Paul A. Langevin’s contributions to nonlinear acoustics

Paul A. Langevin made several important contributions to nonlinear acoustics, but our knowledge of these contributions is mainly due to accounts given by others, most notably Biquard (Ann. Phys., 1936). At the end of Chapter 1 in Nonlinear Acoustics (ASA, 2008), Blackstock summarizes Biquard’s account, which is in turn based on lectures delivered by Langevin at the Collège de France in 1923. Langevin derived the coefficient of nonlinearity for liquids, predating the quantity subsequently expressed as β = 1 + B/2A, and provided measured values for several liquids. He also obtained an expression for the profile of a steady shock wave and described its subsequent decay, predating the classical Fay solution published in 1931. However, Langevin is most well known in nonlinear acoustics for a quantity that bears his name, the Langevin radiation pressure, and for what distinguishes it from the Rayleigh radiation pressure [Beyer (JASA, 1978)]. Rayleigh’s result applies to a constrained field such as a standing wave in a closed tube, and it depends on the nonlinearity parameter B/A, whereas Langevin’s result applies to an unconstrained field such as a sound beam, which is more common in practice, and it is independent of B/A.