- #1
craig.16
- 42
- 0
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 + [tex]\pi[/tex]), where all quantities are expressed in SI units.
i) Determine values (with appropriate units) for the period, wavelength, and phase
velocity of the wave. [3]
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+[tex]\omega[/tex]t)
Ek=1/2[/tex]mv2
The Attempt at a Solution
For part (i):
period, t=2[tex]\pi[/tex]/[tex]\omega[/tex]=2[tex]\pi[/tex]/200=[tex]\pi[/tex]/100=0.0314 seconds (3dp)
wavelength, [tex]\lambda[/tex]=2[tex]\pi[/tex]/k=2[tex]\pi[/tex]/4=[tex]\pi[/tex]/2= 1.57 m (3 sf)
phase velocity, v=[tex]\omega[/tex]/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 isn't right. Thanks in advance.