Mean Intensity of Sound in an Auditorium and Optimum Reverberation

The optimum time of reverberation was determined experimentally for the piano, the violin, the violoncello, for bass and soprano voices and human speech in a room of 260 ${\mathrm{m}}^3$. The experimental determinations (1.08-1.14 sec.) give the mean value of 1.11 sec. An earlier investigation in a smaller hall of 126 ${\mathrm{m}}^3$ gave a mean optimum time of $T_{o}p=1.06\mathrm{}$ sec. It is evident that a mean intensity of sound exists which is the same for human speech and muiscal performances of different kinds, with respect to which our ear determines the optimum of the impression. The value of this intensity (${10}^{6n}$ times minimum audible intensity, $i$) is given by the formula: $1.333n+{log}_{10}\left(a{S}_1\right)=3.07\mathrm{}$. For $a{S}_1=49.5\mathrm{}$, the mean intensity is equal to ${10}^{6.019}$. From this, we have as the formula for the optimum time of reverberation, for a room of $W$ ${\mathrm{m}}^3$ volume: ${log}_{10}W=8.5+{log}_{10}{T}_{\mathrm{op}}-\frac{6.194}{2\sqrt{T_{\mathrm{op}}}}.$