halfperiod

Half-period is the duration of half of one complete cycle of a periodic phenomenon. In a sinusoidal wave, it is the time interval from a maximum to the next minimum, or from a zero crossing with positive slope to the next zero crossing with negative slope. It is a measure of how long each half-cycle lasts in the oscillation.

Mathematically, if the full cycle period is T and the frequency is f, then the half-period is T/2 and equals 1/(2f). In angular form, with angular frequency ω = 2πf, the half-period is π/ω. This reflects a phase change of π radians (or 180 degrees) during the half-period.

Applications and contexts include mechanical and electrical oscillations, wave propagation, and signal processing. The current or voltage in alternating current systems changes sign every half-period, and a half-period corresponds to half of a complete phase cycle. In optics and acoustics, half-periods relate to phase shifts of π radians between complementary waves or components.

Measurement and interpretation: the half-period can be determined from time-domain data using an oscilloscope by measuring the interval between successive identical points (such as consecutive peaks) separated by half a cycle, or between successive zero-crossings with opposite slope. In damped or non-sinusoidal signals, the half-period remains defined as the time to complete half a cycle, though amplitude and shape may vary.

Related concepts include period, frequency, phase, and cycle.