Modeling Reverberation Time

Sabine is credited with modeling the reverberation time with the simple relationship which is called the Sabine formula:

where V is the volume of the enclosure and

and a is the absorption coefficient associated with a given area S.

Discussion

Calculation

Estimating reverberation time from sound decay

Index

Auditorium acoustics

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Sound Absorption Coefficient

When a sound wave in a room strikes a surface, a certain fraction of it is absorbed, and a certain amount is transmitted into the surface. Both of these amounts are lost from the room, and the fractional loss is characterized by an absorption coefficient a which can take values between 0 and 1, 1 being a perfect absorber.

Absorption coefficient = a
Effective absorbing area = aS

The effective absorbing area is a factor in determining the reverberation time of an auditorium. The absorption coefficient of a surface typically changes with frequency, so the reverberation time is likewise frequency dependent. A table of absorption coefficients can be used in calculations of reverberation time with the Sabine formula.

Table of absorption coefficients

Index

Auditorium acoustics

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Sabine Formula Discussion

The Sabine formula works reasonably well for medium sized auditoriums but is not to be taken as an exact relationship. It tends to overestimate the reverberation times for enclosures of high absorption coefficient. A better approximation for such enclosures utilizes an overall average absorption coefficient:

Note that this reduces the calculated reverberation time. The Sabine formula also neglects air absorption, which can be significant for large auditoriums.

Table of absorption coefficients

Index

Auditorium acoustics

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Table of Absorption Coefficients

Nature of surface	Sound Absorption Coefficients at Frequency(Hz)
	125	250	500	1000	2000	4000
Acoustic tile, rigid mount	0.2	0.4	0.7	0.8	0.6	0.4
Acoustic tile, suspended	0.5	0.7	0.6	0.7	0.7	0.5
Acoustical plaster	0.1	0.2	0.5	0.6	0.7	0.7
Ordinary plaster, on lath	0.2	0.15	0.1	0.05	0.04	0.05
Gypsum wallboard, 1/2" on studs	0.3	0.1	0.05	0.04	0.07	0.1
Plywood sheet, 1/4" on studs	0.6	0.3	0.1	0.1	0.1	0.1
Concrete block, unpainted	0.4	0.4	0.3	0.3	0.4	0.3
Concrete block, painted	0.1	0.05	0.06	0.07	0.1	0.1
Concrete, poured	0.01	0.01	0.02	0.02	0.02	0.03
Brick	0.03	0.03	0.03	0.04	0.05	0.07
Vinyl tile on concrete	0.02	0.03	0.03	0.03	0.03	0.02
Heavy carpet on concrete	0.02	0.06	0.15	0.4	0.6	0.6
Heavy carpet on felt backing	0.1	0.3	0.4	0.5	0.6	0.7
Platform floor, wooden	0.4	0.3	0.2	0.2	0.15	0.1
Ordinary window glass	0.3	0.2	0.2	0.1	0.07	0.04
Heavy plate glass	0.2	0.06	0.04	0.03	0.02	0.02
Draperies, medium velour	0.07	0.3	0.5	0.7	0.7	0.6
Upholstered seating, unoccupied	0.2	0.4	0.6	0.7	0.6	0.6
Upholstered seating, occupied	0.4	0.6	0.8	0.9	0.9	0.9
Wood seating, unoccupied	0.02	0.03	0.03	0.06	0.06	0.05
Wooden pews, occupied	0.4	0.4	0.7	0.7	0.8	0.7

Data from Hall, 2nd. Ed., Table 15.1

Definition of absorption coefficient

Calculation of reverberation time

Index

Auditorium acoustics

Reference
Hall

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Air Absorption

Air absorption is usually neglected in calculations of reverberation times for auditoriums, but for large enclosures it may become significant. Air absorption is greater for high frequencies and is dependent upon air temperature and relative humidity. Rossing reports the following values and the modification of the Sabine formula:

Air absorption m per cubic meter:
Air at	2000 Hz	4000 Hz	8000 Hz
20°C, 30% RH	0.012	0.038	0.136
20°C, 50% RH	0.010	0.024	0.086

Air absorption m per cubic foot:
Air at	2000 Hz	4000 Hz	8000 Hz
20°C, 30% RH	0.004	0.012	0.041
20°C, 50% RH	0.003	0.007	0.026

Index

Auditorium acoustics

Reference
Rossing
Science of Sound

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