Question

An ocean wave traveling in one direction has a wavelength of 1.0 m and a frequency of 1.25 Hz. Take the direction of wave propagation lo be the positive x direction.
(a) What is the speed (in m/s) of this ocean wave?
(b) Assuming that this wave is harmonic, and its amplitude is 2.0 m, what equation would describe its motion? Let the displacement at t = 0 s and x = 0 m be a maximum.
(c) What will be the height of the wave 3.0 m from the origin at t = 10 s?

Answer 1

Answer:

a) $v=1*1.25=1.25\: m/s$

b) $y(x,t)=2sin(2\pi( x-1.25 t)$  

c) $y(3,10)=1.73 m$    

Explanation:

a) The speed of a wave is given by the following equation:

$v=\lambda f$

Where:

λ is the wavelength

f is the frequency

$v=1*1.25=1.25\: m/s$

b) The harmonic wave has the following equation:

$y=Asin(kx-\omega t)$

A is the amplitude (2 m)

k is the wavenumber (2π/λ)  

ω is the angular frequency (2πf)

$y(x,t)=2sin(2\pi x-2\pi*1.25 t)$  

$y(x,t)=2sin(2\pi( x-1.25 t)$  

c) Here we need to find the heigth at x=3 m and t =10 s, so we need to find y(3,10).

$y(3,10)=2sin(2\pi(3-1.25*10)$

$y(3,10)=2sin(2\pi(3-1.25*10)$              

$y(3,10)=1.73 m$              

I hope it helps you!