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 http://www.ima.bth.se/ |
| Authors e-mail: | claes.hedberg@bth.se |
| 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 |
