What happens to the waves from a moving source — and what is a sonic boom?
▶ Launch the interactive simulationA source emits circular wavefronts at a fixed rate while moving at speed v = M·c. In the source's frame, read the wavelength ahead of and behind it straight off the wavefront pattern, and (above M=1) the Mach-cone half-angle; sweep the Mach number from subsonic through the sound barrier to supersonic.
the Doppler shift f′ = f·c/(c ∓ v) = f/(1 ∓ M) — wavefronts bunch ahead (blueshift) and stretch behind (redshift), and the wavelength read off the pattern recovers the ratio (exact to the digit at steady speed; it lags a few % while the speed sweeps); and past M=1 the source outruns its own waves into a trailing Mach cone of half-angle sin μ = c/v = 1/M (the sonic boom) — 90° (a flat pile-up) at the sound barrier M=1, narrowing as M grows