The sound tube experiment was performed in gas Carbon Dioxide at temperature 20

Question

The sound tube experiment was performed in gas Carbon Dioxide at temperature 20 deg. C. The students partnering on the bench obtained for the slope of the straight line fitting of the experimental points the value 365.0. Compare the speed of sound following from that slope to the calculated speed of sound from the gas properties? For CO2, Cp/Cv = 1.289, and the mass of one mol CO2 is 0.044 kg. The sound tube length is 0.367 m. The additional necessary datum is given in the text. When continuing the work described in problem 1, one of the students inadvertently shifted, without noticing, the rod with the microphone a little bit inward into the sound tube. At the same other conditions as described in problem 1, the speed of sound was determined as 273.1 m/s by direct measurement of the travel time of a sound pulse for 8 bi-directional traverses along the sound tube. Because of the discrepancy with the experimental result from the previous method, the partners examined the setup, and found what was the cause. What distance was shifted the microphone if both methods produce the same accuracy.

Explanation / Answer

Using

P = nRT/V

density = d = mass / volume = n*0.044/V

r=Cp/Cv = 1.289

Now

c = sqrt(r*P/d)

= sqrt(r*(nRT/V)/(n*0.044/V))

=sqrt(r*RT/0.044)

= sqrt(1.289*8.314*(273.15+20)/0.044)

= 267.20 m/s

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