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The speed of sound in air derived with ideal and real gas behaviorSpenser Joyce
11-5-2014
Physics Comprehensive
• = 1 + …Truncate at B
•Sub in V =
•Expansion:[1+}]
Derivation of Coefficients
From Cramer paper and references
• = 1.4029
• R = 8.31448
• M = 28.9643704*
• p = 101325 Pa
• T = 273.15 K
B = -13.5* = 66* = -155*
• = 331.6648
• -11.51
• 10.25
• -9.382
Departures from ideal gas behavior:
[1+}]
Ideal gas behavior, p = 101325 Pa and T is variable
K temps
Non-ideal behavior including second virial
coefficient B
Temperature (K) Temperature (ºC)
Speed o
f Sound
(m/s
)
Speed o
f Sound (
m/s
)
*Cramer valid only for temps 0ºC-30ºC
*Greenspan paper
• –2.0739* • *
References• Cramer, Owen. "The variation of the specific-heat ratio and the speed
of sound in air with temperature, pressure, humidity, and CO2 concentrations." Journal of the Acoustical Society of America 93.5 (1993): 2510-2516. Print.
• Bird, R. Byron, Charles F. Curtiss, and Joseph O. Hirschfelder. Molecular Theory of Gases and Liquids. New York: n.p., 1954. Print.
• Wong, George S. K. “Speed of sound in standard air.” Journal of the Acoustical Society of America 79 (1986): 1359-1366. Print.
• Greenspan, Martin. “Comments on “Speed of sound in standard air” [J. Acoust. Soc. Am. 79, 1359-1366 (1986)].” Journal of the Acoustical Society of America 82 (1987): 370-372. Print.
Questions?