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Standing waves and banjo string

  1. Oct 19, 2011 #1
    1. A banjo string 36.0 cm long oscillates in a standing wave pattern. It resonates in its
    fundamental mode at a frequency of 250 Hz. What is the tension in the string if 80.0 cm of the
    string has a mass of 0.75 grams?



    2. Relevant equations

    k=2pi/lamda
    velocity=sqrt(F_tension/miu)
    miu=m/l
    w=2pif

    3. The attempt at a solution
    v=sqrt(F_t/miu)
    solved for miu and plugged into equation: 7.5*10^-4/.8
    v=lamdaf
    L=lamda/2
    --> v=2Lf
    v=2(.8)(250)
    then equated both equations

    i think i got confused with which length to use
     
  2. jcsd
  3. Oct 19, 2011 #2
    I think your work is ok.

    Yes - mu =m/L and for fundamental frequency lambda = 2L.
     
  4. Oct 19, 2011 #3
    I'm not sure when to use the length of the banjo string (36cm) :[
     
  5. Oct 19, 2011 #4
    When the string is vibrating in its first overtone, i.e. its second harmonic, then the length of string will be the wavelenght.
     
  6. Oct 19, 2011 #5
    thank u. my answer is still incorrect.... i would appreciate any more help. thank you
     
  7. Oct 19, 2011 #6
    May I correct my own contribution above.

    mu = m/L where L = 0.80m but lambda = 2 x 0.36 since this is the length which is oscillating.
     
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