## 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 m^{3} and A is the room's absorption
in m^{2}, which can be
calculated from

(2)

where Si is the surface area in m^{2} 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 m^{3})

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 (m^{2}) |
||

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 |