= Sonic flow
{title2=$M=1$}
A <sonic flow> has <Mach number> exactly one: the local <fluid> speed relative to the body equals the local <sound speed>. In uniform <gas> flowing at $U=c$ past a resting body, an upstream-directed <acoustic wave> has zero body-frame <velocity>. A <sonic point> is a location where this equality holds. In the <moving-point acoustic wavefronts> construction, old <spheres> touch the source at the origin; the <Mach angle> tends to $90^\circ$ as the <supersonic flow> approaches this threshold.
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