frequencies

Frequency is the number of occurrences of a repeating event per unit time. In physics, it is most commonly associated with waves and oscillations. The standard unit is the hertz (Hz), defined as one cycle per second. The symbol f is often used for frequency, though the Greek letter ν is also common in some contexts; angular frequency ω = 2πf expresses the rate in radians per second.

For a traveling wave, frequency is related to the wave's speed v and wavelength λ by f = v/λ, and to period T by f = 1/T. Temporal frequency refers to cycles over time; spatial frequency refers to cycles per unit distance, such as cycles per meter, used in optics and imaging (k = 2π/λ).

In acoustics, audible frequencies range roughly from 20 Hz to 20 kHz, while in electronics, the concept appears in carrier frequencies, modulation, clock rates, and sampling rates. The Nyquist theorem states that to capture a signal without aliasing, sampling frequency must be at least twice the highest frequency present.

In data analysis, frequencies are analyzed via Fourier transforms, yielding a frequency spectrum that reveals the signal's constituent components. The term natural or resonant frequency denotes the rate at which a system tends to oscillate in the absence of damping. Understanding frequency underpins disciplines from music to radio to quantum physics.