Result

Mach cone angle

sin θ = \frac{v}{v _{s}}

Statement

The half-angle of the shock cone trailing a source moving at speed v_s greater than the wave speed v.

Symbols and units

$θ$	Mach cone half-angle	degrees
$v$	wave speed in the medium	m/s
$v_{s}$	source speed	m/s

When it applies

A source moving faster than the wave speed in the medium (v_s > v).

Don't use when

Only defined for a source moving faster than the wave speed (supersonic); at or below the wave speed no Mach cone forms.

Derivation

Each wavefront expands from where it was emitted; with the source outrunning its own wavefronts, their common tangent forms a cone whose half-angle satisfies:

sin θ = \frac{v}{v _{s}}

Watch out for

Only defined for v_s > v (supersonic motion). At v_s = v exactly, θ = 90° — the wavefronts pile up directly at the source, the onset of the shock.