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Water wave/Deep water waves

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A water wave is called a deep-water wave if the water's depth is more than 1/4 of the wavelength. The speed of a deep water wave depends on its wavelength:

v = sqrt((g.lambda)/2pi).
Longer wavelengths travel faster. Let's apply to this to a standing wave. 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 3 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?

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