Analytical Formulas for Efficient Calculations of Acoustic Field Inside a Hemi-Cylindrical Room Enclosed by a Quarter-Spherical Impedance Dome

Abstract The analytical formulas describing the acoustic field inside the hemi-cylindrical room with the quarter-spherical dome were obtained. The considered enclosure can represent an interior of a sacral or historical object, as well as a room of modern architectural design. It was assumed that a point source generates an acoustic field, and a sound energy can be absorbed by materials on the floor and on an inner surface of the dome. The two appropriate solutions were proposed. One of them describes the sound field inside the hemi-cylindrical part of the room, and the second one presents the sound field inside the dome. Then, these solutions were coupled with the use of the continuity conditions. The formulas and the methodology to calculate the eigenfrequencies of the considered room were also presented. The results given by the obtained formulas agree with those provided by the finite element method (FEM). Moreover, the numerical simulations proved that the use of the presented formulas to calculate the sound pressure amplitude can be more numerically efficient than the FEM and can provide more accurate results. This means that the obtained formulas can be used instead of the FEM to improve the analysis of the sound field inside the considered room. The presented formulas can be used to predict the acoustical behavior of the considered room and consequently to design the room with appropriate acoustic conditions. As an example, the distributions of the acoustic pressure amplitude were predicted by using the obtained formulas.