# Displacement of a Transverse Wave on a String Question

## Homework Statement

Question 1
(a) The displacement of a transverse wave on a string is described by:
y(x, t) = 0.01 sin(4x + 200t + $$\pi$$), where all quantities are expressed in SI units.
i) Determine values (with appropriate units) for the period, wavelength, and phase
velocity of the wave. 
ii) Determine from first principles the average kinetic energy per metre of this wave on a
string of mass per unit length 5 × 10 -2 kg m-1.

## Homework Equations

y(x,t)=Asin(kx+$$\omega$$t)
Ek=1/2[/tex]mv2

## The Attempt at a Solution

For part (i):
period, t=2$$\pi$$/$$\omega$$=2$$\pi$$/200=$$\pi$$/100=0.0314 seconds (3dp)
wavelength, $$\lambda$$=2$$\pi$$/k=2$$\pi$$/4=$$\pi$$/2= 1.57 m (3 sf)
phase velocity, v=$$\omega$$/k=200/4=50ms-1

For part (ii):

Ek=1/2[/tex]mv2=1/2[/tex](5*10-2)(1.57)(50)2=98.1J

Just need confirmation on whether the first part is correct. As for the second part it was a blatant guess by using the SI units and knowing the original equation for kinetic energy, so I need some help on this one if it is incorrect. Also how do you do a fraction on this properly? I tried the first one in the "Above and Below" section but that isnt right. Thanks in advance.