The relationship between eigenfrequency and image source distributions in rectangular rooms

A famous theorem of Herman Weyl links the eigenfrequency distribution of a room to its Green function. The underlying theory is presented here, and the decomposition of the Green function on the image sources, valid for rectangular rooms, is used to evaluate the eigenfrequency distribution. In this particular case, it reduces the computation of the modal density to the distribution of image sources. The modal density thus obtained is compared to classical modal theory, and a link to Maa's mode counting scheme is derived.