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Mach
(mɑːk, mæk, ‖ maːx)
The name of Ernst Mach (1838–1916), Austrian physicist and philosopher: a. Used, usu. attrib., to designate certain concepts associated with his work on aerodynamics, as Mach('s) angle, the angle between a generator of the Mach cone and its axis; Mach cone, a cone that extends backwards from a body moving at supersonic speed and coincides with the shock wave it produces, separating a region affected by the motion (inside the cone) from a region unaffected by it (outside the cone); Mach('s) number, the ratio of the relative speed of a body and a fluid to the speed of sound at the same point; so Mach one, Mach two (or Mach 1, Mach 2), etc., a speed corresponding to a Mach number of one, two, etc.
1930Dougall & Deans tr. Ewald's Physics Solids & Fluids v. 262 During a small interval of time τ, a point source of disturbance expands to a sphere of radius cτ, the centre of which has moved through a distance qτ. The cone touches this sphere, so that sin a = cτ/qτ = c/q... a is called Mach's angle. 1933Proc. R. Soc. A. CXXXIX. 307 The Mach cone x = y and z = 1 would satisfy the required conditions. 1937Dodge & Thompson Fluid Mech. xiii. 370 The ratio V/c will be found to appear in all flow problems where compressibility is an important factor. It is known as Mach's number..in honor of the Austrian scientist. 1938Jrnl. R. Aeronaut. Soc. XLII. 194 The part of the wave at a distance from the shell moves normal to itself with the speed of sound and this fact determines the angle it makes with the direction of motion of the shell (the ‘Mach angle’). 1947Time 8 Sept. 76/2 During both flights it reached ‘mach ·828’. 1948‘N. Shute’ No Highway 34 It was diving at round about Mach unity, and the wings came off. 1953Sci. News XXIX. 93 The non-dimensional quantity M = V/a is defined as the ‘Mach Number’ of the flow. 1957Spaceflight I. 51/1 In a rocket exhaust where the gases are moving at 6,000 ft./sec.,..the velocity of sound is 2,000 ft./sec., so the Mach No. is 3. 1967Technology Week 23 Jan. 29/2 (Advt.), McDonnell testing and development facilities range from man-rated space chambers to Mach 28 wind tunnels.
b. Used, usu. attrib., to designate an optical illusion first investigated by Mach (in Sitzungsber. der K. Akad. der Wissensch. (Math.-Nat. Classe) (1865)), in which a place where the spatial rate of variation of surface brightness abruptly increases or decreases (as at the inner and outer edges of an indistinct shadow) may appear extra dark or bright to an extent that cannot be accounted for simply in terms of the objective variation in brightness.
1932W. M. Deans tr. Pohl's Physical Princ. Mech. & Acoustics i. 4 Mach's bands have led to much trouble in the carrying out of physical observations. 1936Brit. Jrnl. Psychol. XXVII. 103 The same generalizations can be made about the Mach effect on a rotating colour wheel. 1965Graham & Brown in C. H. Graham et al. Vision xvi. 474/2 Mach rings with spatial variations in color. 1965F. Ratliff Mach Bands ii. 43 The Mach bands appear at once in the shadow cast on a piece of white paper by the edge of a card held under a fluorescent desk lamp, which provides an extended source of light. Covering the ends of the lamp, which usually are not uniformly bright, somewhat enhances the effect. 1970― in Cohen & Seeger Ernst Mach 32 The Mach bands are one of the most compelling of all the visual ‘illusions’, and have been mistaken for objective physical phenomena.
Add:c. Mach's principle Physics [tr. Ger. Machsches Prinzip (A. Einstein 1918, in Ann. d. Physik LV. 241)], the proposition that the inertia of a body depends on the distribution of matter in the universe.
1918Sci. Abstr. A. XXI. 352 Mach's Principle by which the G-field is determined without residue by the masses of the bodies. 1930L. Silberstein Size of Universe ii. 73 Einstein in his ‘cosmological contemplations’ of 1916 set out with the resolute plan of satisfying what he called ‘Mach's principle’ (relativity of inertia). 1951Ann. Math. LIII. 472 In general relativity Mach's principle is interpreted as stating that the nature of space-time is determined by the matter present. 1965J. D. North Measure of Universe xiv. 306 Did Bondi think that ‘Mach's Principle’ was essential to any satisfactory physical theory? 1977J. Narlikar Struct. Universe v. 169 Mach's principle, and its implication that inertia is not an intrinsic property of matter but is due to the background of distant stars, have received a mixed reception in the world of theoretical physics. 1987Nature 6 Aug. 501/2 Ernst Mach advocated that..the vanishing cosmic rotation is part of the empirical basis of what is known as Mach's principle. |