Editing Mach wave (section)

== Mach angle ==
[[File:Sonic boom.svg|thumb|right|250px|A sonic boom produced by an aircraft moving at M=2.92, calculated from the cone angle of 20 degrees. Observers hear nothing until the shock wave, on the edges of the cone, crosses their location.]]
A Mach wave propagates across the flow at the '''Mach angle''' ''μ'', which is the angle formed between the Mach wave wavefront and a vector that points opposite to the vector of motion.<ref name=sasoh>{{cite book |last1=Sasoh |first1=Akihiro |title=Compressible Fluid Dynamics and Shock Waves |date=2020-01-02 |publisher=[[Springer Nature]] Singapore |location=Nagoya, Japan |isbn=978-981-15-0504-1 |pages=80–82 |language=en |chapter=4.3 Oblique Shock Wave|doi=10.1007/978-981-15-0504-1|s2cid=213248761 }}</ref><ref>[http://www.grc.nasa.gov/WWW/K-12/airplane/machang.html Mach angle] at NASA.</ref> It is given by
:<math>\mu = \arcsin\left(\frac{1}{M}\right),</math>
where ''M'' is the [[Mach number]].

Mach waves can be used in [[Schlieren photography|schlieren]] or shadowgraph observations to determine the local Mach number of the flow. Early observations by [[Ernst Mach]] used grooves in the wall of a duct to produce Mach waves in a duct, which were then photographed by the schlieren method, to obtain data about the flow in nozzles and ducts. Mach angles may also occasionally be visualized out of their condensation in air, for example [[vapor cone]]s around aircraft during [[transonic]] flight.