Waves: frequency and wavelength
Frequency, wavelength and propagation speed (v = λf), with the usual media and photon energy for light.
Result
77.955 cm
- Calculation
- λ = v / f = 343 m/s / 440 Hz = 77.955 cm
- Period
- 0.002 272 7 s
- Wavelength
- 77.955 cm
- Frequency
- 440 Hz
- Period
- 0.002 272 7 s
Notes (2)
The wavelength is 77.955 cm.
Dry air at 20 °C: 343 m/s, plus about 0.6 m/s per degree. Fresh water at 20 °C: 1480 m/s. In a cable or a fibre, light travels at 60-70% of c; use the free entry.
Calculation, assumptions and sources
OverviewThe relation v = λ · f in all three directions: wavelength, frequency or speed.
The relation v = λ · f in all three directions: wavelength, frequency or speed. The usual media are preset: light in vacuum (exact c), sound in air at 20 °C, sound in water, or a free speed. The period is also given, and for light the photon energy in electronvolts. The units run from hertz to terahertz and from nanometre to metre.
Method & formulasv = λ × f
The wavelength is the distance travelled during one period: λ = v / f. For light, E = h·f gives the 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 sets the scale of diffraction by an obstacle or a slit.
- 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.
- Electronvolt
- the energy of an electron across one volt, exactly 1.602 176 634 × 10⁻¹⁹ J. The visible spans 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, waves in deep water), each frequency has its own speed, and the group velocity differs from the phase velocity. The preset sound speeds are values at standard conditions.
Reading the resultThe FM band has a wavelength of about 3 m, 2.4 GHz WiFi 12.5 cm, the tuning-fork A (440 Hz) 78 cm in air, the visible 380 to 780 nm.
The FM band has a wavelength of about 3 m, 2.4 GHz WiFi 12.5 cm, the tuning-fork A (440 Hz) 78 cm in air, the visible 380 to 780 nm.