The Effect of Form on the Reverberation of Sound in Rooms

Abstract

Measurements of the mean free path p of sound in three dimensional models of eleven typical auditoriums—such as rectangular rooms (with and without balconies), fan shaped theatres, country and city churches, and rooms with gabled, barreled or domed ceilings—indicate that p varies from about 3.8 V/S (V=volume, S=interior surface) in a large rectangular room with a low ceiling to 4.3 V/S in a cruciform type of church auditorium. The reverberation formula for the impressed vibrations takes the form t=kV−rS loge (1−α)+4mV where k depends upon the shape of the room and has a value of .046 in the large room with the low ceiling, .053 in the cruciform type of church auditorium, and about .049 for the conventional type of room; r is a probability factor which depends upon the location of the absorptive material in a room; and m is the attenuation constant of the air. The more exact theory of reverberation must describe also the rate of decay of the free vibrations in a room. Some measurements of reverberation have been made in a small room which exhibit gross violations of the generally accepted reverberation formula. These measurements reveal the necessity of considering the free vibrations in reverberation theory.