1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Fundamental frequency if string halved and tension * 4

  1. Oct 26, 2015 #1
    1. The problem statement, all variables and given/known data
    The fundamental frequency of vibration of a particular string is f. What would the fundamental frequency be if the length of the string were to be halved and the tension in it were to be increased by a factor of 4?

    Answer: 4 f

    2. The attempt at a solution
    We have f = f1, 0.5 L and 4 T.

    Substitute in: fn = (n / 2 L) * (√ T / μ)
    f1 = (1 / 2 * 0.5 L) * (√ 4 T / μ)
    f1 = (2 √ T / μ) / L
    f1 = (2 v) / L
    f1 L = 2 v
    In general: f1 = v / (2 L) so
    v / 2 = 2 v
    v = 4 v
    f1 = v / (2 L) so
    v = 2 f1 L so
    2 f1 L = 8 f1 L
    f1 = 4 f1
    Because f = f1 then
    f = 4 f

    But I am not sure whether this logic is right or not. Any help please?
     
    Last edited: Oct 26, 2015
  2. jcsd
  3. Oct 26, 2015 #2
    Yes, that is correct. One way to think about this without all the math is, if you cut the length of the rope in half, but the velocity (due to the tension and mass/unit length) stays constant, then the frequency should double since freq*wavelength = velocity. Then, if you quadruple the tension, because the velocity is dependent on the (square) root of the tension, this causes the velocity to increase by a factor of 2, and thus causing the frequency to double since the wavelength is fixed. Therefore, you've essentially doubled the frequency twice; once by cutting the string in half, and then again by quadrupling the tension. Hope that helps.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Fundamental frequency if string halved and tension * 4
Loading...