Mach cone ($\sin \theta =1/M$)

The cone forming the envelope of sound wavefronts from a source moving supersonically at Mach number $M>1$. In the source frame the ray-velocity sphere is centered at $-M{c}_0{\mathbf{e}}_x$ and has radius $c_0$. Its tangent rays make angle ${\sin }^{-1}(1/M)$ to the backward flight direction; all other emitted acoustic rays lie inside that cone.