Modern Engineering Thermodynamics

656 CHAPTER 16: Compressible Fluid Flow
Sound is the propagation of pressure waves in a medium such as air. Sound is created by the motion or
vibration of an object, which causes pressure waves in the surrounding medium. A sound wave has the same
characteristics as any other type of wave. It has a wavelength, frequency, velocity, and amplitude. The velocity of
sound in air at 20 o C (70 o F) is approximately 344 m/s (1130 ft/s), or 770 miles per hour. The speed of sound is
often called the sonic velocity.
WHO WAS ERNST MACH?
Ernst Mach (1838–1916) was a physicist and philosopher who established the basic principles of modern scientific
thought. In 1864, Mach became professor of mathematics at the University of Graz in Austria. He spent his most productive
years as a professor of physics at Charles University in Prague, from 1867 to 1895. In 1881, Mach began a study of the
flight of artillery shells using the new technology of photography. In this research, he discovered that the angle θ of the
shock cone radiating from the leading edge of a supersonic object was related to the speed of sound c and the velocity of
the object V by sin θ = c/V (see Figure 16.4), and θ was later called the Mach angle. The ratio of the local fluid velocity V
to the speed of sound in the fluid c came to be of fundamental value in the study of high-speed aerodynamics, and after
1930, it was called the Mach number (M = V/c).
θ
V < c V= c V> c
(a)
(b)
FIGURE 16.4
(a) The representation of a sound waves produced when an object moves from subsonic (V < c) to sonic (V = c) to supersonic
(V > c) velocity. Generally, a conical shock wave sweeps back from the leading edge of the object with the cone angle proportional
to the ratio of the sonic velocity of the fluid to the supersonic velocity of the object, c/V. (b) The shadowgraph of a supersonic bullet
showing shock waves.
However, Mach would have probably considered his work in aerodynamics insignificant in comparison to his primary contribution
in establishing a connection between physics and psychology. He adopted David Hume’s position that a phenomenon
can be understood from a scientific point of view only in terms of the human observations produced by the
phenomenon. This view leads to the very powerful conclusion that no law of physics is acceptable unless it is experimentally
verifiable. His strict definition of verifiability allowed the rejection of such long-held concepts as absolute time and
space and ultimately provided the framework for the acceptance of Einstein’s relativity theory.