An impedance-based formulation of frequency-domain nonlinearity indicators in finite-amplitude sound propagation

Abstract

Since the Morfey-Howell Q/S was introduced as a single-point frequency-domain nonlinearity indicator for propagation of intense broadband noise [AIAA J. 19, 986–992 (1981)], there has been debate about its validity, utility, and interpretation. In this Letter, the generalized Burgers equation is recast in terms of specific acoustic impedance along with linear absorption and dispersion coefficients, normalized quadspectral density (Q/S), and newly proposed normalized cospectral density (C/S). The formulation leads to a rather straightforward interpretation in which Q/S and C/S, respectively, represent the additional absorption and dispersion at a locale, produced by the passage of a finite-amplitude wave.