Hertz

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

The hertz (symbol: Hz) is the derived unit of frequency in the International System of Units (SI) and is defined as one cycle per second. [1] It is named after Heinrich Rudolf Hertz, the first person to provide conclusive proof of the existence of electromagnetic waves. Hertz are commonly expressed in multiples: kilohertz (103 Hz, kHz), megahertz (106 Hz, MHz), gigahertz (109 Hz, GHz), terahertz (1012 Hz, THz), petahertz (1015 Hz, PHz), exahertz (1018 Hz, EHz), and zettahertz (1021 Hz, ZHz).

Contents

Some of the unit's most common uses are in the description of sine waves 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 energy, via the photon energy equation (E=hν), with one hertz equivalent to h joules.

Definition

The hertz is defined as one cycle per second. The International Committee for Weights and Measures defined the second as "the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" [2] [3] and then adds: "It follows that the hyperfine splitting in the ground state of the caesium 133 atom is exactly 9 192 631 770 hertz, ν(hfs Cs) = 9 192 631 770 Hz." The dimension of the unit hertz is 1/time (1/T). Expressed in base SI units it is 1/second (1/s). Problems can arise because the units of angular measure (cycle or radian) are omitted in SI. [4] [5] [6] [7]

In English, "hertz" is also used as the plural form. [8] 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 cycle per second" (typically that which is being counted is a complete cycle); 100 Hz means "one hundred cycles 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 radioactive decay, in becquerels. [9] Whereas 1 Hz is 1 cycle per second, 1 Bq is 1 aperiodic radionuclide event per second.

Even though angular velocity, angular frequency and the unit hertz all have the dimension 1/s, angular velocity and angular frequency are not expressed in hertz, [10] but rather in an appropriate angular unit such as radians per second. Thus a disc rotating at 60 revolutions per minute (rpm) is said to be rotating at either 2π rad/s or 1 Hz, where the former measures the angular velocity and the latter reflects the number of complete revolutions per second. The conversion between a frequency f measured in hertz and an angular velocity ω measured in 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 1930. [11] 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. One hobby magazine, Electronics Illustrated, declared their intention to stick with the traditional kc., Mc., etc. units. [12]

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.

Vibration

Sound is a traveling longitudinal wave which is an oscillation of pressure. Humans perceive frequency of sound waves as pitch. Each musical note corresponds to a particular frequency which can be measured in hertz. An infant's ear is able to perceive frequencies ranging from 20 Hz to 20,000 Hz; the average adult human can hear sounds between 20 Hz and 16,000 Hz. [14] The range of ultrasound, infrasound and other physical vibrations such as molecular and atomic vibrations extends from a few femtohertz [15] into the terahertz range [16] and beyond.

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 (106 Hz) or gigahertz (109 Hz). This specification refers to the frequency of the CPU's master clock signal. This signal is a square wave, which is an electrical voltage that switches between low and high logic values 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 periods to perform a single operation, while others can perform multiple operations in a single cycle. [17] 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
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 high-energy, or, equivalently, massive particles, although these are not directly observable and must be inferred from their interactions with other phenomena. By convention, these are typically not expressed in hertz, but in terms of the equivalent quantum energy, which is proportional to the frequency by the factor of Planck's constant.

Hertz: Unicode characters. [18]
SymbolNameUnicode number
Hertz (Square HZ)U+3390
Kilohertz (Square KHZ)U+3391
Megahertz (Square MHZ)U+3392
Gigahertz (Square GHZ)U+3393
Terahertz (Square THZ)U+3394

See also

Notes and references

  1. "hertz". (1992). American Heritage Dictionary of the English Language (3rd ed.), Boston: Houghton Mifflin.
  2. "SI brochure: Table 3. Coherent derived units in the SI with special names and symbols".
  3. "[Resolutions of the] CIPM, 1964 – Atomic and molecular frequency standards" (PDF). SI brochure, Appendix 1.
  4. Mohr, J. C.; Phillips, W. D. (2015). "Dimensionless Units in the SI". Metrologia. 52 (1): 40–47. arXiv: 1409.2794 . Bibcode:2015Metro..52...40M. doi:10.1088/0026-1394/52/1/40.
  5. Mills, I. M. (2016). "On the units radian and cycle for the quantity plane angle". Metrologia. 53 (3): 991–997. Bibcode:2016Metro..53..991M. doi:10.1088/0026-1394/53/3/991.
  6. "SI units need reform to avoid confusion". Editorial. Nature. 548 (7666): 135. 7 August 2011. doi: 10.1038/548135b . PMID   28796224.
  7. P. R. Bunker; I. M. Mills; Per Jensen (2019). "The Planck constant and its units". J Quant Spectrosc Radiat Transfer. 237: 106594. Bibcode:2019JQSRT.23706594B. doi:10.1016/j.jqsrt.2019.106594.
  8. NIST Guide to SI Units – 9 Rules and Style Conventions for Spelling Unit Names, National Institute of Standards and Technology
  9. "(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." "BIPM – Table 3". BIPM . Retrieved 24 October 2012.
  10. "SI brochure, Section 2.2.2, paragraph 6". Archived from the original on 1 October 2009.
  11. "IEC History". Iec.ch. 15 September 1904. Retrieved 28 April 2012.
  12. Cartwright, Rufus (March 1967). Beason, Robert G. (ed.). "Will Success Spoil Heinrich Hertz?" (PDF). Electronics Illustrated. Fawcett Publications, Inc. pp. 98–99.
  13. Rekdal, Ole Bjørn (1 August 2014). "Academic urban legends". Social Studies of Science. 44 (4): 638–654. doi:10.1177/0306312714535679. ISSN   0306-3127. PMC   4232290 . PMID   25272616.
  14. 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.
  15. "Black Hole Sound Waves - Science Mission Directorate". science.nasa.go.
  16. Atomic vibrations are typically on the order of tens of terahertz
  17. Asaravala, Amit (30 March 2004). "Good Riddance, Gigahertz". Wired. Retrieved 28 April 2012.
  18. Unicode Consortium (2019). "The Unicode Standard 12.0 – CJK Compatibility ❰ Range: 3300—33FF ❱" (PDF). Unicode.org. Retrieved 24 May 2019.

Related Research Articles

The electromagnetic spectrum is the range of frequencies of electromagnetic radiation and their respective wavelengths and photon energies.

Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. Frequency is measured in units of hertz (Hz) which is equal to one occurrence of a repeating event per second. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example: if a newborn baby's heart beats at a frequency of 120 times a minute, its period, T, — the time interval between beats—is half a second. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light.

Second SI unit of time

The second is the base unit of time in the International System of Units (SI), commonly understood and 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. Analog clocks and watches often have sixty tick marks on their faces, representing seconds, and a "second hand" to mark the passage of time in seconds. Digital clocks and watches often have a two-digit seconds counter. The second is also part of several other units of measurement like meters per second for velocity, meters per second per second for acceleration, and cycles per second for frequency.

A nanosecond (ns) is an SI unit of time equal to one billionth of a second, that is, ​11 000 000 000 of a second, or 10−9 seconds.

A picosecond is an SI unit of time 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.

Radio wave Type of electromagnetic radiation

Radio waves are a type of electromagnetic radiation with wavelengths in the electromagnetic spectrum longer than infrared light. Radio waves have frequencies as high as 300 gigahertz (GHz) to as low as 30 hertz (Hz). At 300 GHz, the corresponding wavelength is 1 mm, and at 30 Hz is 10,000 km. The wavelength of a radio wave can be anywhere from shorter than a grain of rice to longer than the diameter of the Earth. Like all other electromagnetic waves, radio waves travel at the speed of light in vacuum. They are generated by electric charges undergoing acceleration, such as time varying electric currents. Naturally occurring radio waves are emitted by lightning and astronomical objects.

Wavenumber inverse of the wavelength

In the physical sciences, the wavenumber is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance. Whereas temporal frequency can be thought of as the number of waves per unit time, wavenumber is the number of waves per unit distance.

Angular frequency rate of change of the phase angle

In physics, angular frequencyω is a scalar measure of rotation rate. It refers to the angular displacement per unit time or the rate of change of the phase of a sinusoidal waveform, or as the rate of change of the argument of the sine function. Angular frequency is the magnitude of the vector quantity angular velocity. The term angular frequency vector is sometimes used as a synonym for the vector quantity angular velocity.

The clock rate 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 clock cycles per second or its equivalent, the SI unit hertz (Hz). The clock rate of the first generation of computers was measured in hertz or kilohertz (kHz), the first personal computers (PCs) to arrive throughout the 1970s and 1980s had clock rates measured in megahertz (MHz), and in the 21st century the speed of modern CPUs is commonly advertised in gigahertz (GHz). This metric is most useful when comparing processors within the same family, holding constant other features that may affect performance. Video card and CPU manufacturers commonly select their highest performing units from a manufacturing batch and set their maximum clock rate higher, fetching a higher price.

Terahertz or THz may refer to:

Terahertz radiation The 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 1000 GHz. Wavelengths of radiation in the terahertz band correspondingly range from 1 mm to 0.1 mm. Because terahertz radiation begins at a wavelength of around one 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 can be regarded either as microwave or far infrared.

The radio spectrum is the part of the electromagnetic spectrum with frequencies from 30 Hz to 300 GHz. 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).

Revolutions per minute is the number of turns in one minute. It is a unit of rotational speed or the frequency of rotation around a fixed axis.

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.

Cycle per second historic synonym for hertz, the unit of frequency

The cycle per second was a once-common English name for the unit of frequency now known as the hertz (Hz). The plural form was typically used, often written cycles per second, cycles/second, c.p.s., c/s, ~, or, ambiguously, just cycles (Cy./Cyc.). The term comes from the fact that sound waves have a frequency measurable in their number of oscillations, or cycles, per second.

Radian per second unit of angular velocity and angular frequency

The radian per second is the SI unit of angular velocity, commonly denoted by the Greek letter ω (omega). The radian per second is also the unit of angular frequency. The radian per second is defined as the change in the orientation of an object, in radians, every second.

The inverse second, reciprocal second, or per second (s−1) is a unit of frequency, defined as the multiplicative inverse of the second. It is dimensionally equivalent to:

Pulsed radiofrequency is the technique whereby radio frequency (RF) oscillations are gated at a rate of pulses (cycles) per second (one cycle per second is known as a hertz (Hz)). Radio frequency energies occupy 1.0 x 104 Hz to 3.0 x 1011 Hz of the electromagnetic spectrum. Radio frequency electromagnetic energy is routinely produced by RF electrical circuits connected to a transducer, usually an antenna.

Planck constant physical constant representing the quantum of action

The Planck constant, or Planck's constant is the quantum of electromagnetic action that relates a photon's energy to its frequency. The Planck constant multiplied by a photon's frequency is equal to a photon's energy. The Planck constant is a fundamental physical constant denoted as , and of fundamental importance in quantum mechanics. In metrology it is used to define the kilogram in SI units.

Non-ionizing radiation electromagnetic radiation that does not carry enough energy per quantum to ionize atoms or molecules

Non-ionizingradiation refers to any type of electromagnetic radiation that does not carry enough energy per quantum to ionize atoms or molecules—that is, to completely remove an electron from an atom or molecule. Instead of producing charged ions when passing through matter, non-ionizing electromagnetic radiation has sufficient energy only for excitation, the movement of an electron to a higher energy state. In contrast, ionizing radiation has a higher frequency and shorter wavelength than non-ionizing radiation, and can be a serious health hazard; exposure to it can cause burns, radiation sickness, cancer, and genetic damage. Using ionizing radiation requires elaborate radiological protection measures, which in general are not required with non-ionizing radiation.