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Displacement of a Transverse Wave on a String Question

  • Thread starter craig.16
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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 isnt right. Thanks in advance.
 

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