A one-dimensional harmonic wave is described by the equation: F(x, t) = Acos(kx - wt) a. Calculate the partial derivative and and write the wave equation 8y r2 ay at2 b. What is the relation between w and k? what do we call this relationship?Sketch it. c. What is the Group velocity? d. How the phase and group velocity are related through Rayleigh's formula? e. What is the difference between Non-Dispersive Waves and Dispersive Wave f. The general dispersion relation for one-dimensional surface gravity waves (not re- stricted to shallow water) traveling in the x-direction is w = k /gktanhk H - What is the phase speed for these waves? Are these waves dispersive? g. Calculate the speed of a shallow-water surface gravity wave for a fluid having a depth equal to the scale height of the atmosphere ( 8.1 km) (assume zero mean flow). How does this compare with the speed of sound?