Scottish Sensory Centre

Improving the Listening Environment for Deaf Children in Educational Settings

Presented on Tuesday 13 May 2010

Dr Laurent Galbrun
School of the Built Environment
Heriot-Watt University, Edinburgh

Workshop 1 Calculating reverberation time

Objective
The aim of this workshop is to learn how to calculate the reverberation time in a room.
Delegates will observe how changing materials in a room affects reverberation time.

Method
The reverberation time of a room can be calculated using the formula

(1)

where V is the room's volume in m³ and A is the room's absorption in m², which can be calculated from

(2)

where Si is the surface area in m² and α; is the absorption coefficient of each room's surface.

Calculation
Consider a classroom with the following properties:

Dimensions: 5m × 8m × 2.5m (V=100 m³)
Materials: laminate flooring
plastered walls and ceiling

An example of the reverberation time calculation for this classroom is given below, at 500 Hz and at 1000 Hz. In this example, the total absorption A is equal to
floor walls ceiling

• 500 Hz

Using equation (2) and referring to the table of absorption coefficients given below, the absorption of the various surfaces can be calculated:

Hence the total absorption is found,

Using equation (1), the reverberation time is found to be equal to,

• 1000 Hz

Note that the reverberation time varies with frequency. For primary classrooms, the Building Bulletin 93 - Acoustic Design of Schools (Department for Education and Skills) recommends an upper limit for the mid-frequency reverberation time T_mf (average of 500 Hz, 1 kHz and 2kHz results) of 0.6 sec (0.4 sec for classrooms designed specifically for use by hearing impaired students). The values obtained are well above these recommended values.

Table 1.1 Absorption coefficients.

Material	125 Hz	250 Hz	500 Hz	1000 Hz
Plasterboard	0.03	0.03	0.02	0.04
Laminate flooring	0.15	0.1	0.1	0.1
Thin carpet	0.1	0.15	0.25	0.3
Thick carpet	0.2	0.25	0.35	0.4
Suspended ceiling	0.1	0.25	0.70	0.85
Wall panel (board)	0.3	0.3	0.35	0.4

Exercise: increasing absorption
Increase the absorption in the room by changing materials (eg; put a suspended ceiling, put a carpet, add notice boards etc.), and using the table of absorption given below (derived from surfaces and table of absorption coefficients), calculate the new reverberation time for each solution, at 500 Hz and at 1000 Hz. Observe how the reverberation time changes by gradually increasing absorption in the room, as well as differences between the 500 Hz and 1000 Hz results. Check which design comply with the Building Bulletin 93.

Calculate the total absorption A and hence the reverberation time using equation (1).

Table1.2 Absorption of materials.

Material		Absorption (m2)
		500 Hz	1000 Hz
Laminate flooring	Afloor	4	4
Plastered walls	Awalls	1.3	2.6
Plastered ceiling	Aceiling	0.8	1.6
Thin carpet	Afloor	10	12
Thick carpet	Afloor	14	16
Suspended ceiling	Aceiling	28	34
1 wall panel (2m x 2m)	Apanel	1.4	1.6
8 wall panels	Apanels	11.2	12.8

Table 1.3 Reverberation times calculated for a variety of designs.

Material	Reverberation time (sec)
	500 Hz	1000 Hz
Laminate flooring + plastered walls + plastered ceiling
Thin carpet + plastered walls + plastered ceiling
Thick carpet + plastered walls + plastered ceiling
Laminate flooring + plastered walls + suspended ceiling
Laminate flooring + plastered walls + plastered ceiling + 8 wall panels
Thin carpet + plastered walls + plastered ceiling + 8 wall panels
Thick carpet + plastered walls + plastered ceiling + 8 wall panels
Thick carpet + plastered walls + suspended ceiling
Thick carpet + plastered walls + suspended ceiling + 8 wall panels

Where next

• Improving the listening environment