speed of sound, and the cone's half-angle θ satisfies sin θ = 1/M.

At Mach 2, sin θ = 0.5, so the half-angle is 30° (computed). Faster objects make narrower cones. At exactly Mach 1, the cone opens out into a flat wall of pressure.

When the cone sweeps across the ground, people hear a sonic boom. The crack of a whip is a small sonic boom from its tip, and a boat's V-shaped wake is the same geometry for water waves. The same idea, in light, gives Cherenkov radiation from particles moving faster than light does in water.

The formula is for steady speed in still air. Real shock waves near the aircraft are stronger and curved, and a real boom's shape depends on altitude and temperature.