Newton showed that the phase velocity of deep water (depth h >> wavelength 1) waves is given by, v, = (g/27)², where g is the gravitational acceleration, and where minor contribution due to surface tension has been neglected. Find the group velocity vg and how it is related to Vp. (b) In the shallow water (h << 2), v, = (gh)". Find vg and show how it relates to v,. 1/2

Newton showed that the phase velocity of deep water (depth h >> wavelength 1) waves is given by, v, = (g/27)², where g is the gravitational acceleration, and where minor contribution due to surface tension has been neglected. Find the group velocity vg and how it is related to Vp. (b) In the shallow water (h << 2), v, = (gh)". Find vg and show how it relates to v,. 1/2