frequency

Frequency is a measure of how often a repeating event occurs per unit of time. In physics and engineering, the standard unit is the hertz (Hz), equal to one cycle per second. The frequency f is the reciprocal of the period T, f = 1/T, where the period is the duration of one complete cycle. In oscillatory contexts, the angular frequency ω = 2πf is also used, measured in radians per second. Frequency can also describe spatial repetition, expressed as cycles per unit distance (for example, cycles per meter) in fields such as optics and materials science.

In waves and signals, frequency characterizes the distribution of energy across different sinusoidal components. A complex waveform can be decomposed into sinusoids at various frequencies, a process described by the Fourier transform. The frequency content of a signal informs its tone, color, or information-carrying capacity, and underpins concepts such as bandwidth and spectral density. Practical systems are designed to pass, reject, or detect specific frequency ranges.

Measurement and practical considerations include sampling and analysis. The sampling rate fs sets the highest frequency that can be represented without aliasing, namely the Nyquist frequency fs/2. Tools for measuring frequency content include frequency counters, spectrum analyzers, and oscilloscopes equipped with Fourier analysis. In everyday use, frequency is closely tied to musical pitch, with standard references like A4 at 440 Hz, illustrating how frequency relates to perception and qualitative properties of sound.