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Phase Velocity and Group Velocity in Cylindrical and Spherical Waves

Closed-form expressions are derived for phase velocity and group velocity in cylindrical and spherical sound waves. These are plotted and compared for orders 0, 1 and 2, but the expressions are general and may be applied to waves of any order. Dispersion characteristics of these waves are examined and discussed. The implications for thermodynamic applicability of the wave equation and for application of Huygens’ principle are discussed.

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