The spectra of eigenmodes of drums in two dimensions depend on their shapes. Can one deduce univoquely the shape of a drum from its spectrum ? Or, in other words, as it has been asked by Mark Kac :

Can one hear the shape of a drum ?

The answer to this question is NO and has been given by Wolpert, Gordon and Web who invented a pair of drums of different shapes but having the same spectra of eigenmodes. This first pair of isospectral drums is shown in the figure below. We used Smectic Films vibrating in vacuum for an experimental demonstration of the isospectrality of these drums .