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Sound & Music - Tension of a string

  1. Apr 24, 2017 #1
    1. The problem statement, all variables and given/known data

    1. The A string on a violin has a fundamental frequency of 440Hz. The length of the vibrating portion is 32.4cm and has a mass of 0.340g. Under what tension must the string be placed?

    2. Relevant equations
    V = Fλ
    Vs = √t/μ

    3. The attempt at a solution
    I plugged in my info to determine V = 142.604
    then I attempted the second equation as:
    T = .340(142.604^2)
    This gave me the wrong answer
    I also tried:
    T = 1.049(142.604^2) - (.340g/.324m = 1.049g/m)
    This also gave me the wrong answer. I am not sure what to do
     
  2. jcsd
  3. Apr 24, 2017 #2
    Now I realize that v = 285.12. I forgot to multiple length by 2 to get the wavelength.
    But I still can't figure out the second equation
     
  4. Apr 25, 2017 #3

    gneill

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    Staff: Mentor

    Make sure that your units all match (pay attention to your units for μ).
     
  5. Apr 25, 2017 #4
    Should μ be kg/m?
    So... 0.00034/.324m = .001049kg/m?
     
  6. Apr 25, 2017 #5

    gneill

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    Staff: Mentor

    Yes.
     
  7. Apr 25, 2017 #6
    Okay so then I have

    .001049(285.12^2) = 85.277

    So the tension would need to be 85.277N?
     
  8. Apr 25, 2017 #7

    gneill

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    Staff: Mentor

    Looks right to me. Be sure to round to the required number of significant figures.
     
  9. Apr 25, 2017 #8
    Thank you so much!
     
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