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Sensuality & Proportion

A primer in sound for architects.

reverberation

Hard surfaces reflect sounds back. Open windows let them escape. From a listener's perspective, with acute and spatially accurate hearing, the reverberation: the sound that comes back to you - is a key means of understanding the nature and properties of inhabited space - a three dimensional aural map.

Reverberation (the word comes from the Latin reverberare meaning to beat back) has long been observed although only in about 1900 was a quantitative method achieved for measuring and predicting this. The ability to quantify reverberation comes from conceiving sound as energy [1] that is 'soaked up'[2] by absorbent surfaces or escapes through openings.

A sound is made , say the blowing of a horn. The sound stops, one listens to the sound until it dies away. The time this takes is defined as the reverberation time of the space [3]. Imagine if a room were made of totally reflective surfaces, the sound would reverberate for ever. Or if there were no enclosure at all, the sound would immediately escape. Neither condition exists except in our imagination. The reverberation of a room is a result of the deployment of relatively reflective ('hard') and absorbent ('soft') surfaces [4]. Reverberant spaces are called 'wet', absorbent spaces are called 'dry'.

The SABINE equation predicts the reverberation time as:
T (reverberation time) = 0.16V (volume in metres) /A (sum of all absorptions).

It is accurate provided that the total absorption is not more than about a tenth of the reverberation time i.e. in 'normal' circumstances [5]. It takes no account of the shape of the room - this is a room-wide average picture - although it can be calculated for different sizes (wavelengths) of sound since materials will absorb different sized sounds at different rates.

In general the reverberation time of a room is proportional to the volume of the room and inversely proportional to the sum of all absorptions.

In reality every place within a room has its own specific reverberation and this is determined by the size and geometry of the space's boundaries and the sound being made as well as the acoustic qualities of the materials of enclosure. An example of this is a gothic cathedral, where each bay of the vault has faceted, hard surfaces which create local pockets of aural focus. So although reverberation time is a valuable basic measurement - which often throws up a fundamental issue - it should be seen as one step towards understanding a room's actual acoustics.

Some examples of reverberant spaces:

cathedrals 2 - 5 seconds
concert halls 1.2 -2.5 seconds
rooms for speech 0.9 - 1.5 seconds
bathrooms 0.5 - 2 seconds
bedrooms 0.5 seconds

Notes:
[1] The amounts of energy are small. For example the average speaking voice creates about 0.000024 watts of sound energy, a full orchestra at average loudness 0.09 watts, at maximum loudness about 70 watts [Jeans p229]
[2] that is to say converted into other forms of energy, usually heat
[3] The time required for the mean-square sound pressure in that room to decay from a steady state value by 60dB after the sound suddenly ceases.
[4] Examples of acoustically 'hard' surfaces are stone, brickwork, dense plaster on a solid backing, and 'soft' surfaces people, wool, expanded polystyrene. Physically hard and soft are loosely related to acoustically hard and soft. However there are some materials like glass, which perform quite differently at different wavelengths.
[5] Spaces with odd proportions such as shopping malls or tunnels, and spaces with focusing domes or vaults centred around ear level may give results that depart from the Sabine approximation.

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©Marcus Beale

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