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Velocity of Transverse Waves problem

  1. May 28, 2012 #1
    1. The problem statement, all variables and given/known data
    Two children are sending signals along a cord of total mass 0.54 kg tied between tin cans with a tension of 37 N. It takes the vibrations in the string 0.53 s to go from one child to the other. How far apart are the children?

    Express your answer using two significant figures


    2. Relevant equations
    Velocity of transverse wave on a cord = sqrt(F_t/[itex]\mu[/itex])
    F_t = Tension Force
    [itex]\mu[/itex] = mass per unit length -> m/l

    3. The attempt at a solution
    I attempted plugging the given values into the formula for velocity of a transverse wave on a cord, and came up with a distance of 4.387 meters. However, after getting the problem wrong (on masterphysics) I realized that the mass given for the cord is its total mass rather than mass per unit length. Seeing as what I am asked to find is the distance between the children (length of the cord) I dont see any way of solving this problem. Am i simply missing the proper formula? Any help would be greatly appreciated.
     
  2. jcsd
  3. May 28, 2012 #2
    Hello rusty65!! :smile:

    The mass per unit length, as you've written in your relevant equations is m/l. Putting this into the velocity equation and multiplying by time,

    [itex]vt = t\sqrt{\frac{lF}{{m}}}[/itex]

    What is "vt" in that above equation? :wink:
     
  4. May 29, 2012 #3
    vt is equal to the distance, but the trouble im having is that the distance, d, that i am attempting to find is equal to the length of the string, l. So i must either be using the wrong formula, or some key piece of information is escaping me.

    This is where im at right now, using the information given:

    d = t√((F_t * l)/m) ---plugged in----> d = 0.53√(37l/0.54)

    So ive still got two unknowns, d and l, which, according to the wording of the problem, seem to me to be equal to one another. :confused:
     
  5. May 29, 2012 #4
    Scratch that, I figured it out!

    Since d = l, I replaced l with d in the equation.

    d = 0.53sqrt(37l/0.54) ---> d = 0.53sqrt(37d/0.54)
    d/sqrt(d) = 0.53sqrt(37/0.54) ---> d/sqrt(d) = 4.387
    d/sqrt(d) = d^(1/2) ---> sqrt(d) = 4.387
    d = (4.387)^2
    d = 19.246!

    Took me a while to get it through my thick head, but I got it now. And thanks for the help!
     
  6. May 29, 2012 #5
    Yep! That is what I was suggesting. Good to see you figured it out :smile:
     
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