I just found out that reverberation is the collection of reflected sounds from the surfaces in an enclosure. It is a desirable property of auditoriums to the extent that it helps to overcome the inverse square law dropoff of sound intensity in the enclosure. Having used reverberation in most of my work, I had to ask myself what is this inverse square law dropoff? Is it really square? Is it a true law, and does it really drop off?
As it turns out, the drop of sound intensity according to the inverse square law emphasizes the rapid loss associated with the inverse square law. This means zero reverberation, or dry sound. In an auditorium, such a rapid loss is unacceptable. In fact, if the inverse square law is at 100% a person sitting in the back of a theatre would hear very little. Hearing over distance is mitigated by the reverberation in a good auditorium.
Therefore, there need to be a variety of surfaces for sound to reflect off in order for it to be heard in large spaces. Usually the shape of the auditorium Will regulate the type of sound produced, and there are many acoustic Studies that have been done to determine the ideal construction and shape of a music hall. The reverberation depends not only on the sounds being reflected off flat surfaces but also cloth, furniture, wallcoverings and wood.
There is a psychoacoustic element to reverberation as well. When we hear something that has been recorded in a large auditorium, the sound is bigger, the sounds blend differently and there is a different balance of sounds in each register. Although there are many arguments for what would be the perfect ambience for an orchestra or ensemble, it is important to remember that the reverberation itself is what projects the sound being a natural space.
So, the inverse square law dropoff is not only a result of the lack of acoustic projection, it is also the default setting for any sound. Not only does reverberation play a part in the perception of music in a space, but there is the default tendency for constructed instruments to compensate for the inverse square law dropoff by the shape of the chambers in instruments as well as the materials used in construction.