Random Sound Fields in Rooms

Responses excited by random noise may exhibit a trend of frequency characteristics of sound paths. This chapter deals with temporal-spatial distributions of reverberation according to the linear system theory. Random sound field may not be uniform, because in-phase summation is possible between direct and reflection or scattered waves on the boundary. Reverberation decay curves are written by a superposition for \(3-\) , \(2-\) , and 1-dimensional fields. The formulation is a hybrid of the wave-theoretic and geometric-acoustical approaches such as the modal density and mean-free-paths. Thus, inherent frequency characteristics in room shape might be well presented by the hybrid formulation. Phase differences in reverberation between a pair of spatial points would be a basis for binaural hearing such as subjective diffuseness or sound image perception. This chapter may imply a function theoretic approach to binaural sound fields, where cepstral analysis may be the key to a bridge between the phase and energetic sound nature. Spatial or inter-aural correlations in random sound field follows a sinc function of the equivalent distance between a pair of receiving positions. The correlation functions imply binaural sound fields constructed by inter-aural level difference with a time delay.