Formula
Wave and speed relation
\[ c = \lambda \, f \qquad \lambda = \dfrac{c}{f} \qquad f = \dfrac{c}{\lambda} \]
What the symbols mean
- c — speed of sound (m/s)
- λ — wavelength (m)
- f — frequency (Hz)
Converter
The curve tightens as frequency rises (λ shrinks) and travels at the speed c.
Speed of sound in air
At fixed composition the speed depends mostly on temperature; humidity raises it slightly and pressure alone has almost no effect.
Entering an altitude adjusts the pressure (standard atmosphere).
Speed of sound in other media
Typical values at ~20 °C (gases at 0 °C noted). For solids: longitudinal waves (bar/bulk), vary with alloy. Click “Use” to load a speed into the converter.
| Medium | Speed (m/s) | Note | |
|---|---|---|---|
| Gases | |||
| Air (20 °C) | 343 | dry, 1 atm | |
| Air (0 °C) | 331 | dry, 1 atm | |
| Helium (0 °C) | 1007 | hence the squeaky voice | |
| Hydrogen (0 °C) | 1270 | very light gas | |
| Carbon dioxide (0 °C) | 259 | heavy gas | |
| Liquids | |||
| Fresh water (20 °C) | 1481 | ≈ 4.3× air | |
| Sea water (20 °C) | 1522 | salinity 35 ‰ | |
| Ethanol (20 °C) | 1144 | ||
| Mercury (20 °C) | 1450 | liquid metal | |
| Solids | |||
| Steel | 5960 | bar, ≈ E/ρ | |
| Aluminium | 6320 | bar | |
| Concrete | 3650 | 3200–3700 by mix | |
| Glass | 5640 | silica | |
| Wood (along grain) | 3800 | ≈ 3300–4000 | |
| Lead | 1960 | dense metal | |
| Diamond | 12000 | fastest of all | |
Understand the theory — the wave, the speed and the mediainteractive
Sound is a wave: a pressure disturbance that travels step by step through a medium. Three quantities describe it and are tied by a single relation, c = λ·f — the speed equals the wavelength times the frequency. In air at 20 °C, sound travels at about 343 m/s, nearly 1235 km/h. Change the temperature below: the speed rises by roughly 0.6 m/s per degree.
The wave relation: c = λ·f
A periodic wave repeats its pattern over a distance, the wavelength \(\lambda\), and in time with a period \(T = 1/f\). During one period the front advances exactly one wavelength, giving the fundamental relation, valid for any wave (sound, light, water):
It follows at once that \(\lambda = c/f\) and \(f = c/\lambda\). At 343 m/s, a 20 Hz bass is over 17 m long, while a 20 kHz treble is just 1.7 cm: that is why low frequencies bend around obstacles and highs are very directional. This single relation is the backbone of room acoustics, loudspeaker design and noise control alike.
Where does the speed in a gas come from?
In an ideal gas, sound is an adiabatic compression. The speed depends on the absolute temperature \(T\) (in kelvin), the adiabatic index \(\gamma\) (1.4 for air), the gas constant \(R\) and the molar mass \(M\):
The speed grows as \(\sqrt{T}\): it depends on neither pressure nor frequency (air is essentially non-dispersive). For air this yields the handy approximation \(c \approx 331.3\,\sqrt{1 + \theta/273.15}\), i.e. the well-known linear rule \(c \approx 331.3 + 0.606\,\theta\) (\(\theta\) in °C). Doubling the absolute temperature would raise the speed by roughly forty percent, yet everyday temperature swings move it only a few percent.
Humidity, pressure and the Cramer formula
Humid air is slightly less dense than dry air (water vapour is lighter than nitrogen and oxygen), which raises the speed a little: about +1 m/s between dry and saturated air at 20 °C. The Cramer (1993) formula, used by this tool, accounts for temperature, humidity, pressure and CO₂ to reach about 0.1 % accuracy. Pressure alone is negligible because, for an ideal gas, density and stiffness scale together. As a rule of thumb, both warmth and moisture nudge the speed upward, though the humidity contribution stays under about one percent.
Worked examples (air at 343 m/s)
| Frequency | Wavelength | Reading |
|---|---|---|
| f = 20 Hz | λ = 17.2 m | bass: bends around obstacles |
| f = 100 Hz | λ = 3.43 m | room-sized |
| f = 1 kHz | λ = 34.3 cm | mid reference |
| f = 20 kHz | λ = 1.7 cm | treble: very directional |
In liquids and solids: far faster
The stiffer a medium is relative to its density, the faster sound travels. In a liquid, \(c = \sqrt{K/\rho}\) (K: bulk modulus); in a solid bar, \(c = \sqrt{E/\rho}\) (E: Young’s modulus). Water (≈ 1480 m/s) is more than 4× faster than air, and steel (≈ 5900 m/s) about 17×. Pick a medium below to compare and see the matching wavelength at 1 kHz:
Outdoors: gradients, wind and refraction
Because the speed depends on temperature, the real atmosphere bends sound rays. By day, air is warmer near the ground: sound is deflected upward and carries less far. At night (temperature inversion) it is bent back down and carries much farther — which is why distant noises seem clearer in the evening. Wind adds its own gradient: you hear better downwind. These effects are formalised in ISO 9613, alongside atmospheric absorption, which mainly attenuates the highs.
When the source outruns the speed of sound
The ratio of a body’s speed to the speed of sound is the Mach number. At Mach 1 the object catches up with its own waves: they pile up into a shock wave (the supersonic “boom”). Since the speed of sound drops with temperature, hence with altitude, Mach 1 corresponds to a lower speed at altitude than at sea level. It is also why a supersonic aircraft drags a ground-level boom carpet several kilometres wide along its path.
- Thinking the speed of sound depends strongly on pressure: at fixed composition it does not — temperature is what matters.
- Confusing period (seconds) with wavelength (metres): linked by the speed, not the same thing.
- Using 340 m/s everywhere: at 0 °C it is 331, at 35 °C nearly 352 m/s.
- Applying the air speed to water or walls: it is 4 to 17 times larger in those media.
Related tools
Sources : J.-C. Pascal, Vibrations et Acoustique (ENSIM, Le Mans Université); O. Cramer, J. Acoust. Soc. Am. 93, 2510 (1993); D. A. Bies & C. H. Hansen, Engineering Noise Control; ISO 9613-1.