Finite-Amplitude Distortion in Air at High Acoustic Pressures

Abstract

This paper treats a problem of acoustic-wave propagation in which the effects of finite amplitude are comparable with the effects of boundary dissipation. The analysis starts with a differential equation for the scalar potential, which embodies thermal boundary dissipation and the quadratic nonlinearities of the propagation, and a differential equation for the amplitude of the vector potential, which embodies viscous boundary dissipation. The acoustic pressure is constrained (for both analysis and experiment) to be a pure sine wave at the start of the tube, and the particle velocity and variational temperature are constrained to vanish all along the wall of the tube. A fourth-order perturbation solution of these equations gives an accurate harmonic analysis (through the fourth harmonic) of the acoustic pressure as a function of axial distance along the tube. Measurements are reported of the harmonic distortion of waves having initial peak pressures as high as 0.1 bar at a fundamental frequency of 445 Hz in air. These waves propagated in tubes of diameters 1.587, 2.66, and 5.26 cm. The tubes were terminated after seven wavelengths or before the experimental shock-formation distance, whichever came first. The theory is confirmed in all essential details.