Periodic Shock Waves in Resonating Gas Columns

Abstract

When an oscillating piston forces the enclosed gas in a Kundt tube to vibrate with a finite amplitude near an acoustic resonance frequency of the gas column, shock waves are generated which travel periodically back and forth in the tube. There is also heating of the gas and a rise in its mean pressure. In this paper a theory of the steady state motion of the gas in its “fundamental” mode has been devised which includes the dissipative effects of wall friction and heat conduction to the tube walls. The dependence of shock strength, mean temperature, and mean pressure on piston amplitude, tube length, gas viscosity, and heat conductivity predicted by the theory are in good qualitative agreement with the small number of experimental data available at present.

Resonant acoustic oscillations with damping: small rate theory

“…These phenomena have been extensively investigated in the recent literature, (Betchov (1958), Saenger and Hudson (1960), Chu and Ying (1963), Chester (1964), Mortell (1971a,b), Collins (1971). Nevertheless, there are associated phenomena dhich need further investigation, and some aspects of the various analyses which need clarification.…”

2000 Physical Acoustics Summer School (PASS 00). Volume III: Background Materials

“…A real physical source would involve displacement of the radiating surface about the point x = 0. Taking into account the finite displacement of the source introduces new distortion components which grow less rapidly with range than those resulting from the nonconstant propagation speed [47]. The new components represent local effects which are significant only on the order of one wavelength from the source, and they are usually ignored.…”

“…It may then be shown that the range where shock formation occurs, i.e., where an infinite slope first appears on the waveform, is given by [47] ßck'…”

“…In our determination of cavitation noise attractors, we used d 2 together with the maximum norm. 47 Equation (12) immediately shows that d 2 can be determined from the slope of the curve obtained when C" (r) is plotted versus r, each on a logarithmic scale.…”

Nonlinear Pressure Wave Analysis by Concentrated Mass Model (1st Report, Suggestion and Validity Verification of Analytic Model)

“…Therefore, basic studies have been conducted. For example, a study of a shock wave occurring in a sound tube excited by a piston (4)- (6) , and an experiment of the phenomenon that a sinusoidal wave generated by a horn driver changes to a shock wave in a straight tube (7) have been carried out. Numerical analyses (2), (3), (6) of these phenomena by the finite difference method were conducted.…”