Speed of sound and Mach number

This function calculates the speed of sound in air at a given temperature or altitude in the atmosphere and the Mach number at a given speed.

The speed of sound in air is significantly influenced by the temperature. Enter the temperature in Celsius or Fahrenheit for the calculation. Alternatively, an altitude in the atmosphere can be specified instead of the temperature. The computer then calculates the average temperature.

As the second parameter, enter the flow velocity for which the Mach number is to be calculated.

Formulas for the speed of sound

Altitude in the atmosphere

The decrease in air temperature with altitude also depends on the moisture content of the air. Depending on the moisture content, the temperature decreases between 0.4 and 0.98 Kelvin per 100m. On average, the air cools by 6.5 Kelvin per kilometer up to a height of 11 kilometers. At an altitude of 11 to 20 kilometers, the temperature remains almost the same at just over minus 55 degrees. From an altitude of 20 to 47 kilometers, the temperature warms up again due to the absorption of UV radiation by the ozone to near zero degrees.

Temperature in the atmosphere

The formulas for calculating the average air temperature apply up to an altitude of 11000 m.

\(\displaystyle Temperature\;[°C]=Altitude\;[km]· 6.5+15\)

\(\displaystyle t=h· 6.5+15\)

Speed of sound at a given temperature °C

\(\displaystyle speed\;of\; sound\;[m/sec]=temperature\;[°C]· 0.62+331\)

\(\displaystyle v=t· 0.62+331\)

\(\displaystyle v[km/h]=v[m/sec]· 3.6\)

Mach number

\(\displaystyle Mach−number = \frac{flow\;velocity\;[v]}{speed\;of\;sound\;[c]}\)

\(\displaystyle Ma=\frac{v}{c}\)