\[c=\sqrt{\frac{\gamma RT}{M}}\]
Variables
cspeed of sound (m/s)
gamma[γ]ratio of specific heats
Runiversal gas constant (J/(mol·K))
Tabsolute temperature (K)
Mmolar mass (kg/mol)
Description
What is this formula?
This formula calculates the speed of sound in an ideal gas as a function of thermodynamic properties. The speed depends on the gas temperature, molar mass, and ratio of specific heats.
When to use it
Use this formula when studying acoustics, gas dynamics, thermodynamics, atmospheric science, or wave propagation in gases.
Example
Given:
γ = 1.4
R = 8.314 J/(mol·K)
T = 293 K
M = 0.02897 kg/mol
Formula:
c = √((γRT)/M)
Substitution:
c = √((1.4 × 8.314 × 293)/0.02897)
c = √(117700)
c = 343 m/s
Result:
c ≈ 343 m/s
Applications
Atmospheric acoustics.
Gas flow analysis.
Aerospace engineering.
Thermodynamics.
Acoustic simulations.