Graphing To Find Linear Mass Density (Waves)

  1. 1. The problem statement, all variables and given/known data

    This is for a lab involving a rope being tied to a frequency generator on one end and a mass string on the other (creating tension on the rope) in order to create standing waves.

    I have to find the u (linear mass density which is kg/m for a rope by plotting it. This is the equation I'm supposed to plot f vs n/2L[sqrt(F)]

    I have the value for f (frequency), n, L (length), and F (tension in the string) so all I have to do is find u. I'm unsure however how plotting the above relation will give me the value for u using various frequencies.

    2. Relevant equations

    f = n/2L[sqrt(F/u)]

    f = frequency (hz)
    n = integer such as 1, 2, 3
    L = length such as 0.100 m
    F = Force of tension on the rope in N (mass*gravity)
    u = Linear mass density (kg/m or mass/length of rope)

    3. The attempt at a solution

    Rearranging the equation, I'm guessing u would be the slope in the relation above. And the slope will equal 1/sqrtu ? Also how many graphs should I draw if I have a changing value for n, L, and F? Would it be a seperate graph for each different value of L and F?
  2. jcsd
  3. If I fix sqrtF/2L then can I use n (harmonics) for the x values?

    Also, would the slope of the graph equal 1/u?
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