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Fourier decomposition of a plane nonlinear sound wave developing from a sinusoidal source
Responsible organisation
2001 (English)In: Acustica, ISSN 0001-7884, Vol. 87, no 2, 163-169 p.Article in journal (Refereed) PublishedAlternative title
Fourierbeskrivning av en ickelinjärt utrbredande våg från en sinuskälla (Swedish)
Abstract [en]

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.

Place, publisher, year, edition, pages
S. Hirzel Verlag , 2001. Vol. 87, no 2, 163-169 p.
Keyword [en]
nonlinear acoustics, nonlinear wave propagation, shock waves
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:bth-10320ISI: 000169170700001Local ID: oai:bth.se:forskinfo0A74C36B0F9DEBBDC1256C29003AA706OAI: oai:DiVA.org:bth-10320DiVA: diva2:838417
Available from: 2012-09-18 Created: 2002-09-03 Last updated: 2015-06-30Bibliographically approved

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