page_title: Compressible flow
section_title: Mach number, wave motion, and sonic speed
hierarchical_section_title: Compressible flow / Mach number, wave motion, and sonic speed
caption_attribution_description: English: Moving Particle with Sound Waves Projecting Radially in All Directions. The particle is accelerating from M=0 to M&gt;1.
context_page_description: 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 is less than 0.3. The study of compressible flow is relevant to high-speed aircraft, jet engines, rocket motors, high-speed entry into a planetary atmosphere, gas pipelines, commercial applications such as abrasive blasting, and many other fields.
context_section_description: 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 340 m/s (1,100 ft/s). 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.
  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:
  where  represents the speed of sound in the gas and  represents the velocity of the object. Although named for Austrian physicist Ernst Mach, these oblique waves were first discovered by Christian Doppler.
caption: Wave motion and the speed of sound
exif: {}