Question

A surfer paddles to where the waves are sinusoidal with crests 14 m apart. He bobs a vertical distance 3.6 m from trough to crest, which takes 1.5 s. Find the wave speed, & describe the wave.

Answer 1

Answer:

v = 9.34 m/s

Explanation:

Given that,

The distance between crests, $\lambda=14\ m$

The vertical distance from trough to crest = 3.6 m

Time taken, t = 1.5 s

The amplitude of wave = vertical distance from trough to crest /2

= 3.6/2

= 1.8 m

The speed of the wave is given by :

$v=f\times \lambda\\\\=\dfrac{\lambda}{T}\\\\=\dfrac{14}{1.5}\\\\=9.34\ m/s$

So, the speed of the wave is 9.34 m/s.