Sound equalization in enclosures using modal reconstruction

The equalization of complex sound pressure in an enclosure is investigated in this paper. The sound field in the enclosure is modeled with the sum of a series of modes. This sound field is controlled by multiple sources distributed in the enclosure so that a certain region in the enclosure has a desired complex sound pressure. First, the optimum solution which minimizes the average potential energy of the error pressure over the region is derived, where the error is defined as the difference between the desired sound pressure and the sound pressure caused by the sources. By using the optimum solution, the achievable best performance can be known for the given region and the source distribution. The optimum solution can also be a useful tool for finding an effective source distribution since the performance of the optimum solution depends only on the source distribution. Furthermore, the eigenvalues of the source coupling matrix, which appears in the derivation of the optimum solution, indicates the effectiveness of the source distribution. The effectiveness of source distribution is discussed with nine examples of source distributions in a two-dimensional enclosure. The multipoint equalization method to approximate the optimum solution is also discussed for the practical use.