Page  489 ï~~Reflection Paths and Phantom Sources The SPS program models the propagation of reflected sound using what is known in geometric acoustics as the phantom source. A phantom source is created every time a sound reflects off a rigid barrier. It is formed on the opposite side of the barrier at a distance from the barrier equal to the length between the barrier and the sound source. The line connecting the source and phantom source is always perpendicular to the wall. When a sound is reflected from the wall it appears to the listener as if the sound originates from a point behind the wall. From the perspective of the listener, a sound emanating directly from the phantom source is equivalent to a sound following its reflected path, since the sound is from the same direction and the paths followed are of the same total length. A useful property of phantom sources is that their location depends only on the position of the generating sound source and the position of the wall off which it reflects, and is entirely independent of the listener location. Two listeners in different positions receive the reflected sound from the same apparent source. One phantom source is generated for each wall of the specified room. These "one bounce" sources are known as first order phantom sources. To find higher order phantom sources (i.e. sources that result from two or more bounces), each phantom source already found is used as a possible source for further phantom sources. The number of phantom sources tends to grow exponentially with each successive order of reflection. SPS can keep track of an arbitrary number of phantom sources or reflection orders. Not all phantom sources produce physically realizable reflection paths. Each phantom source must be checked for its "legality," but cannot be discarded, since it is possible for illegal phantom sources to give rise to legal phantom sources of higher order. The legality of a particular source depends upon the geometry of the room and the position of the listener within that room. Once the positions of a number of phantom sources have been calculated, one can model the direct and reflected sound received by the listener simply by transmitting the sound from the source and all its phantom sources. Naturally, the amplitude and delay time of wavefronts reaching the listener will depend upon the distances from the source and phantom sources. The amplitude also depends upon the combined effect of the reflectivity coefficients for all walls used in the reflection path for a particular source. Listener Models To this point the environment and the reflections of a sound source in that environment have been accurately modeled in spatial terms. It is necessary to collect the sound at the position of the listener and to provide a means of replaying the sound, to give the subjective impression of immersion in the environment specified. It is also necessary to preserve the directional information associated with each reflection. The SPS program uses what is known as the Receive-ReBroadcast (RRB) listener model to do this. This can be visualized as a listener with a circular wall around him. As all the sounds from the environment travel towards him they strike the circular wall and proceed no further. The model must then transmit all the sounds hitting the wall inwards to the listener in the most accurate way possible. Ideally, one would have hundreds of speakers arrayed around the listener on the circumference of the circle, and if a sound came from a particular angle one specific speaker at that precise angle would rebroadcast that sound. In practise, however, only a few speakers, spaced equidistantly from each other, can be used, and energy is distributed proportionally between two speakers if the sound arrives at an angle between them. SPS supports an RRB listener model with 2 to 8 equally spaced speakers, plus another type of RRB model specifically designed for stereo playback. Since the listener model is separate from the mechanism that models the reflection of sound within an environment, it will be possible in the future to substitute a binaural listener model suitable for headphone playback. References Manzara, Leonard C. 1990. The Simulation of Acoustical Space by Means of Physical Modeling. Doctoral Dissertation: State University of New York at Buffalo, Buffalo, New York. 490 4901CMC PROCEEDINGS 1995

Page  490 ï~~Accurate Computer Simulation of Acoustic Space Leonard Manzara Trillium Sound Research Inc. (403) 284-9278 manzara@ trillium.ab.ca ABSTRACT: The SPS program creates accurate simulations of the spatial and reverberant characteristics of user-specified environments using the techniques of geometric acoustics in two dimensions. The user can specify wall locations, wall reflectivity and roughness, sound source locations and volumes, listener location and orientation, and air temperature. All these elements can be varied independently over time, giving the composer a tool to simulate fanciful dynamic environments, as well as more standard static hall acoustics. Effects such as Doppler shift arise naturally since the program directly models the physical propagation of sound. Introduction SPS (Simulation of Physical Space) is a computer program which uses geometric modeling techniques to accurately simulate acoustic space. Unlike traditional methods of reverberation generation, the program preserves the directional information of both direct and reflected sound, and properly deals with the propagation of waveforms from moving sources. This gives the user the ability to create arbitrary acoustic environments, where reverberant and spatial characteristics are accurately modeled, and where Doppler shift is naturally created by moving the listener or sound source. Although intended primarily as a tool for the composer to process pre-existing recorded or synthesized sound, the program is also useful in architectural acoustics, applied psychoacoustics, and in theoretical and experimental physics. Specifying the Virtual Acoustic Environment SPS operates in two dimensions. The user-specified "room" can have an arbitrary number of vertical walls, and the floor and ceiling are considered infinitely absorptive. The listener and an arbitrary number of sound sources can be located anywhere within this room. The walls can move about, as can the listener and sound sources, but they must remain within the walls of the room. Normally, such movement is linear in nature, but discontinuous jumps in location are also possible. The user-specified room must always be a convex polygon. In other words, as the walls of the room change location, the interior angle at every corner can never exceed 180 degrees. The user specifies the dimensions of the room with a list of vertices, where each vertex corresponds to a corner of the polygon. There must be at least 3 walls, and the number of walls must remain fixed throughout a simulation. The user can specify the reflectivity of each wall independently. The reflectivity coefficient can vary from 0 to 1, where 0 means the wall is totally absorptive, and 1 means the wall reflects all sound directed at it. Each wall also has an angular and front-to-back "roughness" associated with it. These coefficients describe a range of statistical variation from the normal surface of the wall. Essentially, this means that sound rays reflected off a rough wall will vary slightly in angle and/or depth; each ray is randomly varied within the specified range. Unlike most real-world rooms, the reflectivity and roughness of each wall can change over time. As mentioned above, the sound sources and listener can move anywhere within the defined space of the room. The listener also has an angular orientation, and can rotate in a clockwise or counter-clockwise direction. Since a sound source is treated as a point source, its angular orientation cannot be specified. However, the volume of each source can be varied over time, so it is possible to create a sort of spatial musique concrete. The temperature of the air within the room is specified in degrees centigrade, and is used to determine the speed of sound. ICMC PROCEEDINGS 199548 489