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Frequency is the measurement of the number of occurrences of a repeated event per unit of time.

## Measurement

To calculate the frequency of the 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.

To calculate the frequency of an event in experimental work however (for example calculating the frequency of an oscillating pendulum) it is crucial that the time taken for a fixed number of occurrences is recorded, rather than the number of occurrences within a fixed time. This is because your random error is significantly increased performing the experiment the other way around. It [the frequency] is still calculated by dividing the number of occurrences by the time interval, however, the number of occurrences is fixed, not the time interval.

In SI units, the result is measured in hertz (Hz), named after the German physicist Heinrich Rudolf Hertz. 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. Other units that are used to measure frequency include revolutions per minute (rpm). Heart rate and musical tempo are measured in beats per minute (BPM). Often, angular frequency is used instead of frequency, measured in radians per second (rad/s).

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

where

T is the period.

A more accurate measurement takes many cycles into account and averages the period between each.

## Frequency of waves

Frequency has an inverse relationship to the concept of wavelength. The frequency f is equal to the speed v of the wave divided by the wavelength λ (lambda) of the wave:

When waves travel from one medium to another, their frequency remains exactly the same — only their wavelength and speed change.

Frequency is also a measure of temperature, as for when the temperature of a molecule is increased it will vibrate faster. The faster the molecule will vibrate the higher the frequency.

## Examples

) and known as concert pitch, to which an orchestra tunes.

• A baby can hear tones with oscillations up to approximately 20,000 Hz, but these frequencies become more difficult to hear as people age.