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Wave Equation applied to a spring with longitudinal waves?

  1. Sep 23, 2013 #1
    1. The problem statement, all variables and given/known data
    A spring of mass m, stiffness s and length L is stretched to a length L + l. When longitudinal waves propagate along the spring the equation of motion of a length dx may be written pdx second partial derivative of n with respect to t = partial derivative of F with respect to x dx where p is the mass per unit length of the spring, n is the longitudinal displacement and F is the restoring force. Derive the wave equation to show that the wave velocity v is given by v^2 = s(L + l)/p.


    2. Relevant equations
    Wave Equation



    3. The attempt at a solution
    I tried comparing the situation with that of longitudinal waves within a solid, and using young's modulus. However, I couldn't quite get the wave velocity v as that and I am a little confused as to where to start.
     
  2. jcsd
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