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Diffusion and scattering coefficients for room surfaces

For the last century acoustics has had a coefficient to measure energy lost on reflection; the absorption coefficient. Now, as our understanding and modelling of indoor and outdoor spaces becomes increasing sophisticated, a need has developed to produce a coefficient to measure the degree of scattering produced on reflection; a diffusion coefficient. This project has developed such a coefficient, which has now been enshrined in an international standard information document.

Diffusion and scattering coefficients

A three year research grant funded by the Engineering and Physical Sciences Research Council (EPSRC), grant number GR/L13124, 1996-1999. Alpha 4 rated.

Summary from final report

Surface diffusion or scattering often plays a key role in determining the sound field within an enclosed space, whether this comes from specialist diffusers used in performance spaces, or accidental diffusers such as machinery in factories. To take one example from the Barbican Concert Hall in London, specialist Schroeder diffusers have been applied to the rear wall on the main floor to prevent late arriving echoes disturbing the audience and musicians.

The last few decades has seen a return to a greater number of diffusing surfaces in performance spaces, but there has been no standard definition for a coefficient to measure diffuse scattering produced by these surfaces. This has meant it was impossible to draw up specifications at the design stage, or even to readily compare the merits of different surfaces. With the diffusion coefficient developed by this project this is now possible. For example, the post-production studio walls and ceiling shown right were designed used the new diffusion coefficient to evaluate the worth of different designs. With the diffusion coefficient definition being enshrined in standards, it is hoped that its use will become more widespread.

Furthermore, correct characterisation of diffuse reflections is vital to enable accurate predictions using geometric room acoustic models. This industry standard modelling technique is based on approximating sound as high frequency incoherent energy. It is necessary however, to also account for the wave nature of sound, and the fact that diffraction plays an important role in determining the sound field. This is done via various diffusion modelling techniques which require a diffusion coefficient. This project has investigated the performance of the diffuse reflection modelling using various definitions, and found them to be wanting in many regards. This has indicated an avenue for future research.

Relevant publications:

  • T. J. Cox and P. D’Antonio, “Acoustic Absorbers and Diffusers: Theory, Design and Application,” Spon Press, (2004).
  • T J Hargreaves, T J Cox, Y W Lam and P D'Antonio. Surface Diffusion Coefficients for Room Acoustics: Free Field Measures. J.Acoust.Soc.Am. 108 (4), 1710-1720 (2000).
  • AES-4id-2001. J.Audio.Eng.Soc. March 2001.
  • T J Hargreaves. Acoustic Diffusion and Scattering Coefficients for Room Surfaces. Ph.D. Thesis University of Salford (2000).
  • ISO 17497-2

Principal investigator:Trevor J. Cox; Co- Investigator: Prof Y. W. Lam

Collaborator: Dr Peter D'Antonio* Research Assistant: Dr Tristan Hargreaves.

*Dr. D'Antonio is president of RPG Diffusor Systems Inc. 651-C Commerce Drive Upper Marlboro MS 20774 USA (