Practical Formula For Dry Air
The approximate speed of sound in dry (0% humidity) air, in meters per second (m·s−1), at temperatures near 0 °C, can be calculated from:
where is the temperature in degrees Celsius (°C).
This equation is derived from the first two terms of the Taylor expansion of the following more accurate equation:
Dividing the first part, and multiplying the second part, on the right hand side, by gives the exactly equivalent form:
The value of 331.3 m/s, which represents the speed at 0 °C (or 273.15 °K), is based on theoretical (and some measured) values of the heat capacity ratio, as well as on the fact that at 1 atm real air is very well described by the ideal gas approximation. Commonly found values for the speed of sound at 0 °C may vary from 331.2 to 331.6 due to the assumptions made when it is calculated. If ideal gas is assumed to be 7/5 = 1.4 exactly, the 0 °C speed is calculated (see section below) to be 331.3 m/s, the coefficient used above.
This equation is correct to a much wider temperature range, but still depends on the approximation of heat capacity ratio being independent of temperature, and for this reason will fail, particularly at higher temperatures. It gives good predictions in relatively dry, cold, low pressure conditions, such as the Earth's stratosphere. The equation fails at extremely low pressures and short wavelengths, due to dependence on the assumption that the wavelength of the sound in the gas is much longer than the average mean free path between gas molecule collisions. A derivation of these equations will be given in the following section.
A graph comparing results of the two equations is at right, using the slightly different value of 331.5 m/s for the speed of sound at 0°C.
Read more about this topic: Speed Of Sound
Famous quotes containing the words practical, formula, dry and/or air:
“Juggling produces both practical and psychological benefits.... A woman’s involvement in one role can enhance her functioning in another. Being a wife can make it easier to work outside the home. Being a mother can facilitate the activities and foster the skills of the efficient wife or of the effective worker. And employment outside the home can contribute in substantial, practical ways to how one works within the home, as a spouse and as a parent.”
—Faye J. Crosby (20th century)
“Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective positions of the beings which compose it, if moreover this intelligence were vast enough to submit these data to analysis, it would embrace in the same formula both the movements of the largest bodies in the universe and those of the lightest atom; to it nothing would be uncertain, and the future as the past would be present to its eyes.”
—Pierre Simon De Laplace (1749–1827)
“Woodlands, meadows,streams and rivers—
Blind to all of it all my life long.
Triolets, villanelles, rondels, rondeaus,
Seeds in a dry pod, tick, tick, tick,”
—Edgar Lee Masters (1869–1950)
“Music, in performance, is a type of sculpture. The air in the performance is sculpted into something.”
—Frank Zappa (1940–1994)