Chapter 6.10, Problem 70E

Wave velocity Use Exercise 69 to do the following calculations.

1. a. Find the velocity of a wave where λ = 50 m and d = 20 m.
2. b. Determine the depth of the water if a wave with λ = 15 m is traveling at v = 4.5 m/s.

69. Wavelength The velocity of a surface wave on the ocean is given by $v=\sqrt{\frac{g\lambda }{2\pi }\tanh \left(\frac{2\pi d}{\lambda }\right)}$ (Example 8). Use a graphing utility or root finder to approximate the wavelength λ of an ocean wave traveling at v = 7 m/s in water that is d = 10 m deep.