Sound travels at a fixed speed. Go slower than it and your noise spreads out ahead of you as rings. Go FASTER and you outrun your own sound — the rings pile into a cone dragging behind you, and when that cone sweeps past an ear it arrives all at once as a sonic boom. Slide past the speed of sound and watch the rings collapse into the cone.
A source moving at speed v emits wavefronts that travel at the sound speed c; the ratio M = v/c is the Mach number. For M < 1 the wavefronts nest ahead of the source (only a Doppler pile-up). For M > 1 they can never get ahead — their envelope is a cone whose half-angle satisfies sinθ = 1/M (the Mach angle); the shock at the cone is the sonic boom, and the faster you go the tighter the cone. A fail-loud self-check throws unless M=2 gives a real cone (30°) and M<1 gives none. ◆ real gas dynamics, node-verified.
An ideal point source with equal-speed circular wavefronts (a weak-shock / Mach-cone geometry); real booms are finite-strength N-waves shaped by the body — the sinθ=1/M cone and the no-cone-below-Mach-1 threshold are exact.