# frequency

Physical size
Surname frequency
Formula symbol ${\ displaystyle f, \, \ nu}$
Size and
unit system
unit dimension
SI Hz T −1

The frequency (from Latin frequentia 'frequency' ; also called the number of vibrations ) is a measure in physics and technology of how quickly the repetitions follow one another in a periodic process, e.g. B. with a continuous oscillation . The frequency is the reciprocal of the period duration .

The unit of frequency is the derived SI unit with the special name Hertz ( unit symbol Hz); 1 Hz = 1 s −1 ("one per second"). Occasionally, however, other units are also used, such as B. min −1 or h −1 . When specifying the frequency from numerical value and unit, the numerical value indicates how many periods take place within the selected time unit.

The terms repetition frequency , pulse repetition frequency or stroke frequency are also used for some processes, and speed for rotary movements .

## Definition and nature of the frequency

The frequency of a regularly repeating process is defined as the reciprocal of the period duration  : ${\ displaystyle f}$${\ displaystyle T}$

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

Since a number of the periodically repeating processes require the time interval , the following also applies: ${\ displaystyle \ Delta N}$ ${\ displaystyle \ Delta t = \ Delta N \ cdot T}$

${\ displaystyle f = {\ frac {\ Delta N} {\ Delta t}} \,}$

This is sometimes given as the definition of frequency. The nature of the frequency is a finely variable, continuous variable.

## Frequency of waves

In the case of waves , the frequency is linked to their wavelength via the phase velocity : ${\ displaystyle c}$ ${\ displaystyle \ lambda}$

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

For electromagnetic waves, and . The natural constant is the speed of light , the wavelength in a vacuum and the refractive index of the medium. When a wave changes medium during its propagation, the propagation speed and the wavelength change. Their frequency, however, remains the same. ${\ displaystyle c = {\ tfrac {c_ {0}} {n}}}$${\ displaystyle \ lambda = {\ tfrac {\ lambda _ {0}} {n}}}$${\ displaystyle c_ {0}}$${\ displaystyle \ lambda _ {0}}$${\ displaystyle n}$

## Frequency in everyday life

A frequency can be specified for every periodic process in nature and in everyday life. The day-night change is repeated, for example, with a frequency of . When the body is at rest, the human heart has a pulse rate of approx. 50–90 min −1 (this corresponds to 0.83–1.5 Hz), the breathing rate is 12 to 50 breaths per minute, depending on the age of humans. In music, the standard concert pitch with a frequency of 440 Hz is known. The perceived pitch of a tone is mainly determined by the frequency of its fundamental vibration . The human ear perceives sound waves with frequencies between 20 Hz and a maximum of 20,000 Hz; with increasing age, the upper limit generally drops to 10,000 Hz and less. ${\ displaystyle {\ tfrac {1} {24 \; \ mathrm {h}}} \ \ approx 10 ^ {- 5} \; \ mathrm {Hz \,}}$

The frequencies of electromagnetic waves that can be produced by electronic means are divided into frequency bands (e.g. long wave , short wave , medium wave , VHF , UHF ) in the range between approx. 100 kHz and a few GHz for the purposes of broadcasting and radio traffic . The light perceptible to humans is in the range between 400 THz and 750 THz.

## Measurement

A number of different measuring devices are listed under Frequency Meter . In digital measurement technology, the frequency is very easy to measure, since only its oscillations or pulses have to be counted during a suitable time, so that these measurement devices are then referred to as frequency counters.

The relative error limit of the frequency measurement results directly from the relative error limit of the time limit. For this purpose, periods of time are formed from a number of periods of a frequency generator that is as precise as possible, such as a quartz oscillator . Even as a consumer item, quartz crystals have relative error limits in the order of magnitude of 0.001%.

Otherwise such small error limits can only be achieved with extreme effort or not at all in measurement technology .

Note: 0.001% = 1 in 100,000 ≈ 1 s per day = ½ min per month; this value is often undercut by the measurement deviation in watches.

## Frequency spectrum

Real, non-discrete oscillations always consist of several superimposed oscillations with different frequencies, since no perfectly sinusoidal oscillations exist in nature . One of the reasons for this is that real oscillations have a finite length and are therefore limited by a decay and settling process. Vibrating systems can also be disturbed from the outside, which is associated with the introduction of further frequencies into the vibration. A mathematically exact sine wave, on the other hand, is unlimited in time and undisturbed. The totality of the frequencies represented in an oscillation with their respective amplitudes is called the frequency spectrum . The determination of the frequency spectrum of a given vibration is called Fourier analysis .

## Special frequencies

size unit description Examples
Natural frequency Hz An oscillation frequency with which a system can oscillate as an eigenmode after a single excitation ideal oscillating circuit
Resonance frequency Hz A frequency when a system is excited at which the amplitude increases more than when excited with neighboring frequencies real, periodically excited oscillating circuit
Speed or rotational frequency min −1 , s −1 When rotating, the number of revolutions z. B. a wave in a period of time, based on this period with rotary movements, electric motor
Stroke frequency min −1 In drive technology, the number of strokes based on the duration of the count with linear movements, reciprocating engine
Pulse repetition rate Hz Number of pulses sent in relation to the period of observation Radar technology

## Related sizes

size unit description Examples
Angular frequency s −1 Often used instead of frequency in calculations with trigonometric functions Complex AC bill
Spatial frequency m −1 Reciprocal value of the spatial period length in a locally periodic process waves

Even in the case of other quantities that have the dimension of a rate, i. H. have the SI unit s −1 , but do not represent a frequency, such as the radioactive decay rate , the unit hertz should not be used.

## literature

• Horst Stöcker: Pocket book of physics . 6th edition. Publisher Harri Deutsch, Frankfurt am Main 2010, ISBN 978-3-8171-1860-1 .
• Michael Dickreiter: Handbook of the recording studio technology . 7th edition. KG Saur, Munich 2008, ISBN 978-3-598-11765-7 .

Commons : Frequency  - collection of images, videos and audio files
Wiktionary: Frequency  - explanations of meanings, word origins, synonyms, translations

## annotation

1. The frequency is occasionally referred to as a discrete or digital variable due to its easy measurability through (limited) counting (e.g. Rainer Felderhoff: Elektrical Messtechnik. 2nd edition. Hanser 1979, p. 133). However, this statement only relates to the measured value obtained using a digital measurement method and does not apply in general.

## Individual evidence

1. Lexicon of Physics: Schwingungszahl - Spektrum.de (accessed on June 16, 2020); there with reference to frequency and there also with "vibration number"
2. a b Robert Wichard Pohl: Pohl's introduction to physics . 20th edition. tape 1 . Springer, 2008, ISBN 3-540-76337-6 , pp. 8 .
3. ^ Dieter Meschede: Gerthsen Physics. 24., revised. Edition. Springer, 2010, ISBN 978-3-642-12894-3 , p. 25.
4. DIN 1311-1 "Vibrations and vibratory systems"
5. DIN 1304-1 "Formula symbols"
6. a b DIN 1301-1, -2 "Units"
7. Heinz Gascha, Stefan planting: Large Manual physics . Compact, 2004, ISBN 3-8174-7429-6 , pp. 92 .
8. Reinhard Lerch: Electrical measurement technology: analog, digital and computer-based methods. Springer Vieweg, 6th edition 2012, p. 395.
9. Wolfgang Böge, Wilfried Plaßmann: Vieweg handbook electrical engineering: Basics and applications for electrical engineers. Vieweg, 3rd edition 2004, p. 426.