THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

244 11. Acoustics of Enclosed Spaces: Architectural AcousticsIn this chapter we shall examine the behavior of sound in enclosed spaces, anddevelop the fundamental equations that are used in optimizing the acoustics ofauditoriums, music halls, and lecture rooms. We shall also study the means of improvingroom acoustics through installation of appropriate materials. This chapterconcludes with descriptions of a number of outstanding acoustical facilities.11.2 Sound FieldsThe distribution of acoustic energy, whether originating from a single or multiplesound sources in an enclosure, depends on the room size and geometry and on thecombined effects of reflection, diffraction, and absorption. With the appreciablediffusion of sound waves due to all of these effects it is no longer germane toconsider individual wave fronts, but to refer to a sound field, which is simply theregion surrounding the source. A free field is a region surrounding the source,where the sound pattern emulates that of an open space. From a point source thesound waves will be spherical, and the intensity will approximate the inverse squarelaw. Neither reflection nor diffraction occurs to interfere with the waves emanatingfrom the source. Because of the interaction of sound with the room boundaries andwith objects within the room, the free field will be of very limited extent.If one is close to a sound source in a large room having considerably absorbentsurfaces, the sound energy will be detected predominantly from the sound sourceand not from the multiple reflections from surroundings. A free field can be simulatedthroughout an entire enclosure if all of the surrounding surfaces are linedwith almost totally absorbent materials. An example of such an effort to simulatea free field is the extremely large anechoic (echoless) chamber at Lucent TechnologiesBell Laboratories in Murray Hill, New Jersey, shown in the photographof Figure 11.1. Such a chamber is typically lined with long wedges of absorbentfoam or fiberglass and the “floor” consists of either wire mesh or grating suspendedover wedges installed over (and covering entirely) the “real” floor underneath. Preciselycontrolled experiments on sound sources and directivity patterns of soundpropagation are rendered possible in this sort of chamber.A diffuse field is said to occur when a large number of reflected or diffractedwaves combine to render the sound energy uniform throughout the region underconsideration. Figure 11.2 illustrates how diffusion results from multiple reflections.The degree of diffusivity will be increased if the room surfaces are notparallel so there is no preferred direction for sound propagation. Concave surfaceswith radii of curvature comparable to sound wavelengths tend to cause focusing,but convex surfaces will promote diffusion. Multiple speakers in amplifying systemsauditoriums are used to achieved better diffusion, and special baffles may behung from ceilings to deflect sound in the appropriate directions.Sound reflected from walls generates a reverberant field that is time dependent.When the source suddenly ceases, a sound field persists for a finite interval asthe result of multiple reflections and the low velocity of sound propagation. Thisresidual acoustic energy constitutes the reverberant field. The sound that reaches a