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:
“Wisdom is not just knowing fundamental truths, if these are unconnected with the guidance of life or with a perspective on its meaning. If the deep truths physicists describe about the origin and functioning of the universe have little practical import and do not change our picture of the meaning of the universe and our place within it, then knowing them would not count as wisdom.”
—Robert Nozick (b. 1938)
“So, if we must give a general formula applicable to all kinds of soul, we must describe it as the first actuality [entelechy] of a natural organized body.”
—Aristotle (384–323 B.C.)
“But oh, not the hills of Habersham,
And oh, not the valleys of Hall
Avail: I am fain for to water the plain.
Downward, the voices of Duty call—
Downward, to toil and be mixed with the main,
The dry fields burn, and the mills are to turn,
And a myriad flowers mortally yearn,
And the lordly main from beyond the plain
Calls o’er the hills of Habersham,
Calls through the valleys of Hall.”
—Sidney Lanier (1842–1881)
“[Allegory] should ... be very sparingly practised, lest, whilst the writer plays with his own fancies and diverts himself by cutting the air with his wide spread wings, he should soar out of view of his readers, leaving them in confusion and perplexity to explore his viewless track.”
—Sarah Fielding (1710–1768)