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Mach wave

Pressure wave

Wikipedia contributorsAdapted for Fathomly · View authors
1 min read
Source updated July 3, 2025
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In fluid dynamics, a Mach wave, also known as a weak discontinuity, is a pressure wave traveling with the speed of sound caused by a slight change of pressure added to a compressible flow. These weak waves can combine in supersonic flow to become a shock wave if sufficient Mach waves are present at any location. Such a shock wave is called a Mach stem or Mach front. Thus, it is possible to have shockless compression or expansion in a supersonic flow by having the production of Mach waves sufficiently spaced (cf. isentropic compression in supersonic flows). A Mach wave is the weak limit of an oblique shock wave where time averages of flow quantities don't change (a normal shock is the other limit). If the size of the object moving at the speed of sound is near 0, then this domain of influence of the wave is called a Mach cone.

01Mach angle

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. It is given by

\mu =\arcsin \left({\frac {1}{M}}\right),

where M is the Mach number.

Mach waves can be used in 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 cones around aircraft during transonic flight.

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 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.
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Sources and credits

This article is adapted from the Wikipedia article “Mach wave”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

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Related topics

Compressible flow

Compressible flow is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows are compressible, flows are usually treated as being incompressible when the Mach number (the ratio of the speed of the flow to the speed of sound) is smaller than 0.3 (since the density change due to velocity is about 5% in that case).

Prandtl-Meyer expansion fan

A Prandtl-Meyer expansion fan is a two-dimensional simple wave that occurs when a supersonic flow turns around a sharp convex corner. The fan consists of an infinite number of Mach waves, diverging from a sharp corner.

Shadowgraph

Shadowgraph is an optical method that reveals non-uniformities in transparent media like air, water, or glass. It is related to, but simpler than, the schlieren and schlieren photography methods that perform a similar function.