# Example

The figure below presents the Sabine sound absorption coefficients in third octave bands for a 40-mm thick rock wool. Measurement were performed by Mickael Duranteau in 2006 [Dur06] at ENTPE (two vertical red lines are reported at frequencies 200 Hz and 2 500 Hz to identified absorption values considered to compute the SAA).

The measured sound absorption coefficient $\alpha_{i}$ per 1/3 octave band are reported in the table below.

1/3 octave freq. Absorption measured
1000.19
1250.15
1600.50
2000.67
2500.89
3150.86
4001.04
5001.05
6301.01
8001.07
1 0000.67
1 2500.80
1 6000.76
2 0000.82
2 5000.71
3 1500.74
4 0000.71
5 0000.74
6 3000.78
8 0000.99

From the measurement values above, the SAA is found to be equal to 0.86.

The Sound Absorption Average should be used with care:

• The frequency range used to compute the SAA is quite limited compared to the human hearing frequency area [20 - 20 000] Hz. In particular, the third octave bands around 4 000 Hz are not used in its computation.
• The third octave values used are equally weighted which does not correspond to the natural sensitivity of sound by a human ear.

# Script

Follow the link compute_SAA.m to download a Matlab/GNU Octave script which compute the Sound Absorption Average from 1/3 octave band measurements.
% Compute the Sound Absorption Average (SAA)
% from absorption measurements in diffuse field.
%
% Measurements performed on a 40 mm-thick rock wool
% by Mickael Duranteau during his 'DEUST VAS 2'
% internship at ENTPE in 2006.
%
% Commands for the rotation of tick labels are
% borrowed from rotateticklabel.m
%   Written Oct 14, 2005 by Andy Bliss
%   Copyleft 2005 by Andy Bliss
%
% Everything else is copyleft 2006 luc.jaouen@matelys.com
% cf. APMR on the web,
% Standards/SAA