Waves: frequency and wavelength
v = λ × f
The relation v = λ · f all three ways: wavelength from frequency, frequency from wavelength, or speed from both. The usual media are preset: light in vacuum (exact c), sound in air at 20 °C, sound in water, or any freely entered speed. The period is always returned, and for light the tool adds the photon energy in electronvolts, exact since SI 2019. The frequency units (Hz to THz) and wavelength units (nm to m) span from the tuning fork to X-rays.
77.955 cm
- Calculation
- λ = v / f = 343 m/s / 440 Hz = 77.955 cm
- Period
- 0.0022727 s
The wavelength is 77.955 cm.
The wavelength is the distance travelled during one period: a fast or slow wave at the same frequency does not have the same wavelength. When changing medium, the frequency is conserved; it is the wavelength that changes with the speed.
The proposed speeds are usual values: 343 m/s for dry air at 20 °C (the speed of sound grows by about 0.6 m/s per degree), 1480 m/s for fresh water at 20 °C. In a cable or a fibre, light travels at 60-70% of c: use the free input.
Scientific dossier
What the tool computes, what it assumes, where it stops being valid, and where its data comes from.
Method & formulasv = λ × f
v = λ × f
λ = v / f
T = 1 / f
E = h × f (light)
The wavelength is the distance travelled during one period: the wave advances v metres per second and repeats f times per second, so each pattern spans v / f metres. For light, E = h·f links frequency and photon energy; in electronvolts, E(eV) = h·f / e, with h and e exact.
- Wavelength λ
- · the spatial period: the distance between two crests, in metres. It is what an obstacle or a slit sees.
- Frequency f
- · the number of oscillations per second, in hertz. It is set by the source and conserved from one medium to the next.
- Period T
- · the duration of one oscillation, T = 1/f. The temporal counterpart of λ.
- Electronvolt
- · the energy of one electron under one volt, exactly 1.602 176 634 × 10⁻¹⁹ J. The natural unit of photons: the visible runs from about 1.6 to 3.3 eV.
Validity domainThe relation v = λf holds for any periodic wave in a medium where the speed does not depend on frequency.
The relation v = λf holds for any periodic wave in a medium where the speed does not depend on frequency. In a dispersive medium (glass for light, deep-water waves), each frequency has its own speed, and the speed of a wave packet (group) differs from that of the crests (phase): the tool computes with the speed you give it, choosing the right one is up to you. The preset sound speeds are standard-condition values, not constants.
Reading the resultA few landmarks to place a result: the FM band around 3 m, 2.
A few landmarks to place a result: the FM band around 3 m, 2.4 GHz WiFi at 12.5 cm, the tuning-fork A at 78 cm in air, the visible between 380 and 780 nm. When a wave changes medium, its frequency does not change; its wavelength adapts to the new speed: red stays red under water, even though λ is a quarter shorter there.