Velocity Dispersion of Isotropic Rods of Square Cross Section Vibrating in the Lowest-Order Longitudinal Mode

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Abstract
The velocity dispersion of the first-order longitudinal mode of two isotropic 24ST aluminum rods of square and circular cross sections has been investigated and the results compared with the experimental results of Morse and the theory of Nigro. It is shown that the theory of Nigro does not adequately account for the lowest-order velocity dispersion in a square rod. Morse observed that the velocity dispersion curves of a square and of a circular rod coincide as a function of diameter-to-wavelength ratio, provided the equivalent diameter of the square rod is assumed to be 1.13 times the thickness of the rod. An equivalent diameter of 1.155 times the thickness of the square rod is shown to be superior for the present experimental results, as it ensures almost full coincidence of the two dispersion curves over the full range of diameter-to-wavelength ratio.

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