Speed of Sound Calculator
Compute the speed of sound in an ideal gas v=√(γ·R·T/M). Air: γ=1.4, M=0.02897, T=20°C → v≈343 m/s. Also outputs km/h, ft/s and time per km.
Input Data
Results
At a glance:In an ideal gas the speed of sound is v=√(γ·R·T/M), where γ is the adiabatic index (Cp/Cv), R=8.314 J/(mol·K) is the gas constant, T is the absolute temperature (K) and M is the molar mass (kg/mol). It arises because a sound wave is a small adiabatic pressure disturbance; the stiffness comes from γp and the inertia from density ρ=M·p/(R·T), giving v=√(γp/ρ)=√(γRT/M). Properties: (1) v rises with √T (warmer air → faster sound; about +0.6 m/s per °C near room temperature); (2) v is independent of pressure at fixed T (density and stiffness scale together); (3) lighter gas (smaller M) carries sound faster (helium > air). Example: air γ=1.4, M=0.02897 kg/mol, T=20°C=293.15 K → v=√(1.4×8.314×293.15/0.02897)≈343 m/s. At 0°C it is 331 m/s. Applications: (1) musical instruments and tuning (temperature shifts pitch); (2) aircraft Mach number (v at altitude is lower); (3) meteorology and atmospheric sound propagation; (4) sonar and underwater acoustics (speed in water ≈1480 m/s, dominated by bulk modulus not molar mass); (5) DSE Physics.
Formula
Speed of sound: v = √(γ·R·T/M)
R = 8.314 J/(mol·K); T in Kelvin
Air: γ=1.4, M=0.02897 kg/mol → 343 m/s at 20°C
Rises with √T; independent of pressure at fixed T
$$v = \sqrt{\frac{\gamma R T}{M}}$$How to Use
- Enter gas temperature T (°C; +273.15 to Kelvin).
- Enter adiabatic index γ (air 1.4) and molar mass M (kg/mol).
- The tool outputs speed in m/s, km/h, ft/s, v/c and time per km.
Case Studies
Speed of sound in air at 20°C
γ=1.4, M=0.02897, T=20°C=293.15 K.
v = √(1.4×8.314×293.15/0.02897).
≈ 343 m/s (about 1235 km/h).
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.