Europhys. Lett, 47 (5), pp. 531-537 (1999)

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

C. Even and P. Pieranski

Laboratoire de Physique des Solides, Université Paris-Sud, Bât. 510 - 91405 Orsay, France

(received 28 September 1998; accepted in final form 1 July 1999)

PACS. 03.65Ge - Solutions of wave equations: bound states.
PACS. 43.40Dx - Vibrations of membranes and plates.
PACS. 68.15 - Liquid thin films.

Abstract:

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

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