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Standing sound waves for fundamental and first two overtones

  1. Mar 21, 2012 #1
    1. The problem statement, all variables and given/known data
    Standing sound waves are produced in a pipe that is 1.40 m long. For the
    fundamental frequency and the first two overtones, determine the locations along the
    pipe (measured from the left end) of the displacement nodes if the pipe is open at both
    ends.


    2. Relevant equations
    fundamental frequency of tube with both ends open - L=λ/2
    first overtone - L=2λ/2

    3. The attempt at a solution
    fundamental: λ=2.8m
    first overtone: λ=1.4m
     
  2. jcsd
  3. Mar 21, 2012 #2

    PeterO

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    Homework Helper

    Those two wavelengths you have calculated are indeed correct, though you were also asked about the next overtone.

    You are now after the position of the displacement nodes. in each of the 3 cases.

    Do you know what a displacement node is and how to locate them?
     
  4. Mar 21, 2012 #3
    actually my teacher said there wasnt enough data given for the problem to be solved. :/
     
  5. Mar 21, 2012 #4
    The data is indeed not enough.

    You are told that the pipe is open at both ends.

    You also need to know if you are after the pressure nodes or the displacement nodes.(EDITED: READ FOOTNOTE BELOW)

    Usually for sound we are after the pressure nodes/antinodes.

    Now L=n(lambda/2)

    as you correctly said.


    Now, Ends of an open pipe are pressure nodes (Why?)

    Calculate the position of other nodes using the value of wavelength you obtained.

    Remember nodes are seperated by a distance of lambda/2 from each other.


    P.S.
    Oh yeah.Its stated that you are after displacement nodes.

    So you have all the data except speed of sound in air which you can take to be 340m/s.

    Its needed for finding the frequency.

    Remember, open ends of pipe are displacement antinodes
     
    Last edited: Mar 21, 2012
  6. Mar 21, 2012 #5

    PeterO

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    There is all the information you need!!!!
    1.4
    0.7 and 2.1
    You can work out the three for the second overtone.

    EDIT: one of the points for the 2nd overtone [and the 4th, 6th 8th etc] is 1.4m - the others are 0.473 and 2.327

    The easy way to work it out is

    Fundamental - L/2
    1st overtone - L/4, 3L/4
    2nd overtone - L/6, 3L/6, 5L/6
    3rd overtone - L/8, 3L/8, 5L/8, 7L/8

    See the pattern evolving - now all you have to do is draw some diagrams to show why that is true !!
     
    Last edited: Mar 22, 2012
  7. Mar 22, 2012 #6

    PeterO

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    Just read OP and see I had the wrong pipe length when I gave numerical lengths.

    Fundamental: 0.7
    1st O'tone 0.35, 1.05
    2nd O'tone 0.267 , 0.7, 1.167

    The answers in terms of L are correct.
     
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