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:
“Whatever practical people may say, this world is, after all, absolutely governed by ideas, and very often by the wildest and most hypothetical ideas. It is a matter of the very greatest importance that our theories of things that seem a long way apart from our daily lives, should be as far as possible true, and as far as possible removed from error.”
—Thomas Henry Huxley (1825–95)
“In the most desirable conditions, the child learns to manage anxiety by being exposed to just the right amounts of it, not much more and not much less. This optimal amount of anxiety varies with the child’s age and temperament. It may also vary with cultural values.... There is no mathematical formula for calculating exact amounts of optimal anxiety. This is why child rearing is an art and not a science.”
—Alicia F. Lieberman (20th century)
“I can love both fair and brown;
Her whom abundance melts, and her whom want betrays;
Her who loves loneness best, and her who masks and plays;
Her whom the country formed, and whom the town;
Her who believes, and her who tries;
Her who still weeps with spongy eyes;
And her who is dry cork, and never cries.
I can love her, and her, and you and you,
I can love any, so she be not true.”
—John Donne (1572–1631)
“I date the end of the old republic and the birth of the empire to the invention, in the late thirties, of air conditioning. Before air conditioning, Washington was deserted from mid-June to September.... But after air conditioning and the Second World War arrived, more or less at the same time, Congress sits and sits while the presidents—or at least their staffs—never stop making mischief.”
—Gore Vidal (b. 1925)