In 1877 Austrian physicists Ernst Mach and P. Salcher in Prague published "Photographische Fixirung der durch Projectile in der Luft eingeleiteten Vorgänge," Sitzungsber. k. Akad. Wiss., math.-naturwiss. Classe, 95 (1887) 764-80. The paper reproduced the first photograph of a shock wave in front of an object (in this case a bullet) moving at supersonic speed, and the first mathematical formula describing the physics of the shock wave.
“The angle α, which the shock wave surrounding the envelope of an advancing gas cone makes with the direction of its motion, was shown to be related to the velocity of sound ν and the velocity of the projectile ω as sinα = ν/ω when ω > ν. After 1907, following the work of Ludwig Prandtl at the Kaiser Wilhelm Institut für Strömungsforschung in Göttingen, the angle α was called the Mach angle. Recognizing that the value of ω/ν (the ratio of the speed of an object to the speed of sound in the undisturbed medium in which the object is traveling) was becoming increasingly significant in aerodynamics for high-speed projectile studies, J. Ackeret in his inaugural lecture in 1929 as Privatdozent at the Eidgenössischen Technische Hochschule, Zürich, suggested the term ‘Mach number’ for this ratio" (Dictonary of Scientific Biography).
Anderson, History of Aerodynamics (1999) 376.