One can hear the composition of a string: experiments with an inverse eigenvalue problem (Q2879879)

The paper deals with a finite-dimensional inverse problem consisting in the determination of the positions and masses of beads vibrating on a string from the frequencies of vibration. The authors aim at giving an introduction to the inverse spectral theory accessible to students with an undergraduate background in linear algebra and illustrating it by numerics and mechanical experiments. A system of differential equations is derived, the experimental setup is introduced, and various algorithms are used for determining bead locations and masses from two sets of eigenvalues. Finally, it is confirmed, by using real data, that one set of eigenvalues suffices to reveal uniquely the locations and masses of symmetrically placed beads.