From auditorium ray acoustics to wave acoustics: The next giant step

Abstract

For at least five decades, architectural acousticians have used straight-line, infinite-frequency rays to determine which regions of an auditorium are insonified by a sound source and which are shadowed. In the next decade, leading acoustical designers of auditoriums will turn to predictions of the timing and amplitude of the different frequencies which partially reflect and bend around real auditorium components such as proscenium arches and boxes. The frequency dependence of wave reflection from rigid, finite surfaces has been developed by Clay et al. [J. Acoust. Soc. Am. 94, 2279 (1993)]. The calculation of the frequency dependence of the diffraction component, which some have called the BTM technique, is a digitally formulated, finite-wedge, frequency-spectral interpretation of the classic Biot–Tolstoy (1957) theory for impulse scatter from an infinite wedge. The BTM technique, which we described first at an ASA meeting in 1978, has been applied to shadowing by highway noise barriers [Medwin, J. Acoust. Soc. Am. 69, 1060–1064 (1981)] and to multifrequency reverberation from randomly rough, ocean surfaces [Keiffer and Novarini, in Computational Acoustics, edited by D. Lee et al. (1990), Vol. 1, pp. 67–81]. The procedure is explained in detail in Medwin and Clay [Fundamentals of Acoustical Oceanography (Academic, New York, 1998)]. The justification and analytical extension of this method have recently been formulated by Svensson [J. Acoust. Soc. Am. 106, 2331–2344 (1999)], who has made the program available on his web site and has suggested applications to auditoriums. The physical interpretation of the BTM technique will be described in terms of the spectral and temporal behavior of finite plates and wedges as modules of more complex components of auditorium surfaces.