Speed Of Sound⚠ unverified
Aerospace / Atmosphere · Compute the speed of sound in air
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| T | T | K | 1.0 | Air temperature |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | a | m/s | Speed of sound, in metres per second (m/s) |
The science & history
Understanding the Parameters
- $\gamma$ — stiffer gas (higher $\gamma$) → higher $a$ at fixed $T$.
-
$R$ — per unit mass. The live calculator labels $R$ as dimensionless; it must be J/(kg·K) (or equivalent). Air ≈ 287; water vapour and other gases differ.
-
$T$ — absolute temperature (kelvin). $a \propto \sqrt{T}$ for ideal gas.
- $a$ — in air at 288 K, $a \approx 340$ m/s.
Derivation (Approaching a Proof)
From continuum acoustics, $a^{2} = (\partial p/\partial\rho)_s$ (isentropic derivative). For an ideal gas $p = \rho R T$ and isentropic $p/\rho^{\gamma} = \mathrm{const}$, one finds
$$a = \sqrt{\gamma p/\rho} = \sqrt{\gamma R T}.$$
Liquids and solids use bulk modulus: $a = \sqrt{K/\rho}$ — not this ideal-gas card.
History
Newton’s incorrect isothermal $a$, Laplace’s adiabatic correction, and 19th-century thermodynamics produced $\sqrt{\gamma R T}$; it underpins all compressible-flow Mach tables.
Related Concepts: Mach Number, Dynamic Pressure, Bernoulli Total Pressure, Thrust
Notes: Registry calculator fluids-speed-of-sound (unverified). Ideal gas, isentropic small-
signal speed. Unit bug: $R$ labelled dimensionless — should be J/(kg·K) or m²/(s²·K).