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Resonance tube experiment

  1. Feb 15, 2014 #1

    utkarshakash

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    1. The problem statement, all variables and given/known data
    A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in air column were obtained by lowering the water level. The resonance with the shorter air column is the first resonance and that with the longer air column is the second resonance. Then choose correct options

    A) The intensity of sound heard at the first resonance was more than that at the second resonance.
    B)the prongs of the tuning fork were kept in a horizontal plane above the resonance tube.
    C)the amplitude of vibration of the ends of the prongs is typically around 1cm.
    D)the length of the air column at the first resonance was somewhat shorter than 1/4th of the wavelength of the sound in air.


    3. The attempt at a solution

    If I consider first option, I don't think it is correct as the intensity will not change. In both cases resonance occurs. So it should be same. option B) is incorrect as it is kept in vertical plane. I have no idea about C). The difference in length of two air columns should be λ/2. But from this I cannot make out about length of first air column.
     
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  3. Feb 15, 2014 #2

    haruspex

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    Seems reasonable.
    Right.
    Roughly how far apart are the prongs (at rest)? Could they oscillate by 1cm?
    What is the arrangement of nodes and antinodes at the first resonance?
     
  4. Feb 16, 2014 #3

    utkarshakash

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    At first resonance antinode is present at the open end of the tube and node is present at the water column.
     
  5. Feb 16, 2014 #4

    haruspex

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    So what fraction of a wavelength does that represent?
     
  6. Feb 17, 2014 #5

    utkarshakash

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    It should be λ/4.
     
  7. Feb 17, 2014 #6

    haruspex

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    Right. So the question is, is there some reason that it would be "somewhat shorter" than that.
    I can't think of one, but I might be missing something. Check your course notes.
     
  8. Feb 18, 2014 #7

    utkarshakash

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    Sometimes we also take in consideration the end correction. So it should be somewhat longer rather than shorter. The correct options according to answer key are A) and D).
     
  9. Feb 19, 2014 #8

    haruspex

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    Are you sure you don't have that backwards? According to http://www.fonema.se/mouthcorr/mouthcorr.htm, "the pipe appears to be acoustically somewhat longer than its physical length". That means the physical length will be less then a quarter wavelength.
     
  10. Feb 19, 2014 #9

    utkarshakash

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    Ok. But what about option A)? My answer key says that it is also the correct option.
     
  11. Feb 19, 2014 #10

    haruspex

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    Can't help you with that one, sorry.
     
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