The number of occurrences of a repeating event per unit time, such as oscillations or waves.Frequency is the number of times a repeating event occurs per unit of time, typically measured in hertz (Hz), where 1 Hz equals one cycle per second. It is a fundamental property of any periodic phenomenon — from the vibration of a guitar string to the oscillation of an electromagnetic wave. Frequency determines the pitch of sound, the color of light, and the energy of photons.
The concept of frequency was formalized in the 17th century by Galileo Galilei, who observed the relationship between pitch and vibration rate, and later by Christian Huygens, who used it in his wave theory of light. The unit 'hertz' was adopted in 1930 in honor of Heinrich Hertz, who experimentally confirmed electromagnetic waves.
For a wave, frequency is the reciprocal of the period (the time for one complete cycle). It is related to wavelength and speed by the equation v = fλ, where v is the wave speed, f is frequency, and λ is wavelength. In quantum mechanics, the energy of a photon is directly proportional to its frequency (E = hf), linking frequency to the microscopic world.
Frequency is used in radio and television broadcasting, Wi-Fi and cellular networks, medical imaging (ultrasound), and the tuning of musical instruments.
The frequency of the cosmic microwave background radiation, the afterglow of the Big Bang, has been stretched by the expansion of the universe from visible light down to microwaves — a shift of about a factor of 1,000.
| E | variable | Energy of a photon — energy joule |
| f | variable | Frequency of the electromagnetic wave — frequency hertz |
| h | constant | Fundamental constant relating energy to frequency in quantum mechanics — planck constant = 6.62607015e-34 joule second |
| Δf | variable | Change in clock frequency — frequency change hertz |
| f | variable | Clock frequency at reference height — frequency hertz |
| g | variable | Local gravitational acceleration — gravitational acceleration metre per second squared |
| Δh | variable | Height difference — height difference metre |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| f | variable | Gravitational wave frequency — frequency hertz |
| h_0 | variable | Dimensionless Hubble constant (H_0/100 km/s/Mpc) — reduced hubble constant |
| Ω_GW | variable | Gravitational wave energy density per logarithmic frequency — gravitational wave energy density parameter |
| ΔN_eff | variable | Effective number of extra neutrino species — effective neutrino number |
| ∫ d ln f | operator | Integration over logarithmic frequency — logarithmic integral |
| f_reh | variable | Gravitational wave knee frequency at reheating — frequency hertz |
| T_reh | variable | Reheating temperature — temperature kelvin |
| \text{ASD}(f) | variable | Amplitude spectral density at frequency f — amplitude spectral density per root hertz |
| S(f) | variable | Power spectral density at frequency f — power spectral density per hertz |
| f | variable | Frequency — frequency hertz |
| \sqrt{} | operator | Mathematical operation taking the square root — square root |
| \dot{f}_{\mathrm{GW} | variable | time derivative of gravitational wave frequency — frequency derivative hertz per second |
| \mathcal{M} | variable | chirp mass of the binary system — chirp mass kilogram |
| f_{\mathrm{GW}} | variable | gravitational wave frequency — frequency hertz |
| G | constant | constant of universal gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| c | constant | speed of light in vacuum — speed of light = 299792458 metre per second |
