Chapter 12.2, Problem 44E

Water waves A snapshot of a water wave moving toward shore is described by the function z = 10 sin (2x – 3y), where z is the height of the water surface above (or below) the xy-plane, which is the level of undisturbed water.

a.    Graph the height function using the window [–5, 5] × [-5, 5] × [–15, 15].

b.    For what values of x and y is z defined?

c.    What are the maximum and minimum values of the water height?

d.    Give a vector in the xy-plane that is orthogonal to the level curves of the crests and troughs of the wave (which is parallel to the direction of wave propagation).