Speed of Sound Calculator
Enter medium bulk modulus and density (or temperature, gas γ, R, M) to compute the speed of sound. Water K=2.2e9, ρ=1000 → c≈1483 m/s; air 20°C → c≈343 m/s.
Input Data
Results
At a glance:The speed of sound c is the propagation speed of a tiny pressure disturbance in a medium. In any fluid c=√(K/ρ), with K the bulk modulus (Pa, a measure of stiffness) and ρ the density (kg/m³). In an ideal gas, using K=γp and p=ρRT/M, this reduces to c=√(γRT/M)=√(γkT/m), where γ is the adiabatic index, R=8.314 J/(mol·K) the gas constant, T the absolute temperature (K) and M the molar mass (kg/mol). In air, a handy approximation is c≈331.3+0.606·T_C (m/s). Term by term: K (or γ, T) reflects stiffness — a stiffer medium raises c; ρ (or M) reflects inertia — a denser medium lowers c. Physical meaning: sound is faster in stiffer and less dense media. Example: water K=2.2e9 Pa, ρ=1000 → c=√(2.2e9/1000)=√(2.2e6)=1483 m/s; air at 20°C, γ=1.4, M=0.02897 → c=√(1.4×8.314×293.15/0.02897)=√(118183)=343.8 m/s. History: Newton first estimated it, Laplace corrected the adiabatic factor γ in 1816. Applications: (1) sonar and underwater ranging; (2) room and auditorium acoustics; (3) musical instruments (the speed sets pitch with length); (4) medical and industrial ultrasound; (5) atmospheric science; (6) the Mach number (v/c) in aerodynamics.
Formula
General fluid: c = √(K/ρ)
Ideal gas: c = √(γRT/M) = √(γkT/m)
Air approx: c ≈ 331.3 + 0.606·T_C (m/s)
K bulk modulus, ρ density, γ adiabatic index
$$c = \sqrt{\frac{K}{\rho}} = \sqrt{\frac{\gamma R T}{M}} = \sqrt{\frac{\gamma k T}{m}}$$How to Use
- Method 1: enter bulk modulus K and density ρ → c=√(K/ρ).
- Method 2: enter temperature T, adiabatic index γ, R and molar mass M → c=√(γRT/M).
- Method 2 also gives the air speed c≈331.3+0.606·T_C.
Case Studies
Water, air and temperature
Water K=2.2e9, ρ=1000 → c=1483 m/s (far faster than air).
Air 20°C: c=√(1.4×8.314×293.15/0.02897)=343.8 m/s.
Air: +1°C ≈ +0.6 m/s — temperature strongly sets the speed (wind bands in orchestras tune by temperature).
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.