frequency

1. The rate of recurrence of any periodic phenomenon, often associated with waves of all kinds.

Without qualification frequency often means temporal frequency, the rate of recurrence of a time-varying function, but could mean spatial frequency, the rate of recurrence of a space-varying function. Spatial frequency is the reciprocal of the repeat distance (sometimes the wavelength). The dimensions of (temporal) frequency are inverse time. A common unit for frequency is cycle per second, formerly abbreviated cps, but superseded by hertz, abbreviated as Hz. The symbol ν is often used for frequency but f is common in engineering. Period is inverse frequency. Related to frequency, and applied especially to sinusoidally varying quantities, is angular or circular frequency, often denoted by ω = 2πν, with units radians per unit time (e.g., radians per second).

1. In statistics, the number of times a specified event occurs in a given series of observations; for example, the number of rainy days observed at a particular station during a certain period of time.
   In many types of studies (hydrometeorological, especially) the reciprocal of frequency, the recurrence interval, is used.

Any function of time f(t) is periodic with period t if f(t) = f(t + τ) for all times t, where τ is the smallest number for which this equality holds.