Sine of Mach cone angle via Mach number

If the speed of a source relative to the medium exceeds the speed of sound in the medium, the Doppler equation no longer applies and this results in shock waves. The wavefronts of the waves originating from the source form a cone, namely a Mach cone. The half-angle of the cone is called the Mach cone angle, which is related to the Mach number of the source. See the illustration of the phenomenon.

Conditions:

1. \(M \ge 1\), i.e. the source speed exceeds the speed of sound in the medium.

Links:

1. Wikipedia.

mach_cone_angle

Mach cone angle, which is the angle between the Mach wave wavefront (the Mach cone) and the vector pointing opposite to the velocity vector of the source.

Symbol:

phi

Latex:

\(\varphi\)

Dimension:

angle

mach_number

mach_number of the moving source.

Symbol:

M

Latex:

\(\text{M}\)

Dimension:

dimensionless

law

sin(phi) = 1 / M

Latex:

\[\sin{\left(\varphi \right)} = \frac{1}{\text{M}}\]