On the Speed of Sound in Gases

Abstract

A DISCUSSION of the speed of sound in fluids was conducted recently in these pages by Professors Truesdell, Murdochow, Morkovin, Millikan, and Munk. In the case of one-dimensional nonlinear unsteady and inviscid flow such as through a rarefaction wave, the local speed of sound may be defined as the rate of propagation into the gas of a characteristic line (Mach wave) with respect to the flow velocity a t the point under consideration. This definition follows as a consequence of the solution of the nonlinear differential equations and does not depend on the linearized equations used in acoustics. This definition was tested experimentally in a wave interaction tube (shock tube) by taking schlieren photographs with a wave speed camera of the rarefaction wave that is therein produced. In the theory of the shock tube it is assumed that , when a diaphragm, which separates a gas a t high pressure from a gas at low pressure in a tube of uniform cross section, is suddenly ruptured, a shock wave and a contact surface are propagated into the lowpressure chamber (expansion chamber) and a centered rarefaction wave is propagated into the high-pressure chamber (compression chamber). The waves are assumed to form instantaneously. I t is also assumed that the waves are plane and travel a t uniform velocities and separate regions of constant state. The theoretical (x, /)-plane of this wave model is shown in Fig. 1. Along with this model are shown two schlieren photographs of the flow in the wave interaction tube, which were taken with the wave speed camera. The tube has a 2.25 in. O.D. and a 1.00in. I .D. The flow is viewed through a lucite window 24 in. long and of a /ie-in. tee cross section. The wave speed camera has a rotating drum 12 in. in diameter. Seventy-millimeter film is used, and it attains a peripheral speed of 215 ft. per sec. The longitudinal striations on the photographic records are in main due to the lucite windows.