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The identity c = fλ connects sound speed, frequency and wavelength. To predict speed from a material model, use the medium’s elastic response and density, with the appropriate thermodynamic assumptions.
By Matan · Updated
A fluid and an ideal gas
For small acoustic disturbances in a fluid, c = √(Bs/ρ), where Bs is the adiabatic bulk modulus. For an ideal gas, c = √(γRT/M), with absolute temperature T and molar mass M. Pressure alone does not set ideal-gas sound speed at fixed temperature and composition. [1]
Worked dry-air estimate
Take γ = 1.40, R = 8.314 J/(mol·K), T = 293 K and M = 0.02897 kg/mol. Then c ≈ 343 m/s. A 1000 Hz tone has wavelength c/f ≈ 0.343 m. At 2000 Hz in the same approximately nondispersive air, wavelength is about 0.172 m; speed has not doubled.
Stiffness and density both matter
At fixed bulk modulus, increasing density lowers c. Solids often transmit sound faster because their elastic stiffness differs, not because density universally raises sound speed. Different longitudinal and shear modes in solids also have different speeds.
Use local conditions
Temperature, composition and humidity can change sound speed. Altitude often correlates with temperature change, but lower pressure by itself is not the ideal-gas explanation for slower sound. The example assumes a small-amplitude gas wave and does not describe shock propagation.
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How this article was checked
Sources checked; calculations checked where shown. Main claims and model assumptions were checked against the references below. Example arithmetic and units were checked separately. Numerical examples are illustrative calculations, not experimental measurements.
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Cite this article
Matan. “Speed of Sound Equation.” Your Physicist. Originally published 2023-03-17; updated 2026-09-10. https://your-physicist.com/speed-of-sound-equation/
Revision history
10 September 2026: Corrected the frequency, density and altitude causation claims and added a material-based speed calculation. Added references and a transparent verification record.
