A sinusoidal surface wave on a body of water that is significantly deeper than half the wave's wavelength has a phase speed of |v| = sqrt(|g|λ/2π) where |g| is the gravitational field strength at the earth's surface = 9.8 m/s². Note that this speed depends on wavelength, so deep water is a dispersive medium for water waves. Consider standing waves in a narrow rectangular pool that has length L and is sufficiently deep. Derive an expression (in terms of |g|, L, and some integer n) for the normal mode frequencies for waves in this pool. In particular, show that these frequencies are not integer multiples of some fundamental frequency. (Hint: Are the ends of the pool more analogous to the free or fixed ends of a string?)