Abstract
Abstract : The problem of reconstructing the density rho(x) of a vibrating string of length L from the knowledge of two spectra (lambda n)1 to infinity and (microns n) 1 to infinity is considered. The method of construction relies (i) on a formula for rho at an arbitrary point x=l in terms of the spectra (lambda n (l)) 1 to infinity and (microns n (l)) 1 to infinity associated with the natural frequencies of vibration of the portion (l, L) of the original string and (ii) on a set of first order differential equations for (lambda n(l))1 to infinity and (micron n (l)) 1 to infinity. The density is deduced by integrating these equations of the spectra and substituting in the above mentioned formula.
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