Use dimensional analysis to determine the dispersion relation (k) for surface tension waves (up to a multiplicative constant), which can only depend on the surface

Use dimensional analysis to determine the dispersion relation ω(k) for surface tension waves (up to a multiplicative constant), which can only depend on the surface tension σ, the density ρ, and the wave number k. Find the phase velocity and the group velocity, and show that v_g = 3v_p/2. Describe how you could distinguish visually between gravity waves and surface waves by observing the way that individual wave crests move through a wave packet.