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# Speed of sound and Mach number

 gas: airhelium neonargonhydrogen nitrogenoxygencarbon dioxide ? molar mass = g/mol γ = cP/cV =

 temperature speed of sound °C m/s K km/h °F ft/s mi/h

 speed of object Mach number m/s Mach km/h ft/s mi/h

The results are rounded to significant figures.

The speed of sound c in a gas depends on the kind of gas and on the temperature. It is calculated by

c = sqrt(γ * R * T / M)

with R being the universal gas constant, T the temperature and M the molar mass of the gas. Please note that the heat capacity of gases is changing with increasing temperature due to vibrational excitation. Therefore γ = cP/cV is changing also. The prescribed values for γ are valid in the range of room temperature. The calculation also is valid only for conditions, under which the medium may be considered as an ideal gas.
In the case of air the value for dry air is given.
The Mach number is defined as the ratio of the speed of an object (e.g. an aeroplane) moving in a gas to the speed of sound of the gas.

Usage: At first choose the gas for which you want to calculate the speed of sound. For some gases the molar mass and γ = cP/cV, the ratio of the heat capacities, already are prescribed. Alternatively, you may choose "?" and type your own values for the molar mass and γ.
Next, type the temperature or the speed of sound into the field behind which you find the correct unit. Click on any free space of the window or on the upper "calculate" button and read the results in the other fields. Use the "reset" button to reset your calculation.
After the calculation of the speed of sound you may calculate the Mach number of a flying object or its speed, if the Mach number is known. Type the value of the speed of the object or its Mach number into the field behind which you find the correct unit. Click on any free space of the window or on the lower "calculate" button and read the results in the other fields.
Move the mouse over a unit or click on it to read its full name.

Example:You want to calculate the speed of an aeroplane that flies with Mach 1.5 through air of 0°C. The molar mass and γ for dry air should be set by default. Type "0" into the field behind which "°C" is written. Click on any free space of the window or on the upper "calculate" button. The speed of sound in dry air at this temperature is 331.69 m/s. Now type "1.5" into the field for the Mach number and click on any free space of the window or on the lower "calculate" button. Read the result in the fields for the object speed (e.g. 1791.1 km/h).

Remarks:
- Large and small numbers are written exponentially. As example 2.3e5 = 2.3⋅105 = 230000 or 4.5e-5 = 4.5⋅10-5 = 0.000045.
- There is no warranty for the conversion. Cactus2000 is not responsible for damage of any kind caused by wrong results.
- Please send an email if you have suggestions or if you would like to see more conversions to be included.

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