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A pulse in a non-uniform string

  1. Jun 19, 2015 #1
    1. The problem statement, all variables and given/known data
    a non uniform string of length L and mass M, has a variable linear density given by μ=kx where k is the distance measured from one side of the string and k is a costant.
    a) find that M=(kL2)/2
    b) show that the time t required to a pulse generated from one side of the string arrives to the other side is given by
    t=√8ML/9F; where F is the tension of in the string

    2. Relevant equations
    μ=m/L...(1)
    v=√F/μ→→→t=Δx/√F/μ...(2)

    3. The attempt at a solution
    i got the first result
    μ=kx=m/l→→→m=kx*L and becouse x=L→→→m=xL2 and becouse the mass is not linear but it stil is distributed in all the string m=(xL2)/2
    the second part of the problem is where i have no idea of what to do where the 8/9 come from?
    and in the eq 2 the linear density is under the force but in the eq that the problem tells the linear density is above the force
     
    Last edited by a moderator: Jun 19, 2015
  2. jcsd
  3. Jun 19, 2015 #2
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