On the information content of natural frequency spectra associated with different angular numbers

The problem of inferring the speed of sound in a contained spherically symmetric fluid solely from its natural frequencies of vibration is considered. An investigation of the case in which the data consist of the two spectra associated with the angular numbers 0 and 1, suggests the possibility that a one-parameter family of slowness profiles can be constructed. These profiles are compatible with the data, up to first order in the non-uniformity of the fluid. It is conjectured that for other angular numbers, the loss of information increases as the difference between them increases.