Ejercicio Exercise 2 · Física I URV 2025

Exercise 2 (10 punts). Kinematics of surface waves

A swimmer at sea notices that the waves propagate periodically with a sinusoidal profile. He estimates that the vertical distance from trough to crest is 0.45 m, and the distance between consecutive crests is roughly 1.8 m. In addition, he records that 12 full wave crests pass by every 2 minutes.

a)

Determine the harmonic wave equation $y(x,t)$ describing these surface waves, assuming propagation toward the swimmer along the positive direction. [2.5 points]

b)

Find the propagation speed of the wave. [1.5 points]

c)

Determine the oscillation velocity of the water particles at a distance of 10 m from where the waves were generated, at time $t = 5\text{ s}$. [2.5 points]

d)

What is the maximum speed that the oscillating water particles can reach? [2.5 points]