Longitudinal and transverse sound velocities of Lennard-Jones systems are calculated at the liquid-solid coexistence using the additivity principle. The results are shown to agree well with the ``exact values obtained from their relations to excess energy and pressure. Some consequences, in particular, in the context of the Lindemanns melting rule and Stokes-Einstein relation between the self-diffusion and viscosity coefficients are discussed. Comparison with available experimental data on the sound velocities of solid argon at melting conditions is provided.
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