Speed of Sound in Gas

v = \sqrt{\frac{\gamma RT}{M}}

Speed of sound depends on temperature and gas properties.

Variables

Sound speed

Speed of sound

Allowed values: greater than 0

m/s

Heat capacity ratio

C_p/C_v

Allowed values: 1 or more

unitless

Gas constant

8.314

In SI units: kg·m²/(s²·mol·K)

Allowed values: greater than 0

J/(mol·K)

Temperature

Absolute temperature

Allowed values: greater than 0

Molar mass

Molecular mass

Allowed values: greater than 0

kg/mol

Derivation

v = √(γP/ρ) = √(γRT/M) using ideal gas law.

Your notes

0/5000

Constants in this formula

Molar Gas Constant

8.314 462 618…. Exact by definition.

J/(mol·K)

Check value

Round inputs run through this page's calculator, with each constant at its tabulated value. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.

γ = 1.5 (Heat capacity ratio)
R = 8.314 462 618… J/(mol·K) (Gas constant)
T = 3 K (Temperature)
M = 4 kg/mol (Molar mass)

Result: v = 3.0583934 m/s

Other waves formulas with the same quantities

Standing Wave (Open Pipe) (Superposition) shares Sound speed
Standing Wave (Closed Pipe) (Superposition) shares Sound speed

Where this formula is listed

Waves formulas, under Sound Waves, alongside Sound Level (Decibels), Beat Frequency, Mach Number, Shock Wave Angle (Mach Cone) and Sound Intensity Level Addition.
In the waves list it comes after Phase Velocity and before Sound Level (Decibels).
Waves formula sheet, one of 37 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Speed of Sound in Gas formula?

Speed of Sound in Gas is written v = √(γRT/M). Speed of sound depends on temperature and gas properties. It belongs to Waves, under Sound Waves.

What are the units in v = √(γRT/M)?

In SI units, v is sound speed, measured in m/s; γ is heat capacity ratio (dimensionless); R is gas constant, measured in kg·m²/(s²·mol·K); T is temperature, measured in K; M is molar mass, measured in kg/mol.

How is the Speed of Sound in Gas formula derived?

v = √(γP/ρ) = √(γRT/M) using ideal gas law. The result is v = √(γRT/M).