On "hearing the shape of drums": An experimental study using vibrating smectic films

Sunada's theorem provides a method for building pairs of drums of different shapes which possess the same spectrum of eigenfrequencies. Our study conc erns the isospectrality of a family of pairs of shapes built from seven tri angles. We model 2D drums using smectic films, which transverse vibrations in vacuum obey the Helmholtz wave equation with Dirichlet boundary conditio n. Our experiment allows us to completely characterize the eigenmodes: spec trum and eigenfunctions. We experimentally check that only the permutationa l symmetries inherent in the building schemes of the two isospectral shapes are relevant for isospectrality.