Early history of nonlinear acoustics: Waveform distortion, disaster, and redemption

Abstract

The first (although slightly incorrect) wave equations for finite-amplitude sound in lossless fluids were obtained independently by Euler in 1759 and Lagrange in 1760. Poisson (1808) provided the first major breakthrough with his exact solution for progressive waves of finite amplitude in a lossless gas. Although a far-reaching result, the progressive waveform distortion (and disastrous consequences) implied by his solution went unrecognized for 40 years. Challis (1848) showed that the Poisson solution is not single valued but did not understand why. Stokes (1848) provided the why. He saw that the Poisson waveform distorts as the wave travels, eventually threatening to become multivalued. He postulated that a discontinuity (shock) develops to avoid waveform overturning. He also saw that viscosity (not accounted for by Poisson) would prevent true discontinuities. Earnshaw (1860) and Riemann (1860) cleaned up plane waves in lossless gases. However, how to predict propagation after shocks form? Rankine (1870) and Hugoniot (1887, 1889) provided the first solutions for propagation when dissipation is included. These were the first steps toward redemption. The curtain rang down on this era of nonlinear acoustics with the excellent papers in 1910 by Rayleigh and Taylor on steady shocks in a thermoviscous fluid.