Sound Decay in Home Cinema Rooms - April 18th, 2009
What happens in a home cinema room when a sound source is turned off? When this happens, the sound we hear is, of course, reverberation, the decay of many, many sound waves (or rays) excited by the source. This decay is quantified by the most important single-figure parameter in room acoustics: reverberation time (RT).
Sabine’s equation is the equation that really started the field of quantitative room acoustics. It allows the home cinema designers to predict a crucial aspect of the acoustics of the home cinema room - its RT - if we know the volume of the room and the total amount of acoustic absorption in the home cinema. Almost as soon as we have defined this useful equation for RT, however, we run into a problem - How should the home cinema designer calculate the total acoustic absorption in a room? One simply needs to weight the absorption coefficient of each surface in the cinema room by its area and sum them. This seems to work well enough for home cinemas with RTs which are not too short. (In home cinema design, an RT prediction error of less than about 0.1 s or 10% is usually the goal.)
However, Sabine’s equation does not work so well for rooms with a lot of absorption, like a dedicated home cinema, where we expect a short RT. Consider a dedicated home cinema room where all the surfaces have an absorption coefficient of 1.0 (such as an anechoic chamber). Sabine’s equation will give a non-zero RT for such a room. This is clearly impossible, since a room with perfectly absorbing boundaries does not support any reflections at all, much less reverberation.
Predicting RT in absorbent rooms (i.e. where the RT is expected to be less than about 0.5 s), like a dedicated home cinema installation, can be done more accurately using one of the several alternative reverberation time equations. The best known of these is that due to Norris and Eyring.