Acoustic design of small rectangular rooms: Normal frequency statistics

The subject of discrete modes in small rectangular rooms has been considered. A new procedure for selecting optimum geometric proportions of rooms has been proposed, taking into account the eigenfrequencies up to the Schroeder frequency and considering also the surface averaged sound absorption coefficient (α) of a given room. This new procedure leads to a series of plots describing the geometric proportions of small rectangular rooms corresponding to the smoothest frequency response for different absorption conditions. When taking α into account, the range of the acceptable dimension ratios X:Y has proved relatively wide, so the standard deviation calculated for the distances between subsequent modes does not exceed 1.5 (as in Bolt’s work). However, the range of the acceptable dimension ratios decreases with decreasing α and for mean absorption coefficient lower or equal 0.3 there are only a few of the ratios for which a uniform distribution of eigenmodes is obtained.