Speed of Sound in Air⚠ unverified
Physics / Acoustics · Speed of sound in air as a function of temperature
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| T | T | °C | 20.0 | Air temperature |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| c | c | m/s | Speed of sound |
The science & history
Understanding the Parameters
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$T$ — must be Celsius for the $T/273.15$ form as written. At 20 degC, $c \approx 343$ m/s. Humidity and CO₂ shift $c$ slightly (not in this model).
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$c$ — used in Doppler, wavelength $\lambda = c/f$, and room acoustics.
Derivation (Approaching a Proof)
For an ideal gas, $c = \sqrt{\gamma R_{\mathrm{specific}} T_K}$. With fixed composition, $c = c_0\sqrt{T_K/T_0}$. Choosing $c_0 = 331.3$ m/s at $T_0 = 273.15$ K and writing $T_K = T + 273.15$ with $T$ in degC yields the registry formula. It is an engineering fit, not a full moist-air model.
History
Laplace corrected Newton’s isothermal sound-speed error by using adiabatic bulk modulus; modern values track temperature as above.
Related Concepts: Speed Of Sound, Doppler Shift, Acoustic Impedance, Mach Number
Notes: Registry calculator sound-speed-air (unverified). Dry-air approximation; $T$ in degC.