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:
“Missionaries, whether of philosophy or religion, rarely make rapid way, unless their preachings fall in with the prepossessions of the multitude of shallow thinkers, or can be made to serve as a stalking-horse for the promotion of the practical aims of the still larger multitude, who do not profess to think much, but are quite certain they want a great deal.”
—Thomas Henry Huxley (1825–95)
“But suppose, asks the student of the professor, we follow all your structural rules for writing, what about that “something else” that brings the book alive? What is the formula for that? The formula for that is not included in the curriculum.”
—Fannie Hurst (1889–1968)
“If you are one of the hewers of wood and drawers of small weekly paychecks, your letters will have to contain some few items of news or they will be accounted dry stuff.... But if you happen to be of a literary turn of mind, or are, in any way, likely to become famous, you may settle down to an afternoon of letter-writing on nothing more sprightly in the way of news than the shifting of the wind from south to south-east.”
—Robert Benchley (1889–1945)
“... anybody is as their land and air is. Anybody is as the sky is low or high, the air heavy or clear and anybody is as there is wind or no wind there. It is that which makes them and the arts they make and the work they do and the way they eat and the way they drink and the way they learn and everything.”
—Gertrude Stein (1874–1946)