Provider: Ingenta Connect
Database: Ingenta Connect
Content: application/x-research-info-systems
TY - ABST
AU - Enflo, Bengt O.
AU - Hedberg, Claes M.
TI - Fourier Decomposition of a Plane Nonlinear Sound Wave Developing from a Sinusoidal Source
JO - Acta Acustica united with Acustica
PY - 2001-03-01T00:00:00///
VL - 87
IS - 2
SP - 163
EP - 169
N2 - 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(-*ɛ*σ), where *ɛ* is a dimensionless measure of dissipation and σ is a dimensionless measure of distance from the boundary.
Curves of the Fourier coefficients as functions of σ are given for σ > 0.9. They join smoothly to Fubini's solution (valid for σ < 1 and corrected for dissipation) and to Fay's solution (valid for σ ≫ 1). Maxima for the Fourier coefficients of the higher harmonics
are given as functions of σ. These maxima lie in a region where neither Fubini's nor Fay's solution can be used.
UR - https://www.ingentaconnect.com/content/dav/aaua/2001/00000087/00000002/art00001
ER -