Question

A surfing physicist paddles out beyond the breaking surf to a deep-water region where the ocean waves are sinusoidal (can obey a sine or cosine function) in shape, with crest 14 m apart. The surfer rises a vertical distance 3.6 m from wave trough to crest, a process that takes 1.5s. Find the wave speed, and describe it with an equation. Take a wave crest to be at x=0 at time = 0, with the positive x direction toward the open ocean.

Answer 1

The amplitude is A = 1.8 m, and the wavelength is L = 14 m. The period is P = 3.0 s. Use a cosine function to make the deflection a crest at t = 0 and x = 0.

y = A cos [2 pi (t/P - x/L]