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Solving for linear mass density of a string

  1. Mar 29, 2012 #1
    HELP: Solving for equation of linear mass density of a string

    1. The problem statement, all variables and given/known data
    You will plot frequency vs. number of segments and determine a slope. Write the expression which will allow you to solve for the linear mass density of the string in terms of L, T, and the slope of your plot

    2. Relevant equations
    1) μ=M/L
    2) T=2∏√(m/k) ???
    3) λ=2L/n
    4) df/dn=???
    5) k=2∏/λ

    3. The attempt at a solution
    So what I've done is take equation 2 solve for m which is m=(T/2∏)2*k, with substitution from equation 5, then substitution from equation 3 to get the equation:
    m=(T2*n)/(4∏L) which I substituted into equation 1 to get:
    μ=(T2*n)/(4∏L2)
    So so far I have the equation in terms of L and T but not in terms of the slope of my plot which would be df/dn.

    Thanks!
     
    Last edited: Mar 29, 2012
  2. jcsd
  3. Mar 29, 2012 #2
    So I completely redid the problem a different way and I think this is right. Let me know if it is or not:
    Equations:
    1) v=√(T/μ)
    2) v=(2Lf)/n

    Attempt at solution:
    Solve equation 1 for μ=T/v2, then solve equation 2 for f=vn/2L. Then derive f equation to get in terms of df/dn (slope of graph)= v/2L, solve for v, v=(df/dn)*2L and plug into the equation for μ to get μ=T/((df/dn)*2L)2.
    This works right?
     
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