Application of number theory sequences in architectural acoustics

Abstract

One of the challenges in architectural acoustics is to develop contemporary diffusing surfaces that complement contemporary architecture in the way that statuary, columns, and relief ornamentation complemented classic architecture. Number theory sequences invented by Schroeder [J. Acoust. Soc. Am. 65, 958–963 (1979)] and further developed by D’Antonio et al. [Appl. Acoust. 60, 143–165 (2000)] have been used for two decades to design reflection phase gratings, which provide useful sound diffusion in architectural acoustics. The use of modulation techniques, to enhance performance, and the development of proof-of-performance techniques, to evaluate their performance, will be described. The development of flat and curve optimized binary amplitude gratings will also be presented. The current state-of-the-art utilizing boundary-element multidimensional optimization to design 1- and 2-D diffusors, which incorporate aesthetic constraints, will offer a view of future design possibilities. Photos of installations using these acoustic tools will also be presented to illustrate the usefulness of these devices and their impact on architectural acoustics.