Fourier decomposition of a plane nonlinear sound wave developing from a sinusoidal source

Document type: Journal Articles
Article type: Original article
Peer reviewed: Yes
Author(s): Bengt Enflo, Claes Hedberg
Title: Fourier decomposition of a plane nonlinear sound wave developing from a sinusoidal source
Translated title: Fourierbeskrivning av en ickelinjärt utrbredande våg från en sinuskälla
Journal: Acustica-Acta Acustica
Year: 2001
Volume: 87
Issue: 2
Pagination: 163-169
ISSN: 0001-7884
Publisher: S. Hirzel Verlag
ISI number: 000169170700001
Organization: Blekinge Institute of Technology
Department: Dept. of Mechanical Engineering (Institutionen för maskinteknik)
Dept. of Mechanical Engineering S-371 79 Karlskrona
+46 455 38 50 00
Authors e-mail:
Language: English
Abstract: Burgers' equation describes plane sound wave propagation through a thermoviscous fluid. If the boundary condition at the sound source is given as a pure sine wave, the exact solution given by the Cole-Hopftransformation is a quotient between two Fourier series. Two approximate Fourier series representations of this solution are known: Fubini's (1935) solution, neglecting dissipation and valid at short distance from the sound source, and Fay's solution, valid far from the source. In the present investigation a linear system of equations is found, from which the coefficients in a series expansion of each Fourier coefficient can be derived one by one. Curves which join smoothly to Fubini's solution (valid up to slightly before shock formation) and to Fay's solution (valid for approximately three shock formation distances). Maxima for the Fourier coefficients of the higher harmonics are given. These maxima are situated in a region where neither Fubini's nor Fay's solution is valid.
Subject: Mechanical Engineering\General
Keywords: nonlinear acoustics, nonlinear wave propagation, shock waves