Does anyone knows the application and Significance of group velocity?
Sure, gravity waves on water is the physical exemplar.
Remember that the water particles (group) have an epicyclic motion and low speed compared to the speed of the wave phase speed on which one surfs.
Every time you send information on a wave - i.e. you modulate it in some way, the speed of transmission of the information is the group velocity. Wiki gives a pretty good summary of the meaning and significance of group velocity here.
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