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 rel
tively 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. The stratosphere (/?str?t?sfr/) is the second major layer of Earth's atmosphere, just above the troposphere, and below the mesosphere. It is stratified in temperature, with warmer layers higher up and cooler layers farther down. This is in contrast to the troposphere near the Earth's surface, which is cooler higher up and warmer farther down. The border of the troposphere and stratosphere, the tropopause, is marked by where this inversion begins, which in terms of atmospheric thermodynamics is the equilibrium level. The stratosphere is situated between about 10 km (6 mi) and 50 km (30 mi) altitude above the surface at moderate latitudes, while at the poles it starts at about 8 km (5 mi) altitude.