  The distribution of eigenvalues of the wave equation in a bounded domain is
known as Weyl's problem. We describe several computational projects related to
the cumulative state number, defined as the number of states having wavenumber
up to a maximum value. This quantity and its derivative, the density of states,
have important applications in nuclear physics, degenerate Fermi gases,
blackbody radiation, Bose-Einstein condensation and the Casimir effect. Weyl's
theorem states that, in the limit of large wavenumbers, the cumulative state
number depends only on the volume of the bounding domain and not on its shape.
Corrections to this behavior are well known and depend on the surface area of
the bounding domain, its curvature and other features. We describe several
projects that allow readers to investigate this dependence for three bounding
domains - a rectangular box, a sphere, and a circular cylinder. Quasi-one- and
two-dimensional systems can be analyzed by considering various limits. The
projects have applications in statistical mechanics, but can also be integrated
into quantum mechanics, nuclear physics, or computational physics courses.
