Vincent Repain
today professor at
Université Paris Diderot
Embedded Files
L2 UPS
Février 1998
Directed by
Catherine Even
today professor at
Université Orsay-Saclay
Marc Kac
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 .
Drawing of a smectic film on the "cocotte" frame
Evolution toward a constant thickness
Carolyn Gordon and David Webb
Experimental set-up used in this study. The detection of vibrations is optical. The spectra of smectic drums recorded with this set-up are shown below.
As expected, the frequencies of eigenmodes are identical.
Spectrum of eigen modes of the "cocotte" drum.
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