Frequency is a measure of the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency. The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency.

Definitions and units

For cyclical processes, such as rotation, oscillations, or waves, frequency is defined as a number of cycles, or periods, per unit time. In physics and engineering disciplines, such as optics, acoustics, and radio, frequency is usually denoted by a Latin letter f or by a Greek letter ν (nu).

In SI units, the unit of frequency is hertz (Hz), named after the German physicist Heinrich Hertz. For example, 1 Hz means that an event repeats once per second, 2 Hz is twice per second, and so on . This unit was originally called a cycle per second (cps), which is still sometimes used. Heart rate and musical tempo are measured in beats per minute (BPM). Frequency of rotation is often expressed as a number of revolutions per minute (rpm). BPM and rpm values must be divided by 60 to obtain the corresponding value in Hz: thus, 60 BPM translates into 1 Hz.

The period is usually denoted as T, and is the reciprocal of the frequency f:

T = \frac{1}{f}. The SI (as well as English) unit for period is the second (s).

By timing

To calculate the frequency of an event, the number of occurrences of the event within a fixed time interval are counted, and then divided by the length of the time interval.

In experimental work (for example, calculating the frequency of an oscillating pendulum) it is more accurate to measure the time taken for a fixed number of occurrences, rather than the number of occurrences within a fixed time. The latter method introduces — if N is the number of counted occurrences — a random error between zero and one count, so on average half a count, causing an biased underestimation of f by ½ f / (N + ½)Fact: date=August 2008 in its expected value. In the first method, which is more accurate, frequency is still calculated by dividing the number of occurrences by the time interval; however it is the number of occurrences that is fixed, not the time interval.

An alternative method to calculate frequency is to measure the time between two consecutive occurrences of the event (the period T) and then compute the frequency f as the reciprocal of this time:

f = \frac{1}{T}.

A more accurate measurement can be obtained by taking many cycles into account and averaging the periods between each.

By stroboscope effect, or frequency beats

In case when the frequency is so high that counting is difficult or impossible with the available means, another method is used, based on a source (such as a laser, a tuning fork, or a waveform generator) of a known reference frequency f₀, that must be tunable or very close to the measured frequency f. Both the observed frequency and the reference frequency are simultaneously produced, and frequency beats are observed at a much lower frequency Δf, which can be measured by counting. This is sometimes referred to as a stroboscope effect. The unknown frequency is then found from $f=f\_0\backslash pm\; \backslash Delta\; f$.