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Velocity of wave along a rubber cord

  1. May 15, 2010 #1
    ]1. The problem statement, all variables and given/known data

    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]

    2. Relevant 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

    3. The attempt at a solution

    I have part A down

    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)=k(vt/3 -2x)
    and the linear mass density
    u(t)=m/(vt/3 +2x)

    i plugged those into the velocity equation but i didnt get the result....Iam sure i have to use differentials but iam not so good at that so if anyone can point me in teh right direction
    Thanks :)![/QUOTE]
     
  2. jcsd
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