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.,[latex] \mathrm{T}_1=\frac{0.167 \mathrm{~V}}{\sum \mathrm{as}} [/latex]
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, [latex] \quad T_2=\frac{0.167 \mathrm{~V}}{\sum \mathrm{as}+\mathrm{a}_1 \mathrm{~s}_1} [/latex]
where a1 is the absorption coefficient of the material having area S1
eqn (3) and eqn (4)
[latex] \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} [/latex]
Subtracting Eqn (3) from Eqn (4)
[latex] \therefore \quad \frac{1}{\mathrm{~T}_{2}}-\frac{1}{\mathrm{~T}_{1}}=\frac{\mathrm{a}_{1} \mathrm{~s}_{1}}{0.167 \mathrm{~V}} [/latex]
[latex] \mathrm{a}_{1}=\frac{0.167 \mathrm{~V}}{\mathrm{~s}_{1}}\left(\frac{1}{\mathrm{~T}_{2}}-\frac{1}{\mathrm{~T}_{1}}\right) [/latex]
By knowing the values of T1 , T2 , V and S1 , the absorption coefficient (α1) of the given material is calculated.
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