A Novel Method for Determining Optimum Dimension Ratios for Small Rectangular Rooms

Abstract

A new method for determining optimum dimension ratios for small rectangular rooms has been presented. In a theoretical model, an exact description of the room impulse response was used. Based on the impulse response, a frequency response of a room was calculated to find changes in the sound pressure level over the frequency range 20–200 Hz. These changes depend on the source and receiver positions, thus, a new metric equivalent to an average frequency response was introduced to quantify the overall sound pressure variation within the room for a selected source position. A numerical procedure was employed to seek a minimum value of the deviation of the sound pressure level response from a smooth fitted response determined by the quadratic polynomial regression. The most smooth frequency responses were obtained when the source was located at one of the eight corners of a room. Thus, to find the best possible dimension ratios, in the numerical procedure the optimal source position was assumed. Calculation results have shown that optimum dimension ratios depend on the room volume and the sound damping inside a room, and for small and medium volumes these ratios are roughly 1 : 1.48 : 2.12, 1 : 1.4 : 1.89 and 1 : 1.2 : 1.45. When the room volume was suitably large, the ratio 1 : 1.2 : 1.44 was found to be the best one.