6.1.1 Reverberation Time

Much attention has been paid to the acoustics of concert halls and other enclosed spaces for lectures and the performing arts. Many factors, both physical and psychological, influence the judgment of the acoustic quality of rooms and many descriptors have been introduced and used in an effort to quantify various aspects of this concept. Systematic work in room acoustics began almost 100 years ago with the pioneering studies by Sabine, then a physics professor at Harvard. For further comments on Sabine, see Section 1.2.2.

We start by deriving Sabine s formula for the reverberation time in a room. The sound field is assumed to be diffuse which means that at a point in the room sound arrives from all direction with equal probability and intensity. Thus, if the point of observation is surrounded by a spherical control surface, the contribution to the acoustic energy density within the sphere from every solid angle element d ? on the sphere will be the same and we express it as ( I ₀ /c) d ?, where I ₀ is an intensity and c the sound speed (see Chapter 3). The fact that the field is diffuse means that these contributions are all uncorrelated so that their energies add. Then, with a total solid angle of the spherical control surface of 4 ?, the total energy density becomes

Again, using the intensity I ₀, we can express the acoustic...