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:
“And so we ask for peace for the gods of our fathers, for the gods of our native land. It is reasonable that whatever each of us worships is really to be considered one and the same. We gaze up at the same stars, the sky covers us all, the same universe compasses us. What does it matter what practical systems we adopt in our search for the truth. Not by one avenue only can we arrive at so tremendous a secret.”
—Quintus Aurelius Symmachus (A.D. c. 340–402)
“I take it that what all men are really after is some form or perhaps only some formula of peace.”
—Joseph Conrad (1857–1924)
“‘Tis not such lines as almost crack the stage
When Bajazet begins to rage;
Nor a tall met’phor in the bombast way,
Nor the dry chips of short-lunged Seneca.
Nor upon all things to obtrude
And force some odd similitude.
What is it then, which like the power divine
We only can by negatives define?”
—Abraham Cowley (1618–1667)
“Speak the speech, I pray you, as I pronounced it to you—trippingly on the tongue; but if you mouth it, as many of your players do, I had as lief the town-crier spoke my lines. Nor do not saw the air too much with your hand, thus, but use all gently; for in the very torrent, tempest, and as I may say, the whirlwind of your passion, you must acquire and beget a temperance that may give it smoothness.”
—William Shakespeare (1564–1616)