How to find fundamental frequency

  1. 1. The problem statement, all variables and given/known data
    When a 70kg aluminum (density = 2.7 g/cm3) sculpture is hung from a steel wire, the fundamental frequency for transverse standing waves on the wire is 250.0 Hz. The sculpture (but not the wire) is then completely submerged in water. What is the new fundamental frequency?


    2. Relevant equations
    f=ma
    fundamental frequency = (1/2L)((Tensional force/linear density)^1/2)


    3. The attempt at a solution
    250=(1/2L)((686N/u)^1/2))
    (stuck there)
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. rl.bhat

    rl.bhat 4,435
    Homework Helper

    According to the Archimedes principle, the loss of weight is equal to the weight of the displaced liquid. In the problem the liquid is the water whose density is 1 g/cm^3.
    Hence when the sculpture is immersed in water, the new tension is
    T' = mg - mg*ρ(w)/ρ(Al)
    The frequency is directly proportional to the square root of the tension. Hence
    f/f' = sqrt(T/T')
    250/f' = sqrt[1/(1 - 1/2.7)]
    Now solve for f'.
     
    Last edited: Sep 5, 2010
  4. so in this equation, the 70kg value does not matter?

    by the way, thanks a lot! :)
     
  5. rl.bhat

    rl.bhat 4,435
    Homework Helper

    Since we are taking the ratio of tensions, 70 kg does not matter.
     
  6. thank you!
     
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