Hertz

Last updated

hertz
FrequencyAnimation.gif
Top to bottom: Lights flashing at frequencies f = 0.5 Hz, 1.0 Hz and 2.0 Hz; that is, at 0.5, 1.0 and 2.0 flashes per second, respectively. The time between each flash – the period T – is given by 1f (the reciprocal of f); that is, 2, 1 and 0.5 seconds, respectively.
General information
Unit system SI
Unit of frequency
SymbolHz
Named after Heinrich Hertz
In SI base units s−1

The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. [1] [lower-alpha 1] The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that one hertz is the reciprocal of one second. [2] It is named after Heinrich Rudolf Hertz (1857–1894), the first person to provide conclusive proof of the existence of electromagnetic waves. Hertz are commonly expressed in multiples: kilohertz (kHz), megahertz (MHz), gigahertz (GHz), terahertz (THz).

Contents

Some of the unit's most common uses are in the description of periodic waveforms and musical tones, particularly those used in radio- and audio-related applications. It is also used to describe the clock speeds at which computers and other electronics are driven. The units are sometimes also used as a representation of the energy of a photon, via the Planck relation E = , where E is the photon's energy, ν is its frequency, and h is the Planck constant.

Definition

The hertz is equivalent to one cycle per second. The International Committee for Weights and Measures defined the second as "the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" [3] [4] and then adds: "It follows that the hyperfine splitting in the ground state of the caesium 133 atom is exactly 9192631770 hertz, νhfs Cs = 9192631770 Hz." The dimension of the unit hertz is 1/time (T−1). Expressed in base SI units, the unit is the reciprocal second (1/s).

In English, "hertz" is also used as the plural form. [5] As an SI unit, Hz can be prefixed; commonly used multiples are kHz (kilohertz, 103 Hz), MHz (megahertz, 106 Hz), GHz (gigahertz, 109 Hz) and THz (terahertz, 1012 Hz). One hertz simply means "one event per second" (where the event being counted may be a complete cycle); 100 Hz means "one hundred events per second", and so on. The unit may be applied to any periodic event—for example, a clock might be said to tick at 1 Hz, or a human heart might be said to beat at 1.2 Hz.

The occurrence rate of aperiodic or stochastic events is expressed in reciprocal second or inverse second (1/s or s−1) in general or, in the specific case of radioactivity, in becquerels. [lower-alpha 2] Whereas 1 Hz is one cycle (or periodic event) per second, 1 Bq is one radionuclide event per second on average.

Even though frequency, angular velocity, angular frequency and radioactivity all have the dimension T−1, of these only frequency is expressed using the unit hertz. [7] Thus a disc rotating at 60 revolutions per minute (rpm) is said to have an angular velocity of 2π rad/s and a frequency of rotation of 1 Hz. The correspondence between a frequency f with the unit hertz and an angular velocity ω with the unit radians per second is

and

The hertz is named after Heinrich Hertz . As with every SI unit named for a person, its symbol starts with an upper case letter (Hz), but when written in full, it follows the rules for capitalisation of a common noun ; i.e., hertz becomes capitalised at the beginning of a sentence and in titles but is otherwise in lower case.

History

The hertz is named after the German physicist Heinrich Hertz (1857–1894), who made important scientific contributions to the study of electromagnetism. The name was established by the International Electrotechnical Commission (IEC) in 1935. [8] It was adopted by the General Conference on Weights and Measures (CGPM) (Conférence générale des poids et mesures) in 1960, replacing the previous name for the unit, "cycles per second" (cps), along with its related multiples, primarily "kilocycles per second" (kc/s) and "megacycles per second" (Mc/s), and occasionally "kilomegacycles per second" (kMc/s). The term "cycles per second" was largely replaced by "hertz" by the 1970s. [9] [ failed verification ]

In some usage, the "per second" was omitted, so that "megacycles" (Mc) was used as an abbreviation of "megacycles per second" (that is, megahertz (MHz)). [10]

Applications

A sine wave with varying frequency Wave frequency.gif
A sine wave with varying frequency
A heartbeat is an example of a non-sinusoidal periodic phenomenon that may be analyzed in terms of frequency. Two cycles are illustrated. Wiggers Diagram.svg
A heartbeat is an example of a non-sinusoidal periodic phenomenon that may be analyzed in terms of frequency. Two cycles are illustrated.

Sound and vibration

Sound is a traveling longitudinal wave, which is an oscillation of pressure. Humans perceive the frequency of a sound as its pitch. Each musical note corresponds to a particular frequency. An infant's ear is able to perceive frequencies ranging from 20 Hz to 20000 Hz; the average adult human can hear sounds between 20 Hz and 16000 Hz. [11] The range of ultrasound, infrasound and other physical vibrations such as molecular and atomic vibrations extends from a few femtohertz [12] into the terahertz range [lower-alpha 3] and beyond. [13]

Electromagnetic radiation

Electromagnetic radiation is often described by its frequency—the number of oscillations of the perpendicular electric and magnetic fields per second—expressed in hertz.

Radio frequency radiation is usually measured in kilohertz (kHz), megahertz (MHz), or gigahertz (GHz). Light is electromagnetic radiation that is even higher in frequency, and has frequencies in the range of tens (infrared) to thousands (ultraviolet) of terahertz. Electromagnetic radiation with frequencies in the low terahertz range (intermediate between those of the highest normally usable radio frequencies and long-wave infrared light) is often called terahertz radiation. Even higher frequencies exist, such as that of gamma rays, which can be measured in exahertz (EHz). (For historical reasons, the frequencies of light and higher frequency electromagnetic radiation are more commonly specified in terms of their wavelengths or photon energies: for a more detailed treatment of this and the above frequency ranges, see Electromagnetic spectrum .)

Computers

In computers, most central processing units (CPU) are labeled in terms of their clock rate expressed in megahertz (MHz) or gigahertz (GHz). This specification refers to the frequency of the CPU's master clock signal. This signal is nominally a square wave, which is an electrical voltage that switches between low and high logic levels at regular intervals. As the hertz has become the primary unit of measurement accepted by the general populace to determine the performance of a CPU, many experts have criticized this approach, which they claim is an easily manipulable benchmark. Some processors use multiple clock cycles to perform a single operation, while others can perform multiple operations in a single cycle. [14] For personal computers, CPU clock speeds have ranged from approximately 1 MHz in the late 1970s (Atari, Commodore, Apple computers) to up to 6 GHz in IBM Power microprocessors.

Various computer buses, such as the front-side bus connecting the CPU and northbridge, also operate at various frequencies in the megahertz range.

SI multiples

SI multiples of hertz (Hz)
SubmultiplesMultiples
ValueSI symbolNameValueSI symbolName
10−1 HzdHzdecihertz101 HzdaHzdecahertz
10−2 HzcHzcentihertz102 HzhHzhectohertz
10−3 HzmHzmillihertz103 HzkHzkilohertz
10−6 HzμHzmicrohertz106 HzMHzmegahertz
10−9 HznHznanohertz109 HzGHzgigahertz
10−12 HzpHzpicohertz1012 HzTHzterahertz
10−15 HzfHzfemtohertz1015 HzPHzpetahertz
10−18 HzaHzattohertz1018 HzEHzexahertz
10−21 HzzHzzeptohertz1021 HzZHzzettahertz
10−24 HzyHzyoctohertz1024 HzYHzyottahertz
10−27 HzrHzrontohertz1027 HzRHzronnahertz
10−30 HzqHzquectohertz1030 HzQHzquettahertz
Common prefixed units are in bold face.

Higher frequencies than the International System of Units provides prefixes for are believed to occur naturally in the frequencies of the quantum-mechanical vibrations of massive particles, although these are not directly observable and must be inferred through other phenomena. By convention, these are typically not expressed in hertz, but in terms of the equivalent energy, which is proportional to the frequency by the factor of the Planck constant.

Unicode

The CJK Compatibility block in Unicode contains characters for common SI units for frequency. These are intended for compatibility with East Asian character encodings, and not for use in new documents (which would be expected to use Latin letters, e.g. "MHz"). [15]

See also

Notes

  1. Although hertz is equivalent to cycle per second (cps), the SI explicitly states that "cycle" and "cps" are not units in the SI, likely due to ambiguity in the terms. [2]
  2. "(d) The hertz is used only for periodic phenomena, and the becquerel (Bq) is used only for stochastic processes in activity referred to a radionuclide." [6]
  3. Atomic vibrations are typically on the order of tens of terahertz

Related Research Articles

<span class="mw-page-title-main">Electromagnetic spectrum</span> Range of frequencies or wavelengths of electromagnetic radiation

The electromagnetic spectrum is the full range of electromagnetic radiation, organized by frequency or wavelength. The spectrum is divided into separate bands, with different names for the electromagnetic waves within each band. From low to high frequency these are: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. The electromagnetic waves in each of these bands have different characteristics, such as how they are produced, how they interact with matter, and their practical applications.

<span class="mw-page-title-main">Frequency</span> Number of occurrences or cycles per unit time

Frequency, most often measured in hertz, is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as temporal frequency for clarity and to distinguish it from spatial frequency. Ordinary frequency is related to angular frequency by a factor of 2π. The period is the interval of time between events, so the period is the reciprocal of the frequency: T = 1/f.

Mega is a unit prefix in metric systems of units denoting a factor of one million (106 or 1000000). It has the unit symbol M. It was confirmed for use in the International System of Units (SI) in 1960. Mega comes from Ancient Greek: μέγας, romanized: mégas, lit. 'great'.

<span class="mw-page-title-main">Microwave</span> Electromagnetic radiation with wavelengths from 1 m to 1 mm

Microwave is a form of electromagnetic radiation with wavelengths shorter than other radio waves but longer than infrared waves. Its wavelength ranges from about one meter to one millimeter, corresponding to frequencies between 300 MHz and 300 GHz, broadly construed. A more common definition in radio-frequency engineering is the range between 1 and 100 GHz, or between 1 and 3000 GHz . The prefix micro- in microwave is not meant to suggest a wavelength in the micrometer range; rather, it indicates that microwaves are small, compared to the radio waves used in prior radio technology.

<span class="mw-page-title-main">Second</span> SI unit of time

The second is the unit of time in the International System of Units (SI), historically defined as 186400 of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds each. "Minute" comes from the Latin pars minuta prima, meaning "first small part", and "second" comes from the pars minuta secunda, "second small part".

A nanosecond (ns) is a unit of time in the International System of Units (SI) equal to one billionth of a second, that is, 11 000 000 000 of a second, or 10−9 seconds.

<span class="mw-page-title-main">Caesium standard</span> Primary frequency standard

The caesium standard is a primary frequency standard in which the photon absorption by transitions between the two hyperfine ground states of caesium-133 atoms is used to control the output frequency. The first caesium clock was built by Louis Essen in 1955 at the National Physical Laboratory in the UK. and promoted worldwide by Gernot M. R. Winkler of the United States Naval Observatory.

A picosecond is a unit of time in the International System of Units (SI) equal to 10−12 or 11 000 000 000 000 of a second. That is one trillionth, or one millionth of one millionth of a second, or 0.000 000 000 001 seconds. A picosecond is to one second as one second is to approximately 31,689 years. Multiple technical approaches achieve imaging within single-digit picoseconds: for example, the streak camera or intensified CCD (ICCD) cameras are able to picture the motion of light.

<span class="mw-page-title-main">Radio wave</span> Type of electromagnetic radiation

Radio waves are a type of electromagnetic radiation with the lowest frequencies and the longest wavelengths in the electromagnetic spectrum, typically with frequencies below 300 gigahertz (GHz) and wavelengths greater than 1 millimeter, about the diameter of a grain of rice. Like all electromagnetic waves, radio waves in a vacuum travel at the speed of light, and in the Earth's atmosphere at a slightly slower speed. Radio waves are generated by charged particles undergoing acceleration, such as time-varying electric currents. Naturally occurring radio waves are emitted by lightning and astronomical objects, and are part of the blackbody radiation emitted by all warm objects.

<span class="mw-page-title-main">Becquerel</span> SI derived unit of radioactivity

The becquerel is the unit of radioactivity in the International System of Units (SI). One becquerel is defined as an activity of one decay per second. For applications relating to human health this is a small quantity, and SI multiples of the unit are commonly used.

<span class="mw-page-title-main">Clock rate</span> Frequency at which CPU chip or core is operating

In computing, the clock rate or clock speed typically refers to the frequency at which the clock generator of a processor can generate pulses, which are used to synchronize the operations of its components, and is used as an indicator of the processor's speed. It is measured in the SI unit of frequency hertz (Hz).

Terahertz or THz may refer to:

<span class="mw-page-title-main">Terahertz radiation</span> Range 300-3000 GHz of the electromagnetic spectrum

Terahertz radiation – also known as submillimeter radiation, terahertz waves, tremendously high frequency (THF), T-rays, T-waves, T-light, T-lux or THz – consists of electromagnetic waves within the ITU-designated band of frequencies from 0.3 to 3 terahertz (THz), although the upper boundary is somewhat arbitrary and is considered by some sources as 30 THz. One terahertz is 1012 Hz or 1,000 GHz. Wavelengths of radiation in the terahertz band correspondingly range from 1 mm to 0.1 mm = 100 μm. Because terahertz radiation begins at a wavelength of around 1 millimeter and proceeds into shorter wavelengths, it is sometimes known as the submillimeter band, and its radiation as submillimeter waves, especially in astronomy. This band of electromagnetic radiation lies within the transition region between microwave and far infrared, and can be regarded as either.

The radio spectrum is the part of the electromagnetic spectrum with frequencies from 3 Hz to 3,000 GHz (3 THz). Electromagnetic waves in this frequency range, called radio waves, are widely used in modern technology, particularly in telecommunication. To prevent interference between different users, the generation and transmission of radio waves is strictly regulated by national laws, coordinated by an international body, the International Telecommunication Union (ITU).

The megahertz myth, or in more recent cases the gigahertz myth, refers to the misconception of only using clock rate to compare the performance of different microprocessors. While clock rates are a valid way of comparing the performance of different speeds of the same model and type of processor, other factors such as an amount of execution units, pipeline depth, cache hierarchy, branch prediction, and instruction sets can greatly affect the performance when considering different processors. For example, one processor may take two clock cycles to add two numbers and another clock cycle to multiply by a third number, whereas another processor may do the same calculation in two clock cycles. Comparisons between different types of processors are difficult because performance varies depending on the type of task. A benchmark is a more thorough way of measuring and comparing computer performance.

<span class="mw-page-title-main">Cycle per second</span> Historical synonym for hertz, the unit of frequency

The cycle per second is a once-common English name for the unit of frequency now known as the hertz (Hz). Cycles per second may be denoted by c.p.s., c/s, or, ambiguously, just "cycles". The term comes from repetitive phenomena such as sound waves having a frequency measurable as a number of oscillations, or cycles, per second.

Photomixing is the generation of continuous wave terahertz radiation from two lasers. The beams are mixed together and focused onto a photomixer device which generates the terahertz radiation. It is technologically significant because there are few sources capable of providing radiation in this waveband, others include frequency multiplied electronic/microwave sources, quantum cascade laser and ultrashort pulsed lasers with photoconductive switches as used in terahertz time-domain spectroscopy. The advantages of this technique are that it is continuously tunable over the frequency range from 300 GHz to 3 THz, and spectral resolutions in the order of 1 MHz can be achieved. However, the achievable power is on the order of 10−8 W.

The inverse second or reciprocal second (s−1), also called per second, is a unit defined as the multiplicative inverse of the second. It is applicable for physical quantities of dimension reciprocal time, such as frequency and strain rate.

<span class="mw-page-title-main">Terahertz metamaterial</span>

A terahertz metamaterial is a class of composite metamaterials designed to interact at terahertz (THz) frequencies. The terahertz frequency range used in materials research is usually defined as 0.1 to 10 THz.

<span class="mw-page-title-main">2019 redefinition of the SI base units</span> Definition of the units kg, A, K and mol

In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artifacts such as the standard kilogram. Effective 20 May 2019, the 144th anniversary of the Metre Convention, the kilogram, ampere, kelvin, and mole are now defined by setting exact numerical values, when expressed in SI units, for the Planck constant, the elementary electric charge, the Boltzmann constant, and the Avogadro constant, respectively. The second, metre, and candela had previously been redefined using physical constants. The four new definitions aimed to improve the SI without changing the value of any units, ensuring continuity with existing measurements. In November 2018, the 26th General Conference on Weights and Measures (CGPM) unanimously approved these changes, which the International Committee for Weights and Measures (CIPM) had proposed earlier that year after determining that previously agreed conditions for the change had been met. These conditions were satisfied by a series of experiments that measured the constants to high accuracy relative to the old SI definitions, and were the culmination of decades of research.

References

  1. "hertz". (1992). American Heritage Dictionary of the English Language (3rd ed.), Boston: Houghton Mifflin.
  2. 1 2 "SI Brochure: The International System of Units (SI) – 9th edition" (PDF). BIPM: 26. Retrieved 7 August 2022.
  3. "SI Brochure: The International System of Units (SI) § 2.3.1 Base units" (PDF) (in British English and French) (9th ed.). BIPM. 2019. p. 130. Retrieved 2 February 2021.
  4. "SI Brochure: The International System of Units (SI) § Appendix 1. Decisions of the CGPM and the CIPM" (PDF) (in British English and French) (9th ed.). BIPM. 2019. p. 169. Retrieved 2 February 2021.
  5. NIST Guide to SI Units – 9 Rules and Style Conventions for Spelling Unit Names, National Institute of Standards and Technology
  6. "BIPM – Table 3". BIPM . Retrieved 24 October 2012.
  7. "SI brochure, Section 2.2.2, paragraph 6". Archived from the original on 1 October 2009.
  8. "IEC History". Iec.ch. Archived from the original on 19 May 2013. Retrieved 6 January 2021.
  9. Cartwright, Rufus (March 1967). Beason, Robert G. (ed.). "Will Success Spoil Heinrich Hertz?" (PDF). Electronics Illustrated. Fawcett Publications, Inc. pp. 98–99.
  10. Pellam, J. R.; Galt, J. K. (1946). "Ultrasonic Propagation in Liquids: I. Application of Pulse Technique to Velocity and Absorption Measurements at 15 Megacycles". The Journal of Chemical Physics. 14 (10): 608–614. Bibcode:1946JChPh..14..608P. doi:10.1063/1.1724072. hdl: 1721.1/5042 .
  11. Ernst Terhardt (20 February 2000). "Dominant spectral region". Mmk.e-technik.tu-muenchen.de. Archived from the original on 26 April 2012. Retrieved 28 April 2012.
  12. "Black Hole Sound Waves – Science Mission Directorate". science.nasa.go.
  13. "Black Hole Sound Waves – Science Mission Directorate". science.nasa.go.
  14. Asaravala, Amit (30 March 2004). "Good Riddance, Gigahertz". Wired. Retrieved 28 April 2012.
  15. Unicode Consortium (2019). "The Unicode Standard 12.0 – CJK Compatibility ❰ Range: 3300—33FF ❱" (PDF). Unicode.org. Retrieved 24 May 2019.