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.
A theoretical method has been presented to describe sound decay in building enclosures and to simulate the room impulse response (RIR) employed for prediction of the indoor reverberation characteristics. The method was based on a solution of wave equation having the form of a series whose time-decaying components represent responses of acoustic modes to an impulse sound source. For small sound absorption on room walls this solution was found by means of the method of variation of parameters. A decay function was computed via the time-reverse integration of the squared RIR. Computer simulations carried out for a rectangular enclosure have proved that the RIR function reproduces the structure of a sound field in the initial stage of sound decay suffciently well. They have also shown that band-limitedness of the RIR has evident influence on the shape of the decay function and predicted decay times.