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Standing wave in a column of methane, find gamma of methane

  1. Jul 30, 2016 #1
    1. The problem statement, all variables and given/known data
    A standing wave with a frequency of 1100 Hz in a column of methane at produces nodes that are 0.200 m apart. What is the value of γ for methane? (The molar mass of methane is 16.0 g/mol)


    2. Relevant equations
    v = sqrt ( γRT/M) where R is 8.341, T = 20 °C and M = 16.0 g/mol.
    v=fλ for the standing wave

    3. The attempt at a solution
    From what I understand we have to find the speed of the standing wave and equate it to the speed of methane and solve for γ but the problem is that they've not told us anything about the standing wave, as in how many nodes does it have or the length of the column or if it's open or closed? So how do we calculate the speed of the standing wave?
     
  2. jcsd
  3. Jul 30, 2016 #2

    TSny

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    What can you deduce from this?
     
  4. Jul 31, 2016 #3
    The wavelength?
     
  5. Jul 31, 2016 #4

    TSny

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    Yes, you can determine the wavelength.
     
  6. Jul 31, 2016 #5
    Distance between 2 adjacent nodes is λ/2
    But are there just two nodes? Because the answer for gamma is 1.27 and I don't get that.
    so λ/2=0.2 so λ=0.4 m
    fλ=v=1100 (0.4) = 440 m/s
    v= sqrt (γRT/M)
    (440)=sqrt ( γ (8.341)(20) / 16)
    And I get a really big number for ϒ?
     
  7. Jul 31, 2016 #6

    mukundpa

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    T is absolute temperature and put proper units for R
     
  8. Jul 31, 2016 #7
    Ohhhhh yess my bad regarding the temperature! Thanks!
     
  9. Jul 31, 2016 #8

    mukundpa

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    With that think the units of R to be use.
     
  10. Jul 31, 2016 #9
    (440 m/s )^2 = y(8.314 J / mol.K)(20 +273)K / 16 x 10^-3 kg
    Now gamma = 1.27
    Thanks!
     
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