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Tension In musical strings and wavelength

  1. Mar 24, 2009 #1
    1. The problem statement, all variables and given/known data

    One string of a certain musical instrument is 79.0cm long and has a mass of 8.79g . It is being played in a room where the speed of sound is 344m/s .
    A)To what tension must you adjust the string so that, when vibrating in its second overtone, it produces sound of wavelength 3.39cm ?
    B)What frequency sound does this string produce in its fundamental mode of vibration?


    2. Relevant equations
    v=sqroot(Tension/linear density), linear Density=m/L, v=(f)(lamda)=(omega)/k, k=2(pi)/(lamda)


    3. The attempt at a solution

    I keep trying to get out a way to find T but always end up reducing an eqaution to something pointless such as f=f or (lamda)=(lamda). My real problem is a concept one...Is the v used in equations the speed of sound in the room (334m/s) and when finding linear density do I use .79m or .0339m as the length. Please respond..anything helps and thank you.
     
  2. jcsd
  3. Mar 24, 2009 #2

    Delphi51

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    Homework Helper

    The v must be the velocity of the wave on the string when referring to the wave on the string. But use 344 m/s for the sound "of wavelength 3.39 cm". Use 8.79g/79 cm (in standard units) for the linear density of the string.
     
  4. Mar 24, 2009 #3
    I tried using 344m/s as the v in the eqaution v=sqroot(Tension/linear denstiy)

    so... v^2 = Tension/Linear Density
    so... Tension= v^2 (linear Density) => tension= (344m/s^2)(.00879kg/.79m)=1316.67N.
    However when I tried that it was wrong. I am still confused about the "of wavelength 3.39cm" and the second overtone. Don't they need to come into the problem too? Thank you
     
  5. Mar 24, 2009 #4

    Delphi51

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    Homework Helper

    You are mixing the sound and the vibration on the string incorrectly.
    The thing they have in common is the frequency. Use v = f*lambda for the sound with v=344 and lambda = .0339 to get the frequency for both the wave AND the vibration. Then use that frequency with formulas that apply to the vibrating string.
     
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