Editing Compressible flow (section)

==Mach number, wave motion, and sonic speed== 
The [[Mach number]] (M) is defined as the ratio of the speed of an object (or of a flow) to the speed of sound. For instance, in air at room temperature, the speed of sound is about {{convert|343|m/s|abbr=on}}. M can range from 0 to ∞, but this broad range falls naturally into several flow regimes. These regimes are subsonic, [[transonic]], [[supersonic]], [[hypersonic]], and [[hypervelocity]] flow.  The figure below illustrates the Mach number "spectrum" of these flow regimes.

[[File:Mach Number Flow Regimes.png|thumb|center|400px|Mach number flow regimes spectrum]]

These flow regimes are not chosen arbitrarily, but rather arise naturally from the strong mathematical background that underlies compressible flow (see the cited reference textbooks). At very slow flow speeds the speed of sound is so much faster that it is mathematically ignored, and the Mach number is irrelevant. Once the speed of the flow approaches the speed of sound, however, the Mach number becomes all-important, and shock waves begin to appear.  Thus the transonic regime is described by a different (and much more complex) mathematical treatment.  In the supersonic regime the flow is dominated by wave motion at oblique angles similar to the Mach angle. Above about Mach 5, these wave angles grow so small that a different mathematical approach is required, defining the [[hypersonic speed]] regime.  Finally, at speeds comparable to that of planetary atmospheric entry from orbit, in the range of several km/s, the speed of sound is now comparatively so slow that it is once again mathematically ignored in the [[hypervelocity]] regime.

As an object accelerates from subsonic toward supersonic speed in a gas, different types of wave phenomena occur. To illustrate these changes, the next figure shows a stationary point (M = 0) that emits symmetric sound waves.  The speed of sound is the same in all directions in a uniform fluid, so these waves are simply concentric spheres. As the sound-generating point begins to accelerate, the sound waves "bunch up" in the direction of motion and "stretch out" in the opposite direction. When the point reaches sonic speed (M = 1), it travels at the same speed as the sound waves it creates. Therefore, an infinite number of these sound waves "pile up" ahead of the point, forming a [[Shock wave]]. Upon achieving supersonic flow, the particle is moving so fast that it continuously leaves its sound waves behind. When this occurs, the locus of these waves trailing behind the point creates an angle known as the [[Mach wave]] angle or Mach angle, μ:

:<math>\mu = \arcsin\left(\frac{a}{V}\right) = \arcsin\left(\frac{1}{M}\right)</math>

where <math>a</math> represents the speed of sound in the gas and <math>V</math> represents the velocity of the object. Although named for Austrian physicist [[Ernst Mach]], these oblique waves were first discovered by [[Christian Doppler]].<ref name=Doppler-bio>P. M. Schuster:''Moving the Stars: Christian Doppler - His Life, His Works and Principle and the World After'', Pollauberg, Austria:Living Edition Publishers, 2005</ref>

[[File:Explanation of Sonic Motion.png|thumb|center|400px|Wave motion and the speed of sound]]