In DR V6I4 Part 1, we described a new algorithm that automatically determines optimum room dimensions for a rectangular room, within specified ranges for the length, width and height, given specified absorption coefficients for all boundary surfaces. This program, called the Room Sizer™, is now available commercially and expands RPG's catalog of optimization software offerings.

Prediction Models For the purposes of this discussion, the modal response of the room is defined as the frequency spectrum received by an omnidirectional microphone in a corner of the room, when the room is excited by a point source with a flat power spectrum placed in the opposite corner. Two possible models to predict the modal response are considered, a frequency-based modal decomposition model and a time-based image source model. For more details download "Room Dimensions for Critical Listening Rooms."

The modal decomposition model used is applicable when boundary impedances are large and real. The image source model is a fast prediction model for a cuboid room. The image solution of a rectangular enclosure rapidly approaches an exact solution of the wave equation as the walls of the room become rigid. Reflection factors are approximated to be purely real. Once the energy impulse response is obtained, it is Fourier Transformed to form the modal frequency response. For soft walls, the image source construct becomes less accurate, because representing the image sources as pure point sources is no long applicable. These inaccuracies become greater as the reflection order increases.

Prediction model critique
Both the modal decomposition and image source models offer a better representation of the sound field in the space than the simple modal frequency equation shown in Equation (1), DRV6I4 Part 1. This is primarily because the modal decomposition and image source models allow for absorption, but also because it is possible to calculate a quantity - the modal response - that is easier to relate to the listener experience. Both models, however, are not completely accurate. Figure 1 compares measurements in a listening room to the modal decomposition and image source models. The listening room has dimensions 6.9 x 4.6 x 2.8m. All the walls are smooth plastered concrete, except the back wall which was covered with diffusers. Some diffusers were also on the ceiling and the floor was covered with carpet.

Below 100 Hz, good agreement between the models and the measurement are shown. The agreement diverges above 100Hz, see Figure 1. Slightly better agreement can be achieved by taking more terms in the modal decomposition formula or more orders in the image model.

For the Room Sizer™ program, the image source model was favored over the modal decomposition model. This is because the image source model is considerably faster. For the modal decomposition model, all modes within the frequency range of interest must be considered, plus corrections for those outside the range must be done. In the image source model, all images contribute to the impulse response in a cuboid room. Consequently, using the image source model reduces the optimization time. The relationship between the modal decomposition and the image solutions for a loss-less room has been derived and shown to be equivalent for a rigid boundary.

The method for choosing room dimensions is based on a better prediction model than previous methods. There is, however, scope for future improvement. There are some basic problems with both the modal decomposition and image source models, and currently there are no established solutions to deal with these difficulties. For example, while absorption coefficients for surfaces are widely available, the surface impedances, which includes both phase and magnitude information, are not. Indeed, given that room surfaces at low frequencies will often not behave as isolated local reacting surfaces, defining a surface impedance can be problematical. Consequently, for this work an assumption of no phase change on reflection has to be made, which means that the models are more accurate for walls that are somewhat rigid.

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