Xrthnty

Hertz
Unit system	; SI derived unit;
Unit of	; Frequency;
Symbol	; Hz
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 ¹⁄_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 for 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), and terahertz (10¹² Hz, THz).

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 speeds at which computers and other electronics are driven.

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).

In English, "hertz" is also used as the plural form.^[4] 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.^[5] 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,^[6] 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 2 $π$ 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

omega =2pi f,

and

f=frac omega 2pi ,

.

This SI unit is named after Heinrich Hertz. As with every International System of Units (SI) unit named for a person, the first letter of its symbol is upper case (Hz). However, when an SI unit is spelled out in English, it is treated as a common noun and should always begin with a lower case letter (hertz)—except in a situation where any word in that position would be capitalized, such as at the beginning of a sentence or in material using title 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.^[7] 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.^[8]

Applications

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.

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.^[9] The range of ultrasound, infrasound and other physical vibrations such as molecular and atomic vibrations extends from a few femtohertz^[10] into the terahertz range^[11] 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. (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.^[12] 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 for hertz (Hz)
Value	SI symbol	Name	Value	SI symbol	Name
Submultiples			Multiples
10⁻¹ Hz	dHz	decihertz	10¹ Hz	daHz	decahertz
10⁻² Hz	cHz	centihertz	10² Hz	hHz	hectohertz
10⁻³ Hz	mHz	millihertz	10³ Hz	kHz	kilohertz
10⁻⁶ Hz	µHz	microhertz	10⁶ Hz	MHz	megahertz
10⁻⁹ Hz	nHz	nanohertz	10⁹ Hz	GHz	gigahertz
10⁻¹² Hz	pHz	picohertz	10¹² Hz	THz	terahertz
10⁻¹⁵ Hz	fHz	femtohertz	10¹⁵ Hz	PHz	petahertz
10⁻¹⁸ Hz	aHz	attohertz	10¹⁸ Hz	EHz	exahertz
10⁻²¹ Hz	zHz	zeptohertz	10²¹ Hz	ZHz	zettahertz
10⁻²⁴ Hz	yHz	yoctohertz	10²⁴ Hz	YHz	yottahertz
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.

Notes and references

^ "hertz". (1992). American Heritage Dictionary of the English Language (3rd ed.), Boston: Houghton Mifflin.

^ "SI brochure: Table 3. Coherent derived units in the SI with special names and symbols".

^ "[Resolutions of the] CIPM, 1964 – Atomic and molecular frequency standards" (PDF). SI brochure, Appendix 1.

^ NIST Guide to SI Units – 9 Rules and Style Conventions for Spelling Unit Names, National Institute of Standards and Technology

^ "(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 2012-10-24.

^ "SI brochure, Section 2.2.2, paragraph 6". Archived from the original on 1 October 2009.

^ "IEC History". Iec.ch. 1904-09-15. Retrieved 2012-04-28.

^ Cartwright, Rufus (March 1967). Beason, Robert G., ed. "Will Success Spoil Heinrich Hertz?" (PDF). Electronics Illustrated. Fawcett Publications, Inc. pp. 98–99. Retrieved 2016-03-29.

^ 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.

^ "Black Hole Sound Waves - Science Mission Directorate". science.nasa.go.

^ Atomic vibrations are typically on the order of tens of terahertz

^ Asaravala, Amit (2004-03-30). "Good Riddance, Gigahertz". Wired.com. Retrieved 2012-04-28.

External links

SI Brochure: Unit of time (second)

National Research Council of Canada: Cesium fountain clock

National Physical Laboratory: Trapped ion optical frequency standards

National Research Council of Canada: Optical frequency standard based on a single trapped ion

National Research Council of Canada: Optical frequency comb

Online Tone Generator

[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] NIST Guide to SI Units – 9 Rules and Style Conventions for Spelling Unit Names, National Institute of Standards and Technology

[BIPMtable3-5] "(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 2012-10-24.

[6] "SI brochure, Section 2.2.2, paragraph 6". Archived from the original on 1 October 2009.

[7] "IEC History". Iec.ch. 1904-09-15. Retrieved 2012-04-28.

[8] Cartwright, Rufus (March 1967). Beason, Robert G., ed. "Will Success Spoil Heinrich Hertz?" (PDF). Electronics Illustrated. Fawcett Publications, Inc. pp. 98–99. Retrieved 2016-03-29.

[9] 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.

[10] "Black Hole Sound Waves - Science Mission Directorate". science.nasa.go.

[11] Atomic vibrations are typically on the order of tens of terahertz

[12] Asaravala, Amit (2004-03-30). "Good Riddance, Gigahertz". Wired.com. Retrieved 2012-04-28.

v t e SI units
Authority: International System of Units (BIPM)
Base units	ampere candela kelvin kilogram metre mole second
Derived units with special names	becquerel coulomb degree Celsius farad gray henry hertz joule katal lumen lux newton ohm pascal radian siemens sievert steradian tesla volt watt weber
Other accepted units	astronomical unit bar dalton day decibel degree of arc electronvolt hectare hour litre minute minute of arc neper second of arc tonne atomic units natural units
See also	Conversion of units Metric prefixes Proposed redefinitions Systems of measurement
Book Category

搜尋此網誌

Xrthnty

Hertz

Contents