The local speed of sound is the square root of gamma * R * T

gamma is the diatomic gas constant, 1.4

R is the gas constant for dry air - 287 kJ/kg.K

T is the temperature in Kelvin.

50 degrees C is 323.15 Kelvin.

SQRT (1.4 x 287 x 323.15) = 360 m/s.

If you prefer knots, divide by 0.5144

And you get c = 700 knots.

If you have a local True Airspeed, divide that by c, and you get the Mach number. So, say you are flying at 500 knots TAS, in an air mass at 50deg.C, then your Mach number is 500/700 = 0.714.

Don't forget that if you are working in IAS or EAS, you need to make further conversions - and in particular at non ISA temperatures, even at sea level, you need to correct the EAS/TAS relationship for density altitude. Ideal gas laws are your friend again here.

So relative density = (pressure / standard sea level pressure) * (standard sea level temperature in K / air temperature in K). And TAS = EAS / SQRT (relative density). Relative density is normally written as sigma.

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