[en] An exact solution is developed for the sound field reflected by an infinite rigid rough surface with a periodic rectangular profile. The random-incidence scattering coefficient of this surface is derived from the numerical calculation of this solution for several directions of the incident plane wave. Scattering coefficients’ values are given in this paper for a great number of configurations by varying the geometrical parameters of the periodic profile, leading to a very detailed description of the scattering properties of this kind of profile. In particular, it is shown that, when the ratio H/L of the depth to the spatial period of the profile is small, the key parameter is H/, the ratio of the depth of the profile to the wavelength. The random-incidence scattering coefficient tends to increase with this ratio, as long as H/ is less than 0.3. This evolution is similar to gaussian and sine-shaped profiles analysed in previous studies. For H/ >0.3, the coefficient’s value oscillates while converging to an asymptotic value which depends on the width of the wells. Resonance effects have also been highlighted for periodic rectangular profiles, in particular by comparing the computed scattering coefficients with the few measured values published in the scientific literature. The scattering coefficients’ values published in this paper can be introduced in room acoustics’ models to characterize periodic rectangular surfaces, provided that their dimensions are much greater than the wavelength. Additional measurements and BEM computations are required to deeply analyse the influence of the finite size and the acoustical absorption of real surfaces having this profile.
Disciplines :
Electrical & electronics engineering
Author, co-author :
Embrechts, Jean-Jacques ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Techniques du son et de l'image
Billon, Alexis ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Electroacoustique, acoustique appliquée et éclairage
Language :
English
Title :
Theoretical Determination of the Random-Incidence Scattering Coefficients of Infinite Rigid Surfaces with a Periodic Rectangular Roughness Profile
Alternative titles :
[fr] Détermination théorique du coefficient de dispersion sous incidence diffuse de surfaces rigides, infinies et présentant un profil périodique rectangulaire
ISO 17497-1: Acoustics. Measurement of the sound scattering properties of surfaces. Part 1: Measurement of the random-incidence scattering coefficient in a reverberation room. 2004.
T. J. Cox, P. D'Antonio: Acoustic absorbers and diffusers. Taylor and Francis, London and New York, 2009.
T. J. Cox, B.-I. L. Dalenback, P. D'Antonio, J. J. Embrechts, J. Y. Jeon, E. Mommertz, M. Vorländer: A tutorial on scattering and diffusion coefficients for room acoustic surfaces. Acta Acustica united with Acustica 92 (2006) 1-15.
M. R. Hodgson: Evidence of diffuse surface reflection in rooms. J. Acoust. Soc. Am. 89 (1991) 765-771.
M. Barron: Auditorium acoustics and architectural design. Spon, London and New York, 2000.
Y. W. Lam: A comparison of three diffuse reflection modelling methods used in room acoustics computer models. J. Acoust. Soc. Am. 100 (1996) 2181-2192.
M. Vorländer, J. J. Embrechts, L. De Geetere, G. Vermeir, M. H. de Avelar Gomes: Case studies in measurement of random incidence scattering coefficients. Acta Acustica united with Acustica 90 (2004) 858-867.
L. De Geetere: Analysis and improvement of the experimental techniques to assess the acoustical reflection properties of boundary surfaces. PhD thesis, Laboratorium bouwfysica, University of Leuven, Belgium, 2004.
J. J. Embrechts: Practical aspects of the ISO procedure for measuring the scattering coefficient in a real-scale experiment. Proceedings of Forum Acusticum, Sevilla, Spain, 2002, 6.
I. Schmich: Retour d'expérience sur la mise en application de la norme ISO 17497-1. Proceedings of the 10th C.F.A. (Congrés français d'acoustique), Lyon, France, 2010, 6.
Y.-J. Choi, D.-U. Jeong: Some issues in measurement of the random-incidence scattering coefficients in a reverberation room. Acta Acustica united with Acustica 94 (2008) 769-773.
I. Bork: A comparison of room simulation software. The second round robin on room acoustical computer software. Acta Acustica united with Acustica 86 (2000) 943-956. (Pubitemid 32872611)
J. J. Embrechts, L. De Geetere, G. Vermeir, M. Vorländer, T. Sakuma: Calculation of the random-incidence scattering coefficients of a sine-shaped surface. Acta Acustica united with Acustica 92 (2006) 593-603. (Pubitemid 44351108)
J. J. Embrechts: Random-incidence scattering coefficients of infinite sine-shaped surfaces. Proceedings of Forum Acusticum, Budapest, Hungary, 2005, 4.
T. Sakuma, Y. Kosaka, L. De Geetere, M. Vorländer: Relationship between the scattering coefficients determined with coherent averaging and with directivity correlation. Acta Acustica united with Acustica 95 (2009) 669-677.
J. Redondo, R. Pico, M. R. Avis, T. J. Cox: Prediction of the random-incidence scattering coefficient using a FDTD scheme. Acta Acustica united with Acustica 95 (2009) 1040-1047.
J. A. Hargreaves, J. Cox: A transient boundary element method for acoustic scattering from mixed regular and thin rigid bodies. Acta Acustica united with Acustica 95 (2009) 678-689.
J. J. Embrechts, D. Archambeau, G. B. Stan: Determination of the scattering coefficient of random rough diffusing surfaces for room acoustics applications. Acta Acustica united with Acustica 87 (2001) 482-494. (Pubitemid 32992331)
A. De Bruijn: The sound absorption of an absorbing periodically uneven surface of rectangular profile. Acustica 18 (1967) 123-131.
T. J. Hargreaves, T. J. Cox, Y. W. Lam, P. D'Antonio: Surface diffusion coefficients for room acoustics: Free-field measures. J. Acoust. Soc. Am. 108 (2000) 1710-1720.
R. L. Holford: Scattering of sound waves at a periodic pressure-release surface: An exact solution. J. Acoust. Soc. Am. 70 (1981) 1116-1128. (Pubitemid 12464911)
J. Ducourneau, L. Bos, V. Planeau, A. Faiz, S. S. Lami, A. Nejade: Prediction of the acoustic pressure above periodically uneven facings in industrial workplaces. J. Sound Vib. 329 (2010) 2276-2290.
Y. Ando, K. Kato: Calculations on the sound reflection from periodically uneven surfaces of arbitrary profile. Acustica 35 (1976) 321-329.
G. Dahlquist, A. Björck: Numerical methods. Prentice Hall, Englewood Cliffs, 1974.
I. Schmich. personal communication.
E. I. Thorsos: The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum. J. Acoust. Soc. Am. 83 (1988) 78-92.
M. Vorländer, E. Mommertz: Definition and measurement of random-incidence scattering coefficients. Appl. Acoust. 60 (2000) 187-199.
L. D. Geetere, J. J. Embrechts, G. Vermeir: Calculation of the scattering coefficient of a sine-shaped surface by using the 3D BEM method. Proceedings of the Institute of Acoustics 25 (2003) 75-83.
T. J. Hargreaves: Acoustic diffusion and scattering coefficients for room surfaces. PhD thesis, Department of acoustics and audio engineering, University of Salford, U.K., 2000.