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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)

E

_{k}=1/2[/tex]mv

^{2}

## 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):

E

_{k}=1/2[/tex]mv

^{2}=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.