A plane wave disturbance propagates in a medium with a linear dispersion law v = a + bl, where v is the phase velocity and a and b are constants. Show that whatever the disturbance, its shape, continuously changing, will be periodically restored after time t = dl/dv = 1/b. Show that the ratio of the path s traversed by the disturbance during the time interval t to the duration of this interval is equal to the group velocity.

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