  Sequences of nodal counts store information on the geometry (metric) of the
domain where the wave equation is considered. To demonstrate this statement, we
consider the eigenfunctions of the Laplace-Beltrami operator on surfaces of
revolution. Arranging the wave functions by increasing values of the
eigenvalues, and counting the number of their nodal domains, we obtain the
nodal sequence whose properties we study. This sequence is expressed as a trace
formula, which consists of a smooth (Weyl-like) part which depends on global
geometrical parameters, and a fluctuating part which involves the classical
periodic orbits on the torus and their actions (lengths). The geometrical
content of the nodal sequence is thus explicitly revealed.
