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Boundary Element Modelling of a Novel Simple Enhanced Bandwidth Schroeder Diffuser Offering Comparable Performance to a Fractal Design

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Abstract

It is well established that Schroeder diffusers may be used as surface treatment to promote diffuse sound fields in auditoria over a target frequency range. Quadratic Residue Diffusers are very effective within a design frequency bandwidth, and this frequency bandwidth may be significantly extended by a nested or fractal design. Publicly available data typically publish diffusion coefficients separately for the parent diffuser and the child diffuser, with some ambiguity surrounding the effect the two levels have on each other, and the performance at ‘crossover’ frequencies. This paper uses an optimised 2D boundary element method to investigate the differences in results when the parent and child diffusers are modelled separately, and as an integrated design. It is found that the scattering properties of the child diffuser are significantly modified by the well of the parent diffuser in which it is placed. More interestingly, the excellent scattering properties of the fractal design may be achieved with only a minor loss of bandwidth using a far simpler and more robust geometry in which the child diffuser is replaced by a concave surface at the base of the well in the parent diffuser. The paper outlines the optimisation of the boundary element code for this task, and compares results for a variety of well bottom shapes with the fractal design.

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References

  1. Everest, F.A., Pohlmann, K.C.: Master Handbook of Acoustics, 5th edn. McGraw-Hill, New York (2009)

    Google Scholar 

  2. Cox, T., D’Antonio, P.: Acoustic Absorbers and Diffuser: Theory Design and Application. CRC Press, London (2009)

    Google Scholar 

  3. Schroeder, M.R.: Diffuse sound reflection by maximum-length sequences. J. Acoust. Soc. Am. 57(1), 149–150 (1975)

    Article  Google Scholar 

  4. D’Antonio, P., Konnert, J.: The QRD diffractal: a new one- or two-dimensional fractal sound diffusor. J. Audio Eng. Soc. 40(3), 117–129 (1992)

  5. Rocchi, L.: Quadratic residue diffusers: modelling through the boundary element method. BE(Hons) Thesis, University of Tasmania (2014)

  6. Kirkup, S.: The Boundary Element Method in Acoustics. Integrated Sound Software, Heptonstall (1998)

  7. Lock, A.: Development of a 2D boundary element method to model Schroeder acoustic diffusers, BE(Hons) Thesis University or Tasmania (2014)

  8. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. Applied Mathematics Series, vol. 55. National Bureau of Standards, Washington, DC (1964)

    MATH  Google Scholar 

  9. Wu, T.W.: A direct boundary element method for acoustic radiation and scattering from mixed regular and thin bodies. J. Acoust. Soc. Am. 97(1), 84–91 (1995)

    Article  Google Scholar 

  10. Morse, P.M., Ingard, K.U.: Theoretical Acoustics. Princeton University Press, Princeton (1986)

    Google Scholar 

  11. Kuyama, T.: Some calculated results of the diffraction of sound waves by a cylindrical obstacle. Proc. Physico-Mathematical Soc. Jpn. 15, 366–370 (1933)

    Google Scholar 

  12. Wiener, F.M.: Sound diffraction by rigid spheres and circular cylinders. J. Acoust. Soc. Am. 19(3), 444–451 (1947)

    Article  Google Scholar 

  13. Schroeder, M.R.: Binaural dissimilarity and optimum ceilings for concert halls: more lateral sound diffusion. J. Acoust. Soc. Am. 65(4), 958–963 (1979)

    Article  Google Scholar 

  14. ISO 17497-2:2012: Acoustics—Sound-Scattering Properties of Surfaces Part 2: Measurement of the Directional Diffusion Coefficient in a Free Field. International Organization for Standardization, Geneva (2012)

    Google Scholar 

  15. Fujiwara, K., Miyajima, T.: Absorption characteristics of a practically constructed Schroeder diffuser of quadratic-residue type. Appl. Acoust. 35(2), 149–152 (1992)

  16. Fujiwara, K.: A study on the sound absorption of a quadratic-residue type diffuser. Acta Acust. United Acust. 81(4), 370–378 (1995)

    Google Scholar 

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Acknowledgments

The authors are grateful to Luca Rocchi, who wrote the original BEM code that has been developed for this work.

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Authors and Affiliations

  1. School of Engineering and ICT, University of Tasmania, Sandy Bay, TAS, 7005, Australia

    Andrew Lock & Damien Holloway

Authors
  1. Andrew Lock
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  2. Damien Holloway
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Corresponding author

Correspondence to Andrew Lock.

Additional information

This paper is based on the conference submission that received the Best Student Paper Award, sponsored by Resonate Acoustics, at the Australian Acoustical Society Conference, November 15-18, 2015.

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Lock, A., Holloway, D. Boundary Element Modelling of a Novel Simple Enhanced Bandwidth Schroeder Diffuser Offering Comparable Performance to a Fractal Design. Acoust Aust 44, 137–147 (2016). https://doi.org/10.1007/s40857-016-0049-4

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  • DOI: https://doi.org/10.1007/s40857-016-0049-4

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