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=gλ2π−−√ . 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. 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=gλ2π−−√ . 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.
What are the wavelengths of the first three standing-wave modes for water in the pool?
