Early history of nonlinear acoustics

Abstract

The first (although slightly incorrect) wave equations for finite-amplitude sound in lossless fluids were obtained independently by Euler (1759) and Lagrange (1760). Poisson (1808) provided the first major break-through 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 Poisson's solution is not single valued but did not understand why. Stokes (1848) provided the why. He saw that the Poisson waveform distorts as it travels, eventually threatening to become multivalued. He postulated that a discontinuity (shock) develops to avoid waveform overturning. He also proposed that viscosity (not accounted for by Poisson) would prevent true discontinuities. Earnshaw (1860) and Riemann (1860) cleaned up the theory for 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 thermoviscous dissipation is included. These were the first steps toward redemption. The curtain rang down on this era of nonlinear acoustics with two excellent papers in 1910, one by Rayleigh and another by Taylor, on steady shocks in a thermoviscous fluid.