An examination of the steady-state solution of the differential equation governing indoor sound fields

The use of the characteristic functions to obtain a steady-state sound field is based on the completeness of the set of the characteristic functions. For absorptive boundaries, the characteristic functions are complex functions, and there is no proof in mathematics of whether the set of the characteristic functions is complete. In addition, the use of the characteristic functions to obtain a steady-state sound field of three-dimensional space requires the solving of a huge amount of the complex number image The aims of this paper are to examine whether the set of the characteristic functions can still be complete for strong absorptive boundaries and to provide a practical solving method for image.