# Frequency

File:Sine waves different frequencies.svg
Sinusoidal waves of various frequencies; the bottom waves have higher frequencies than those above.

Frequency is the measurement of the number of occurrences of a repeated event per unit of time. It is also defined as the rate of change of phase of a sinusoidal waveform.

## 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 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:

${\displaystyle f={\frac {1}{T}}}$

where

T= time or period 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:

${\displaystyle f={\frac {v}{\lambda }}}$

In the special case of electromagnetic waves moving through a vacuum, then v = c, where c is the speed of light in a vacuum, and this expression becomes:

${\displaystyle f={\frac {c}{\lambda }}}$

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

Apart from being modified by the Doppler effect or any other nonlinear process, frequency is an invariant quantity in the universe. That is, it cannot be changed by any linearly physical process unlike velocity of propagation or wavelength.

## Examples

• The frequency of the standard pitch A above middle C is usually defined as 440 Hz, that is, 440 cycles per second (Listen ) 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.
• In Europe, the frequency of the alternating current in mains is 50 Hz (close to the tone G), however, in North America, the frequency of the alternating current is 60 Hz (close to the tone B flat — that is, a minor third above the European frequency). The frequency of the 'hum' in an audio recording can show where the recording was made — in Europe, or in America.