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Tension In a string Second Harmonic

  1. Jul 2, 2011 #1
    One string of a certian musical intrument is 79 cm long and it has a mass of 8.74 g. It is being played in a room where the speed of sound is 344m/s
    To what tension must you adjust the string so that when vibrating in its second overtone it produces a wavelenght of 3.39 cm

    v=sqrt(T/mu)
    f=nv/2l
    v=lambda f

    f=344/.0339=10147.49 hertz

    10147.49=v/l=sqrt(T/m/l)/l

    which gives me a tension of 710977.38 N which seems to large for a string on an instrument. Is that right?
     
    Last edited: Jul 2, 2011
  2. jcsd
  3. Jul 3, 2011 #2

    ehild

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    It is correct. Remember, the tension is force/m2 and the diameter of a string is in the mm range. Multiplying the tension with the cross section area of the string results in a small force.

    ehild
     
  4. Jul 3, 2011 #3
    But isnt the force really big?
     
  5. Jul 3, 2011 #4

    ehild

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    Yes, you are right, it is a very big force, I was mistaken. Are you sure that the data are correct?

    ehild
     
  6. Jul 3, 2011 #5
    thats what i was given but it seems to large to be reasonable
     
  7. Jul 3, 2011 #6

    ehild

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    I think the frequency is very high, that is why the tension is so impossibly great.

    ehild
     
    Last edited: Jul 3, 2011
  8. Jul 3, 2011 #7
    So you cant use the speed of sound as v in this problem?
     
  9. Jul 3, 2011 #8
    how about a f of 435.44 does that sound more reasonable

    that gives me 19698 N which still seems to high
     
    Last edited: Jul 3, 2011
  10. Jul 3, 2011 #9

    ehild

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    Your solution was correct. The force corresponds to the numerical data given. The given wavelength in air corresponds to a very high frequency.
    The mass is also too high. If the string is made of steel, the diameter can be of 1.3 mm.
    In case of a guitar string, for example, a typical diameter is of 0.5 mm and the tension of 100 N. But the mass would be about 1 g then.

    ehild
     
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