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Tuning Fork and a Tube of Water - Check My Work!

  1. Nov 29, 2012 #1
    Hi everyone, just me doing my regular Thursday Physics homework and looking for someone to check my work.

    1. The problem statement, all variables and given/known data
    A tuning fork with a frequency of f=528Hz is placed near the top of a tube. The water level is lowered so that the length L slowly increases from an initial value of 20.0cm. Determine the next two values of L that correspond to resonant nodes. Assume the speed of sound in air is 343m/s.

    2. Relevant equations
    I used v=fλ


    3. The attempt at a solution
    First I did λ=343/528, which gave me λ=0.650m.

    Since I know that resonance occurs when length is L/4, 3L/4, 5L/4, and so on, I did
    0.650(1/4)=0.162m
    0.650(3/4)=0.487m

    And finally, I added those lengths to the initial 20m, making the next 2 values of L 20.162m and 20.487m.

    This just seems a little too simple for a 10 point problem, and I would just appreciate if someone could tell me if I am missing an item or something. Thanks!
     
    Last edited: Nov 29, 2012
  2. jcsd
  3. Nov 29, 2012 #2

    Ibix

    User Avatar
    Science Advisor

    It says 20cm, not 20m.

    Even so, I don't think your reasoning is quite right. Presuming that L is the distance from the mouth of the tube to the water surface, the condition for resonance is that L=λ/4+nλ/2, not L/4+nL/2, which is what you wrote.

    Can you do the rest?
     
  4. Nov 29, 2012 #3
    Oh wow thank you for noticing that, now I am really glad I had someone check!
    Thank you for your help, you're right that I should have done L=λ/4. I was reading the equation wrong, and the one I was given claimed L was wavelength and entirely ignored lambda, so shame on them.
     
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