Modeling Reverberation Time

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.

当声波在房间内撞击到表面时，其中一部分会被吸收，另一部分会传入表面。这两部分的损失都会从房间中消失，这种分数损失由吸收系数a来表征，其值在0到1之间，1表示完全吸收。

Absorption coefficient = a
Effective absorbing area = aS

吸收系数 = a 有效吸收面积 = 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.

有效吸声面积是确定礼堂混响时间的一个因素。表面的吸音系数通常随频率变化，因此混响时间也具有频率依赖性。可以使用吸音系数表进行 Sabine 公式中的混响时间计算。

Table of absorption coefficients

吸收系数表

Index

Auditorium acoustics

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Sabine Formula Discussion

Sabine 公式讨论

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:

Sabine 公式对于中等大小的音乐厅来说工作得相当好，但不应视为精确的关系。它倾向于高吸音系数的封闭空间中高估混响时间。对于此类封闭空间，使用总体平均吸音系数可以得到更好的近似值：

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

请注意，这会减少计算出的混响时间。Sabine 公式也忽略了空气吸收，这在大型音乐厅中可能具有显著影响。

Table of absorption coefficients

吸收系数表

Index

Auditorium acoustics

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Table of Absorption Coefficients

吸收系数表

Nature of surface 表面的本质	Sound Absorption Coefficients at Frequency(Hz) 频率(Hz)下的声音吸收系数
	125	250	500	1000	2000	4000
Acoustic tile, rigid mount 声学瓷砖，刚性安装	0.2	0.4	0.7	0.8	0.6	0.4
Acoustic tile, suspended 悬浮的声学瓷砖	0.5	0.7	0.6	0.7	0.7	0.5
Acoustical plaster 声学石膏	0.1	0.2	0.5	0.6	0.7	0.7
Ordinary plaster, on lath 木制隔板上的普通石膏	0.2	0.15	0.1	0.05	0.04	0.05
Gypsum wallboard, 1/2" on studs 石膏板墙，隔板间距1/2英寸	0.3	0.1	0.05	0.04	0.07	0.1
Plywood sheet, 1/4" on studs 胶合板板，1/4英寸的板	0.6	0.3	0.1	0.1	0.1	0.1
Concrete block, unpainted 未涂装的混凝土块	0.4	0.4	0.3	0.3	0.4	0.3
Concrete block, painted painted concrete block	0.1	0.05	0.06	0.07	0.1	0.1
Concrete, poured 现浇混凝土	0.01	0.01	0.02	0.02	0.02	0.03
Brick 砖块	0.03	0.03	0.03	0.04	0.05	0.07
Vinyl tile on concrete 在混凝土上的乙烯基地板	0.02	0.03	0.03	0.03	0.03	0.02
Heavy carpet on concrete 重地毯在混凝土上	0.02	0.06	0.15	0.4	0.6	0.6
Heavy carpet on felt backing 厚重的毛毡背衬地毯	0.1	0.3	0.4	0.5	0.6	0.7
Platform floor, wooden 木质平台地板	0.4	0.3	0.2	0.2	0.15	0.1
Ordinary window glass 普通窗玻璃	0.3	0.2	0.2	0.1	0.07	0.04
Heavy plate glass 厚玻璃板	0.2	0.06	0.04	0.03	0.02	0.02
Draperies, medium velour 窗帘，中等绒面	0.07	0.3	0.5	0.7	0.7	0.6
Upholstered seating, unoccupied 未占用的软垫座椅	0.2	0.4	0.6	0.7	0.6	0.6
Upholstered seating, occupied 有扶手的座椅，被占用	0.4	0.6	0.8	0.9	0.9	0.9
Wood seating, unoccupied 木椅，空置	0.02	0.03	0.03	0.06	0.06	0.05
Wooden pews, occupied 木制长椅，有人坐	0.4	0.4	0.7	0.7	0.8	0.7

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

Definition of absorption coefficient

吸收系数的定义

Calculation of reverberation time

混响时间的计算

Hall, 第2版，表15.1的数据

Index

Auditorium acoustics

Reference
Hall

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Air Absorption

空气吸收

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:

在计算音乐厅的混响时间时，通常忽略空气吸收，但对于大型空间，它可能会变得显著。空气吸收在高频时更大，并且取决于空气温度和相对湿度。Rossing报告了以下数值以及Sabine公式的变化：

Air absorption m per cubic meter: 空气吸收率（每立方米）：
Air at 空气在	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: 每立方英尺空气吸收量：
Air at 空气在	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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