Modal analysis of a rectangular room requires evaluation of the eigenvalues of the Helmholtz operator while taking into account the boundary conditions imposed on the walls of the room. When the walls have finite impedances, the acoustic eigenvalue equation becomes complicated and a numerical method that can find all roots within a given interval is required to solve it. In this study, the interval Newton/generalized bisection ͑IN/GB͒ method is adopted for solving this problem. For an efficient implementation of this method, bounds are derived for the acoustic eigenvalues and their asymptotic behavior explored. The accuracy of the IN/GB method is verified for a canonical problem by comparing the modal solution with the corresponding finite element solution. Furthermore, reverberation times estimated using the IN/GB method are compared to those calculated using the finite difference method. Through these examples, it is demonstrated that the IN/GB method provides a useful and efficient approach for estimating the acoustic responses of rectangular rooms with finite wall impedances.

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Computational models of head-related transfer functions (HRTFs) are useful in investigating the effects of echoes and reverberations in enclosures. These models may be computed at relatively low cost by geometric methods, such as the image source method. However, geometric methods typically ignore several important physical effects, such as diffraction, which effect the fidelity of the resulting HRTF. On the other hand, methods based on solving the wave equation, such as the finite element method, include these effects but tend to be computationally expensive. This study represents a Dirichlet-to-Neumann (DtN) map which significantly reduces the costs associated with using the the finite element method for computing HRTFs in a rectangular room, by analytically eliminating empty regions of the room. The DtN map for rooms with realistic impedance boundary conditions is developed. This work represents an extension of our previous approach for sound-hard rooms [Y. Naka, A.A. Oberai, and B.G. Shinn-Cunningham, Proc. 18th International Congress on Acoustics, Vol. IV, pp. 2477–2480 (2004)]. [Work supported by AFOSR.]