Archives of Acoustics, 42, 4, pp. 677–687, 2017
10.1515/aoa-2017-0070

An Influence of the Wall Acoustic Impedance on the Room Acoustics. The Exact Solution

Adam BRAŃSKI
Rzeszów University of Technology
Poland

Anna KOCAN-KRAWCZYK
Rzeszów University of Technology
Poland

Edyta PRĘDKA
Rzeszów University of Technology
Poland

The Fourier method is applied to the description of the room acoustics field with the combination of uniform impedance boundary conditions imposed on some walls. These acoustic boundary conditions are expressed by absorption coefficient values In this problem, the Fourier method is derived as the combination of three one-dimensional Sturm-Liouville (S-L) problems with Robin-Robin boundary conditions at the first and second dimension and Robin-Neumann ones at the third dimension. The Fourier method requires an evaluation of eigenvalues and eigenfunctions of the Helmholtz equation, via the solution of the eigenvalue equation, in all directions. The graphic-analytical method is adopted to solve it It is assumed that the acoustic force constitutes a monopole source and finally the forced acoustic field is calculated. As a novelty, it is demonstrated that the Fourier method provides a useful and efficient approach for a room acoustics with different values of wall impedances. Theoretical considerations are illustrated for rectangular cross-section of the room with particular ratio. Results obtained in the paper will be a point of reference to the numerical calculations.
Keywords: Fourier analysis; architectural acoustics; absorption coefficients; boundary-value problems
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DOI: 10.1515/aoa-2017-0070

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