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Longitudinal waves in a clamped metal rod

  1. Sep 15, 2009 #1
    1. The problem statement, all variables and given/known data
    The speed of sound in a metal rod is 3600 m s -1. The rod is 1.20m
    long and clamped at one of its ends.
    (a) Determine the frequency of its vibration if longitudinal waves
    are established in the rod and it is vibrating in its first overtone
    mode.
    (d) Determine the frequency of its vibration if clamped in the middle whilst still vibrating in the first overtone.

    2. Relevant equations
    v = f x w where w is the wavelength


    3. The attempt at a solution
    (a) The first overtone is the third harmonic, therefore
    L = (3/4)w
    = 3/4 x 1.60m
    W = (4/3)L = (4/3) x 1.60m
    f= 3600ms-1 / (4/3 x 1.60m) = 1.69kHz; given answer is 2250 Hz

    (d) Still the third harmonic but L is now 0.8m
    f = 3600ms-1 / (4/3 x 0.80m) = 3.38kHz; given answer is 4500 Hz

    What have I done wrong?
     
  2. jcsd
  3. Sep 15, 2009 #2

    Redbelly98

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    Staff Emeritus
    Science Advisor
    Homework Helper

    The rod length is 1.20 m, not 1.60 m.
     
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