A diffuse sound field in reverberation rooms is essential for reliable acoustic measurements, yet is still difficult to characterize, and its properties (homogeneity and isotropy) are usually treated separately. This thesis develops and validates a unified framework to describe the relationship between these properties using two descriptors: the modal density (which describes isotropy); and the inter-modal distance (which characterizes spatial homogeneity).
Numerical simulations were conducted using sound source position as a controlled variable to generate different sound-field configurations. These configurations were analyzed using the proposed descriptors to identify which source positions promote more isotropic or more homogeneous behaviour, leading to the formulation of hypotheses that were subsequently validated through experimental measurements in a reverberation room using a one-dimensional microphone array.
The results show that increasing modal density improves both isotropy and homogeneity, explaining why these properties are often assumed to be equivalent in practice. However, this equivalence is only partial. At relatively high modal density, spatial homogeneity is governed primarily by the minimum inter-modal distance, demonstrating that isotropy and homogeneity are distinct yet complementary aspects of sound-field diffuseness.
These findings are further interpreted within a conceptual framework based on statistical mechanics, using an ideal gas analogy. In this context, a diffuse sound field emerges only when a large number of room modes are excited (isotropy) and their mutual interactions remain negligibly small (homogeneity).