The properties of acoustic kinetic energy density and total energy density of sound fields in lightly damped enclosures have been explored thoroughly in the literature. Their increased spatial uniformity makes them more favorable measurement quantities for various applications than acoustic potential energy density (or squared pressure), which is most often used. In this dissertation, a new acoustic energy quantity, the generalized acoustic energy density (GED), will be introduced. It is defined by introducing weighting factors, α and 1 − α, in the formulation of total acoustic energy density. With the additional degree of freedom, the GED can conform to the traditional acoustic energy density quantities, or be optimized for different applications. The properties and applications of the GED are explored in this dissertation. For enclosed sound fields, it was found that GED with α = 1/4 is spatially more uniform than the acoustic potential energy density, acoustic kinetic energy density, and the total acoustic energy density, which makes it a more favorable measurement quantity than those traditional acoustic energy density quantities for many indoor measurement applications. For some other applications, such as active noise control in diffuse field, different values of α may be considered superior. The numerical verifications in this research are mainly based on a hybrid modal expansion developed for this work, which combines the free field Green's function and a modal expansion. The enclosed sound field is separated into the direct field and reverberant field, which have been treated together in traditional modal analysis. Studies on a point source in rectangular enclosures show that the hybrid modal expansion converges notably faster than the traditional modal expansions, especially in the region near the source, and introduces much smaller errors with a limited number of modes. The hybrid modal expansion can be easily applied to complex sound sources if the free field responses of the sources are known. Damped boundaries are also considered in this dissertation, and a set of modified modal functions is introduced, which is shown to be suitable for many damped boundary conditions.



College and Department

Physical and Mathematical Sciences; Physics and Astronomy



Date Submitted


Document Type





acoustic energy density, statistical room acoustics, modal analysis, acoustic measurement, active noise control