Acoustic Cues from Shapes between Spheres and Cubes

Solids of different shapes resonate according to their peculiar geometry. Although physics, for some fundamental shapes such as the cube and the sphere, provides explicit formulas for determining the modal frequencies, a general resonance analysis of 3-D shapes must be conducted using numerical methods. In this paper, Waveguide Meshes are used to model intermediate geometries between the cube and the sphere. This example is paradigmatic of the general problem of morphing 3-D shapes. We are interested in understanding how smooth shape transitions from sphere to cube translate into a migration of the resonating modes. This work is aimed at assessing the suitability of the waveguide mesh as a tool for such a research, and it is preliminary to further investigations involving human subjects.