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Homework Help: Tension in a vibrating string at a given frequency

  1. May 6, 2010 #1
    1. The problem statement, all variables and given/known data

    A 4.0g string of 0.67m length is vibrating at 300Hz in the third harmonic. The speed of sound in the air is 344 m/s. What is the tension in the string in SI units.

    A) 110
    B) 88
    C) 69
    D) 130
    E) 150

    2. Relevant equations

    //frequency is equal to velocity over wavelength
    f = v/lambda

    3. The attempt at a solution

    So, f sub n = nf sub 1, the fundamental frequency. That means that I can rewrite this using the frequency equation as...

    100*2*L*sqrt(m/L) = sqrt(T)

    => 100*2*0.67*.0773 = sqrt(T)

    => 10.35 = sqrt(T)

    => (10.35)^2 = T

    => T = 107.2

    107.2 is closest to 110, which is choice A, but it isn't exact and I didn't use the speed of sound in the air quantity for anything. I'm not sure if I did this problem correctly or not? Can anybody help?

    Thanks in advance.
    Last edited: May 6, 2010
  2. jcsd
  3. May 6, 2010 #2
    I get the same answer as you.
    For this calculation the speed of sound in air is not needed.
    As the relevant data is given to 2 significant figures, the answer of 110N is correct to the same level of precision/certainty.
  4. Mar 11, 2011 #3
    For what it's worth, over 10 months after you asked the original question, I also got 107.2Hz as the answer. I'm always late to the party... :-(
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