Total Absorption (Sabins)

The sabin is a strange and useful unit: it is an area. One metric sabin is one square metre of perfectly absorbing surface — an open window, essentially, since sound that leaves never comes back. Every real surface is quoted as a fraction of that ideal, the absorption coefficient $\alpha$, and multiplying area by coefficient converts any surface into the equivalent area of open window. Add them all up and the room has a single number describing how greedily it eats sound.

The unit is named for Sabine, and the imperial version — one square foot of perfect absorption — carries his name too, which is a well-laid trap. A "sabin" in a North American catalogue is usually the square-foot kind, and a metric sabin is 10.76 times larger. Mixing the two produces an answer wrong by an order of magnitude, and because reverberation time is inversely proportional to absorption, the error flatters: a room calculated in the wrong sabins looks far deader than it is.

A coefficient is only ever a coefficient at a stated frequency. Porous absorbers — mineral wool, acoustic foam, carpet, fabric-wrapped panels — work by viscous drag as air moves through them, so they need thickness comparable to a quarter wavelength to do anything. That makes a 25 mm panel excellent at 2 kHz, where a quarter wavelength is 43 mm, and nearly useless at 125 Hz, where it is 686 mm. Almost every disappointing acoustic treatment in the world is a thin porous product applied to a low-frequency problem. Membrane and Helmholtz absorbers exist precisely because low frequencies need a different mechanism.

Two habits keep this sum honest. Weight by area, always: a room is not the arithmetic mean of its coefficients, and the common shortcut of averaging the values on three data sheets ignores that the ceiling may be four times the area of the treated wall. And remember the objects. People, upholstered seating, drapery and open doorways are quoted directly in sabins per item rather than per square metre, and they go straight into the total — an audience is often the single largest absorber in a hall, which is why a room tuned while empty is wrong the moment it is used, and why concert halls use seats chosen to absorb about as much as the person who will sit in them.