According to [ASTM C423], The SAA of a material corresponds to the arithmetic average of its 1/3 octave sound absorption coefficient values in diffuse field, $\alpha_{i}$, for the twelve 1/3 octave frequency band ranging from 200 to 2 500 Hz included:
| $\displaystyle{\frac{1}{12}\sum_{i=200Hz}^{i=2500Hz}\alpha_{i}}$ | (1) |
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 |
|---|---|
| 100 | 0.19 |
| 125 | 0.15 |
| 160 | 0.50 |
| 200 | 0.67 |
| 250 | 0.89 |
| 315 | 0.86 |
| 400 | 1.04 |
| 500 | 1.05 |
| 630 | 1.01 |
| 800 | 1.07 |
| 1 000 | 0.67 |
| 1 250 | 0.80 |
| 1 600 | 0.76 |
| 2 000 | 0.82 |
| 2 500 | 0.71 |
| 3 150 | 0.74 |
| 4 000 | 0.71 |
| 5 000 | 0.74 |
| 6 300 | 0.78 |
| 8 000 | 0.99 |
From measurement values above, the SAA is found to be equal to 0.86.
Comments
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.
References
[ASTM-C423] American Society for Testing and Materials Standard Test Method for Sound Absorption and Sound Absorption Coefficients by the Reverberation Room Method
[ISO 11654] International Organization for Standardization Acoustics -- Sound absorbers for use in buildings -- Rating of sound absorption
[Dur06] Duranteau M., Etude de matériaux à double porosité en champ acoustique complexe, ENTPE internship report, 2006 (in French).
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