@article {Enflo:2001:1610-1928:163,
title = "Fourier Decomposition of a Plane Nonlinear Sound Wave Developing from a Sinusoidal Source",
journal = "Acta Acustica united with Acustica",
parent_itemid = "infobike://dav/aaua",
publishercode ="dav",
year = "2001",
volume = "87",
number = "2",
publication date ="2001-03-01T00:00:00",
pages = "163-169",
itemtype = "ARTICLE",
issn = "1610-1928",
url = "https://www.ingentaconnect.com/content/dav/aaua/2001/00000087/00000002/art00001",
author = "Enflo, Bengt O. and Hedberg, Claes M.",
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-Hopf transformation is a quotient between two Fourier series. Two approximate Fourier
series representations of this solution are known: Fubini's [1] 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. The Fourier coefficients turn out to be power series in exp(-), where is a dimensionless measure of dissipation and is a dimensionless measure of distance from the boundary.
Curves of the Fourier coefficients as functions of are given for > 0.9. They join smoothly to Fubini's solution (valid for < 1 and corrected for dissipation) and to Fay's solution (valid for 1). Maxima for the Fourier coefficients of the higher harmonics
are given as functions of . These maxima lie in a region where neither Fubini's nor Fay's solution can be used.",
}