Acoustic Reconstruction of Ancient Structures Using Three-Dimensional Digital Waveguide Mesh Models
Guilherme Campos and David M. Howard
Department of Electronics
University of York, Heslington, York YO1 5DD
The study of the inter-relationship between the acoustics of music performance spaces and the development of musical styles and musical instruments over the centuries, relevant to the fields of music history, musicology and ethno-musicology, calls for the development of accurate room acoustic simulation techniques.
The interest of such techniques extends outside the musicological sphere, since the acoustic behaviour of ancient buildings, particularly prehistoric monuments, can be an important piece in their archaeological investigation, contributing to a more complete understanding of their function and significance. A great number of archaeological sites (e.g. Mayan ruins and Northern European megalithic monuments) feature striking acoustical phenomena.
Accurate acoustic simulation requires a precise knowledge of how the physical characteristics of a room affect its acoustic behaviour, but solving the sound wave equation analytically is virtually impossible in practical situations.
An alternative approach is acoustic modelling based on numerical methods. Models directly based on the wave equation are known as physical models. The digital waveguide models discussed here fall into this category. 1-D and 2-D versions have been successfully applied to sound synthesis and acoustic instrument simulation .
Application to room acoustics requires 3-D waveguide meshes: the enclosed space under analysis is spatially discretised as a regular grid of nodes. In theory, since all wave propagation phenomena are taken into account, accurate results can be attained with a suitably high mesh resolution. Initial validation tests confirm the model's ability to accurately predict the frequency mode distribution and provide appropriate sound localisation cues.
Excessive computational loading has been the model's main drawback for practical application. The main factors affecting computation time are analysed and practical formulae to assess computation time presented. Recent research efforts have been directed towards the development of more efficient model implementations, including the application of parallel processing . Practical application to the study of real rooms is rapidly becoming a realisable prospect.
A complete room acoustic simulation system based on waveguide mesh modelling is proposed, including a 3D CAD front-end for room definition and a mesh generation module extracting data automatically from the CAD files. Such a system would provide a general tool for model validation reliant upon accurate 3D surveys and in situ experimental measurements. A detailed acoustic investigation of the acoustic properties of Neolithic chambers like Newgrange , to help establish whether or not their particular acoustic properties are likely to have been designed, is a particularly interesting application. The irregular boundaries and relatively small sizes that characterise these sites would suit the model particularly well.
 Jahn, R. G.; Devereux, P. and Ibison, M. (1996) "Acoustical resonances of assorted ancient structures" (Journal of the ASA Vol. 99, No. 2, February, pp 649-658)
 Van Duyne, S. A. and Smith III, J. O. (1993) "Physical Modeling with the 2-D Digital Waveguide Mesh" (ICMC Proceedings, pp 40-47).
 Campos, G. and Howard, D. M. (2000) "On the Computation Time of Three-Dimensional Digital Waveguide Mesh Acoustic Models" (Proceedings of the 26th EUROMICRO Conference, Maastricht, Holland, 5-7 Sept., vol. II, pp 332-339).