The Physic Concepts in the Designing of Concert Halls

A very important but little known acoustical phenomena is the Inverse Square Law. As a sound wave propagates spherically, the sound energy is distributed over the ever-increasing surface diameter of the wave front surface. So, when the distance from the source is doubled, the energy carried by the sound is spread over double the distance in all directions, or four times the original area. This means that the intensity will be reduced to a quarter of the original distance. For example, at three times the original distance from a particular source, the intensity will be reduced to one-ninth of that at the starting point. This is refered to as an inverse square law. The sound intensity from a point source of sound will obey the inverse square law if there are no reflections or reverberation.

Reverberation is the collection of reflected sounds from the surfaces in an enclosure like an auditorium. 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. However, too much reverberation makes the sounds run together with loss of articulation - the sound becomes muddy and garbled.

A measure that is used to characterize the reverberation in a room is the reverberation time. Technically speaking, the reverb time is the amount of time it takes for sound pressure level or intensity to decay to 1/1,000,000th (60 dB) of it's original value (or 1/1000th of it's original amplitude.) Longer reverberation times mean that the sound energy stays in the room longer before being absorbed. Reverberation time is associated with what we sometimes call the 'size' of the room. Concert halls have reverberation times of about 1.5 to 2 seconds.

The reverberation time is controlled primarily by two factors - the surfaces in the room, and the size of the room. The surfaces of the room determine how much energy is lost in each reflection. Highly reflective materials, such as a concrete or tile floor, brick walls, and windows, will increase the reverb time as they are very rigid. Absorptive materials, such as curtains, heavy carpet, and people, reduce the reverberation time (and the absorptivity of most materials usually varies with frequency). Bigger rooms tend to have longer reverberation times since, on the average, the sound waves travel a longer distance between reflections. The air in the room itself will also weaken the sound waves, reducing the reverberation time. This weakening varies with the humidity and temperature, and high frequencies are affected most.

The optimum reverberation time for an auditorium or room of course depends upon its intended use.