5 2 points A type of ocean wave found near the equator called a Kelvin wave is described by the following equations du h g 0 t x du x h t H 0 Here h h x t is the height of water u and 9 and H are constants representing gravity and average water height u x t is the water s east west velocity 0 h a Eliminate u from the system of equations to find 32 gHh 0 Hint use Clairaut s Theorem b Solutions to equations involving waves typically look like Acos kx wt The coefficient w is a time frequency of the wave and k describes the wave s spatial frequency Treat A as a constant and substitute this solution into the equation you found in a What is the relationship between w and k c Assume k and w are positive We describe the velocity of waves in two ways The crest of a wave moves with phase speed A group of waves moves with group velocity Show that the phase speed and group velocity of a Kelvin wave are the same We call this type of wave nondispersive which means that it travels without changing shape Kelvin waves take about 2 months to go across the Pacific Ocean