New explicit solutions in acoustics of closed spaces on the basis of divergent series

Abstract

A new approach to the acoustics of closed spaces is developed that involves solutions for polygonal shapes in explicit form. It is shown that exact solutions can be constructed for polygonal geometries where all the interior angles are equal to π/n (n is an integer). It is stated that the set of such polygons consists of the rectangle (known result) and three types of triangles. Some new explicit formulas are obtained for the eigenfrequencies of the triangles. It is demonstrated that the proposed technique also permits an exact representation of the impulse response function for the geometries described.