Resonance (standing waves) in glass tube with water

  1. 1. The problem statement, all variables and given/known data
    The water level in a vertical glass tube (length 1 m) can be adjusted to any position in the tube. A tunning fork vibrating at 660 Hz is held just over the open end of the tube. calculate at what position of the water level will there be resonance (standing waves) in the tube? Assume speed of sound is 330 m/s

    2. Relevant equations
    f=n*v/(4*L) where n is an odd number
    I'm guessing I've gone wrong with relevant equations part

    3. The attempt at a solution
    My fist assumption is that the end with water in it should be considered to be closed even though in reality some sound would go through the water, is this correct? or should i be treating it like the one on this site
    anyway so treating it as closed i can use the above formula re-arranged or length
    n=1: L = 4*660/(1*330) = 8 m
    n=3: L = 4*660/(3*330) = 24 m
    n=5: L = 4*660/(5*330) = 40 m clearly all are going to be to big for tube, i also considered different frequencies with no success, it is unlikely my lecture would give a trick question, am i doing something wrong?
  2. jcsd
  3. If it helps you can ignore the link, only have to treat the water as closed end, the only problem is the above is still wrong (teacher gave us a hint).
    I don't understand what I'm doing wrong I believe its the right formula and also the right method am I stuffing up units?
  4. vk6kro

    vk6kro 4,058
    Science Advisor

    The speed of sound is 340 m / sec

    What is the wavelength of a 660 Hz sound wave ?

    What length is one quarter of this?
  5. 165 Hz giving
    n=1: L = 4*165/(1*340) = 1.9 m
    n=3: L = 4*165/(3*340) = .647 m
    n=5: L = 4*165/(5*340) = 0.388 m
    which is in the right area
    but don't i want resonate frequency which would be a full oscillation?
  6. Or another question is what made you choose to divide by 4? (want to learn a method so I can do future questions)
  7. vk6kro

    vk6kro 4,058
    Science Advisor

    Wavelength is = speed of sound in air (330 m/sec) / frequency ( 660 Hz) = answer in meters.

    I get 0.5 meters as the wavelength, but check it.

    The first resonance for a closed pipe is at the quarter wave position. One quarter of 0.500 M is 0.125 M. This is about 5 inches. Subsequent resonances are at three times this, five times this, etc.

    Those formulas you quoted seem to be totally wrong. You do not need to use them anyway.
    Last edited: Dec 5, 2009
  8. Ah thank you so much its is 0.5 meter wave length, that formula is wrong (my fault) and now I get the right sort of answers being 0.125, 0.375, 0.625 and 0.875 m
    thanks again
    Last edited: Dec 5, 2009
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