- #1

Gravitino22

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## Homework Statement

You have a rubber cord of relaxed length x. It be-

haves according to Hooke's law with a "spring con-

stant" equal to k. You then stretch the cord so it has

a new length equal to 2x. a) Show that a wave will

propagate along the cord with speed

v=[tex]\sqrt{\frac{2kx^{2}}{m}}[/tex]

b) You then stretch the cord further so that the cord's

length increases with speed v/3. Show that the wave

will propagate during the stretching with a speed that

is not constant:

v(t)=[tex]\sqrt{\frac{kx^{2}}{m}(1+t\sqrt{\frac{2k}{9m}})(2+t\sqrt{\frac{2k}{9m}})}[/tex]

## Homework Equations

strings wave propagation speed: v=[tex]\sqrt{\frac{T}{u}}[/tex]

hookes law: F=-kx

Where T is tension and u is linear mass density

## The Attempt at a Solution

On part A i used hookes law to obtain the tension: T = k2x (not sure how to explain the negative sign). And u=m/x ( i don't understand why would you use the orignal length of x to obtain the linear mass density instead of the new length of 2x). Basically plug that in into the equation waves propagation speed and you get the awnser.

My train of thought for part b is that if your length is changing at a constant rate of v/3 then so is thetension. The new tension would be given by

T(t)=vtk/3=([tex]\frac{tk}{3}[/tex])[tex]\sqrt{\frac{2kx^{2}}{m}}[/tex] then i plugged that in into the waves propgation speed equation for T and keeping u=m/x. And then iam stuck...iam not sure how to procceed from there any help/hint is appreciated.

Thanks :)!

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