Waves on deep water with surface tension T and density p are governed by the dispersion relation: ² = gk +k³, where w is the angular frequency of the wave, k the wavenumber, and g is a constant. Calculate: 1- The phase and group velocities of the waves. 2- The critical wavenumber, ke, when the phase speed of the wave reaches a minimum.

Waves on deep water with surface tension T and density p are governed by the dispersion relation: ² = gk +k³, where w is the angular frequency of the wave, k the wavenumber, and g is a constant. Calculate: 1- The phase and group velocities of the waves. 2- The critical wavenumber, ke, when the phase speed of the wave reaches a minimum.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter13: Continuous Systems; Waves

Section: Chapter Questions

Problem 13.18P

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