The parameters of waves are wavelength (l), frequency (cycles/sec), period (sec/cycle) and wave speed  (c = f ^. l).  We used l/2 to measure the distance between resonances.  We also used  c = 2f ^. l / 2 for the speed of sound. We also measured the speed of sound in air and carbon dioxide.
    A microphone and speaker were placed near the end of a glass tube.  The glass tube had an adjustable water level that was controlled by raising and lowering an open jug.  This was connected to the glass cylinder by a long flexible rubber tube.  See the diagram below:

The speaker generates a continuous sine wave that is reflected off the water.  The microphone detects the waves as they reflect from the water level and waves directly from the speaker.  Raising and lowering the open-ended jug determines the water levels.  These adjustments determine the length of the air column.  At certain water levels there is a large amplitude standing wave.  This is achieved when the reflections from the tube are in phase with the speaker vibration.  This increase in amplitude of the sound vibration is detected on the oscilloscope.  When the water levels are very close to the resonance there is a cancellation of the sound.  The phase of the reflected wave cancels the wave from the speaker.  This is what was used to measure the length of the air column for the standing wave.  The average wavelength can be calculated by detecting as many waves a possible in the length of the glass tube.  From the relationships between wavelength, frequency, and speed the wave speed can be calculated to a high degree of precision.
    The apparatus was already assembled as seen in the picture above.  The frequency that was used was determined to be 767 Hz.  The resonance positions were then determined.  This was done by raising and lowering the open-ended jug.  When the oscilloscope flat lined a mark was placed on the glass tube to signify the water level of the resonance.  Once the resonances were recorded, distance between each resonance was measured and recorded as well.  The average distance was then determined to be 22.15cm; this distance is half of a wavelength.  The range was then determined to be 0.9cm.  The variation in this distance was calculated by taking half the range.  The variation was determined to be 0.45cm.  Since the wavelength is twice the separation of resonances, the uncertainty in wavelength is twice the uncertainty in the resonance separation.  The percent uncertainty for air was then calculated to be 2%.  These calculations are shown below:

    (l/2) avg = 22cm + 22.5 cm + 21.6 cm + 22.5 cm = 88.6 / 4 = 22.15 cm

    range = 22.5 cm – 21.6 cm = 0.9 cm

    d(l/2) = 0.9 cm / 2 = 0.45 cm

    relative uncertainty = 0.45 cm / 22.15 cm = 0.02 or 2%

    speed = c = 2f (l/2) = 2 9767 Hz) (0.2215 m) = 339.78 m/s

    339.78 m/s + or – 2%

    339.78 m/s + or – 6.8 m/s = 340 m/s + or – 7 m/s

The speed of sound in air as well as the uncertainty of the speed of sound was then calculated.  The speed was calculated using the equation c = 2f . (l/2).  The speed of sound in air was determined to be 339.78m/s.  The uncertainty was then determined by dividing the relative uncertainty by the speed of sound.  This gave 339.87 m/s + or – 6.8m/s.  It was later converted to 340 m/s + or – 7 m/s for simplicity.
 The experiment was then conducted using carbon dioxide.  First the water was drained out of the tube by lowering the open-ended jug as far as possible.  Then the air was pushed out of the tube by filling the column with carbon dioxide.  To accomplish this a rubber tube that was connected to a CO₂ tank was placed in the glass tube and turned on so that the denser CO₂ sunk to the bottom displacing the air.  The frequency that was used was determined to be 716Hz.  The average of the resonance measurements was determined to be 18.48cm.  The range was determined to be 0.1cm. The variance was determined to be 0.05cm.  The relative uncertainty was determined to be 0.27%.  The speed was determined to be 264.63 m/s + or - 0.27%.  The absolute uncertainty was determined to be 264.63 m/s + or – 0.71m/s.
 Once the calculations for both carbon dioxide and air were calculated, we used the equation for the speed of sound per temperature to solve for gamma.  The equation is shown below:

        c = ÖgRT/ M

    c ² = RT / M

    c² M = gRT
 

     g = c² M / RT

        examples:

    Air = g = (340 m/s) 2 (0.029 kg/ mol) / (8.3 J/mol K) (300 K) = 1.34 + or – 4%

    dg/d = (0.02 + 0.02) = 0.04

The gamma for air was determined to be 1.35.  We then calculated the uncertainty for gamma to be 0.04 or 4% for air.  The gamma for carbon dioxide was determined to be 1.24.  The uncertainly of the gamma was determined to be 0.054 or 0.54%.   A model was calculated for air.  Its conditions of a rigid molecule with 5 degrees freedom were considered and calculated for using the following equation: gamma air = Cp/Cv. were Cv for air equals 5/2 R and Cv = 7/2 R to give a gamma for air of 5/7 or 1.4.  This is great fit for the experimental which was 1.34 + or – 4%.  The model for carbon dioxide was calculated assuming that it had 9 degrees of freedom and wobbled.  This was calculated so that Cv = 9/2 R and Cp = 11/2 R.  This calculation gives a gamma for CO₂ that equals 11/9 or 1.2.  This is a great fit for that of the experimental.  The experimental is 1.24 + or – 0.54%. Thus, it was concluded that Carbon dioxide does wobbles.