# Mach wave

Schlieren photograph of an attached shock on a sharp-nosed supersonic body. The Mach angle is acute, showing that the body exceeds Mach 1.

In fluid dynamics, a Mach wave 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 (a normal shock is the other limit). They propagate across the flow at the Mach angle μ:[1]

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

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, as in the jet photograph below.

U.S. Navy F/A-18 at transonic speed. The white halo is formed by condensed water droplets which are thought to result from an increase in air temperature and pressure behind the shockwave(see Prandtl-Glauert Singularity). The Mach angle of the weak attached shock made visible by the halo is seen to be close to arcsin (1) = 90 degrees.[2][3]