Determination of Absorption Coefficient

Let V be the volume of a hall and be the total absorption in the hall. First the reverberation time in a hall of volume V is measured without keeping the absorbing material. It is given by Sabine’s formula.

eqn (1)

i.e., $\mathrm{T}_1=\frac{0.167 \mathrm{~V}}{\sum \mathrm{as}}$

Now, the absorbing material whose absorption coefficient to be determined is kept in the hall and the reverberation time is measured.

eqn (2)

It is given by, $\quad T_2=\frac{0.167 \mathrm{~V}}{\sum \mathrm{as}+\mathrm{a}_1 \mathrm{~s}_1}$
where a₁ is the absorption coefficient of the material having area S₁

eqn (3) and eqn (4)

$\begin{aligned} \therefore \quad \frac{1}{\mathrm{~T}_1} & =\frac{\sum \mathrm{as}}{0.167 \mathrm{~V}} \\ \frac{1}{\mathrm{~T}_2} & =\frac{\sum \mathrm{as}+\mathrm{a}_1 \mathrm{~s}_1}{0.167 \mathrm{~V}} \end{aligned}$