A water wave is called a deep-water wave if the water’s depth is more than one-quarter of the wavelength. Unlike the waves we’ve considered in this chapter, the speed of a deep-water wave depends on its wavelength:

v = √gλ/2π

Longer wavelengths travel faster. Let’s apply this to standing waves.
Consider a diving pool that is 5.0 m deep and 10.0 m wide. Standing water waves can set up across the width of the pool. Because water sloshes up and down at the sides of the pool, the boundary conditions require antinodes at x = 0 and x = L. Thus a standing water wave resembles a standing sound wave in an open-open tube.
a. What are the wavelengths of the first three standing-wave modes for water in the pool? Do they satisfy the condition for being deep-water waves?
b. What are the wave speeds for each of these waves?
c. Derive a general expression for the frequencies f_m of the possible standing waves. Your expression should be in terms of m, g, and L.
d. What are the oscillation periods of the first three standing wave modes?