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Homework Help: Soundwaves velocity to frequency

  1. Jun 19, 2010 #1
    1. The problem statement, all variables and given/known data
    string on a guitar is plucked to excites 3 harmonic.
    length = 0.3m.
    tension = 100N
    linear mass density (mu) = 0.1 kg/m
    calculate its frequency
    My friend and I wants to find the frequency using the above information. I think we use different approach, but came to the same solution. YET when we compare it with model answers, it is WRONG (i.e. the model answer is 316Hz) can someone explain why? or was the model answer WRONG? (note: it is an known fact that the model answer is occasionally found to be wrong)

    thanks!

    2. Relevant equations
    velocity = sqrt (T/mu)
    L = 3/2 lambda i.e. lambda = (2/3) * L
    velocity = lambda * frequency i.e. frequency = velocity/lambda

    3. The attempt at a solution

    velocity = sqrt(100/.1) =31.6 m/s
    lambda = (2/3) * 0.3m = 0.2
    frequency = 1/0.2 * 31.6 = 158Hz

    the answer I got correlates with the answer a friend got too, but is was off by almost 200Hz when compare to model answer. SO it is definitely not due to rounding error.

    Was we wrong? or was model answer wrong?

    thanks!!
     
    Last edited: Jun 19, 2010
  2. jcsd
  3. Jun 19, 2010 #2

    kuruman

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    Science Advisor
    Homework Helper
    Gold Member

    You and your friend are correct and the model answer is wrong. If you do it symbolically, the nth string harmonic frequency is given by

    [tex]f_n=\frac{n}{2L}\sqrt{T/\mu}[/tex]

    Your answer is exactly half the model answer, so whoever wrote the model answer probably forgot to divide by 2.
     
  4. Jun 19, 2010 #3
    thanks!
     
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