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:
“Philosophy, certainly, is some account of truths the fragments and very insignificant parts of which man will practice in this workshop; truths infinite and in harmony with infinity, in respect to which the very objects and ends of the so-called practical philosopher will be mere propositions, like the rest.”
—Henry David Thoreau (1817–1862)
“I cannot give you the formula for success, but I can give you the formula for failure—which is: Try to please everybody.”
—Herbert B. Swope (1882–1958)
“Since time immemorial, one the dry earth, scraped to the bone, of this immeasurable country, a few men travelled ceaselessly, they owned nothing, but they served no one, free and wretched lords in a strange kingdom. Janine did not know why this idea filled her with a sadness so soft and so vast that she closed her eyes. She only knew that this kingdom, which had always been promised to her would never be her, never again, except at this moment.”
—Albert Camus 1013–1960, French-Algerian novelist, dramatist, philosopher. Janine in Algeria, in The Fall, p. 27, Gallimard (9157)
“Soun is noght but air ybroken,
And every speche that is spoken,
Loud or privee, foul or fair,
In his substaunce is but air;
For as flaumbe is but lighted smoke,
Right so soun is air ybroke.”
—Geoffrey Chaucer (1340–1400)