Archives of Acoustics, 43, 2, pp. 227–233, 2018

A Rough Estimation of Acoustics of the Cuboidal Room with Impedance Walls

Rzeszów University of Technology

Rzeszów University of Technology

The cuboidal room acoustics field is modelled with the Fourier method. A combination of uniform, impedance boundary conditions imposed on walls is assumed, and they are expressed by absorption coefficient values. The absorption coefficient, in the full range of its values in the discrete form, is considered. With above assumptions, the formula for a rough estimation of the cuboidal room acoustics is derived. This approximate formula expresses the mean sound pressure level as a function of the absorption coefficient, frequency, and volume of the room separately. It is derived based on the least-squares approximation theory and it is a novelty in the cuboidal room acoustics.

Theoretical considerations are illustrated via numerical calculations performed for the 3D acoustic problem. Quantitative results received with the help of the approximate formula may be a point of reference to the numerical calculations.
Keywords: Fourier analysis; room acoustics; absorption coefficient; boundary-value problem; impedance boundary conditions
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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


Bistafa R.S., Morrissey J.W. (2003), Numerical solution of the acoustic eigenvalue equation in the rectangular room with arbitrary (uniform) wall impedances, Journal of Sound and Vibration, 263, 205–218.

Blackstock D.T. (2000), Fundamentals of Physical Acoustics, Wiley-Interscience, New York.

Brański A. (2013), Numerical methods to the solution of boundary problems, classification and survey [in Polish], Rzeszow University of Technology Press, Rzeszow. ISBN 978-83-7199-792-1.

Brański A., Borkowska D. (2015), Effectiveness of nonsingular solutions of the boundary problems based on Trefftz methods, Engineering Analysis with Boundary Elements, 59, 97–104.

Brański A., Borkowski M., Borkowska D. (2012), A comparison of boundary methods based on inverse variational formulation, Engineering Analysis with Boundary Elements, 36, 505–510.

Brański A., Kocan-Krawczyk A., Prędka E. (2017), An influence of the wall acoustic impedance on the room acoustics.The exact solution, Archives of Acoustics, 42, 4, 677–687.

Chen W., Zhang J.Y., Fu Z.J. (2014), Singular boundary method for modified Helmholtz equations, Engineering Analysis with Boundary Elements, 44, 112–119.

Dautray R., Lions J.L. (2000), Mathematical analysis and numerical methods for science and technology. Springer, Berlin.

Evans L.C. (2010), Partial Differential Equations: Second Edition, American Mathematical Society, Providence, USA.

Fu Z.J., Chen W., Gu Y. (2014), Burton–Miller-type singular boundary method for acoustic radiation and scattering. Journal of Sound and Vibration, 333, 3776–3793.

Johnson R.S. (2006), An introduction to Sturm-Liouville theory, School of Mathematics & Statistics – University of Newcastle upon Tyne.

Kamisiński T. (2012), Acoustic issues in historic horseshoe-shaped theatre halls, AGH University of Science and Technology Press, Kraków.

Kamisiński T.M., Kulowski A., Kinasz R. (2016), Can Historic Interiors with Large Cubature be Turned Acoustically Correct?, Archives of Acoustics, 41, 1, 3–14.

Kocan-Krawczyk A. (2017), The formula to the evaluation of the room acoustics with impedance walls. Proceedings of LXIV Open Seminar on Acoustics, Advances in Acoustics, pp. 433–438, Piekary Śląskie – PTA Gliwice.

Korany N., Blauert J., Abdel Alim O. (2001), Acoustic simulation of rooms with boundaries of partially specular reflectivity, Applied Acoustic, 62, 875–887.

Kulowski A. (2011), Acoustics of halls. Design recommendations for architects [in Polish], GUT Publishing House, Gdańsk.

Kuttruff H. (2000), Room acoustics, Fundamentals of Physical Acoustics. Wiley-Interscience, New York.

Lehmann E., Johansson A. (2008), Prediction of energy decay in room impulse responses simulated with an image-source model, Journal of the Acoustical Society of America, 124, 269–277.

Lin J., Chen W., Chen C.S. (2014), Numerical treatment of acoustic problems with boundary singularities by the singular boundary method, Journal of Sound and Vibration, 333, 3177–3188.

Lopez J., Carnicero D., Ferrando N., Escolano J. (2013), Parallelization of the finite-difference time-domain method for room acoustics modelling based on CUDA, Mathematical and Computer Modelling, 57, 1822–1831.

Luizard P., Polack J. P., Katz B. (2014), Sound energy decay in coupled spaces using a parametric analytical solution of a diffusion equation, Journal of the Acoustical Society of America, 135, 2765–2776.

Mclachlan N.W. (1961), Bessel functions for Engineers, Oxford University Press, UK.

Meissner M. (2009a), Computer modelling of coupled spaces: variations of eigenmodes frequency due to a change in coupling area, Archives of Acoustics, 34, 157–168.

Meissner M. (2009b), Spectral characteristics and localization of modes in acoustically coupled enclosures, Acta Acustica united with Acustica, 95, 300–305.

Meissner M. (2012), Acoustic energy density distribution and sound intensity vector field inside coupled spaces, Journal of the Acoustical Society of America, 132, 228–238.

Meissner M. (2013a), Analytical and numerical study of acoustic intensity field in irregularly shaped room, Applied Acoustics, 74, 661–668.

Meissner M. (2013b), Evaluation of decay times from noisy room responses with puretone excitation, Archives of Acoustics, 38, 1, 47–54.

Morse P.M., Ingard K.U. (1987), Theoretical acoustics, Princeton University Press, New Jersey.

Naka Y., Oberai A.A., Shinn-Cunningham B.G. (2005), Acoustic eigenvalues of rectangular rooms with arbitrary wall impedances using the interval Newton/generalized bisection method, Journal of the Acoustical Society of America, 118, 3662–3671.

Okuzono T., Otsuru T., Tomiku R., Okamoto N. (2014), A finite-element method using dispersion reduced spline elements for room acoustics simulation, Applied Acoustics, 79, 1–8.

Summers J. (2012), Accounting for delay of energy transfer between coupled rooms in statistical-acoustics models of reverberant-energy decay, Journal of the Acoustical Society of America, 132, 129–134.

Xu B., Sommerfeldt S. (2010), A hybrid modal analysis for enclosed sound fields. Journal of the Acoustical Society of America, 128, 2857–2867.

DOI: 10.24425/122370