Mach Number

Mach number is speed divided by the local speed of sound, and the local speed of sound in an ideal gas depends only on temperature and the gas itself: $a = \sqrt{\gamma R T / M}$. For dry air at 20 °C that is $\sqrt{1.4 \times 8.3145 \times 293.15/0.028964} = 343.2\ \text{m/s}$, the number everyone half-remembers. Notice what is missing: pressure. The speed of sound does not change with altitude because the air thins, it changes because the air gets colder.

The threshold worth carrying around is 0.3. Below it, density varies by less than about 5% and a gas can be treated as incompressible, which is what makes ordinary duct sizing, fan curves and Bernoulli's equation legitimate for air. Above it, compressibility corrections start to matter, and past Mach 1 the physics changes character entirely: shocks form, and information can no longer travel upstream. That last fact is the origin of choked flow, where a nozzle or relief valve reaches Mach 1 at its throat and further lowering the downstream pressure achieves precisely nothing, because the pressure signal cannot get back up through the sonic point.

Choked flow is the reason process engineers care about this at all. A relief valve, a control valve on gas, a leak from a pressurised line: all of them cap out at sonic velocity in the throat, and every sizing standard for compressible service is built around it. The airliner example makes the temperature dependence concrete. At cruise altitude the air is around −50 °C, so sound travels at 299 m/s instead of 343, and Mach 0.85 is 255 m/s rather than the 292 m/s it would be at sea level. The aircraft flies the Mach number, not the airspeed, because it is the Mach number that decides where the shocks form on the wing.