Hertz

The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI) and is defined as one cycle per second.[1][2] 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.[3] 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 (103 Hz, kHz), megahertz (106 Hz, MHz), gigahertz (109 Hz, GHz), terahertz (1012 Hz, THz).

Hertz
Unit systemSI derived unit
Unit ofFrequency
SymbolHz
Named afterHeinrich Hertz
In SI base unitss−1
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.

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 the energy of a photon, via the Planck relation E=hν, where E is the photon's energy, ν is its frequency, and the proportionality constant h is Planck's constant.

Definition

The hertz is defined as 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"[4][5] and then adds: "It follows that the hyperfine splitting in the ground state of the caesium 133 atom is exactly 9192631770 hertz, ν(hfs Cs) = 9192631770 Hz." The dimension of the unit hertz is 1/time (1/T). Expressed in base SI units, the unit is 1/second (1/s).

In English, "hertz" is also used as the plural form.[6] 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.[7] Whereas 1 Hz is one cycle per second, 1 Bq is one aperiodic radionuclide event per second.

Even though angular velocity, angular frequency and the unit hertz all have the dimension 1/T, angular velocity and angular frequency are not expressed in hertz,[8] but rather in an appropriate angular unit such as the radian 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

${\displaystyle \omega =2\pi f\,}$  and ${\displaystyle f={\frac {\omega }{2\pi }}\,}$ .

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.[9] 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.[10]

Sometimes the adjectival form "per second" was omitted, so that "megacycles" (Mc) was used as an abbreviation of "megacycles per second" (that is, megahertz (MHz)).[11]

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 20000 Hz; the average adult human can hear sounds between 20 Hz and 16000 Hz.[12] The range of ultrasound, infrasound and other physical vibrations such as molecular and atomic vibrations extends from a few femtohertz[13] into the terahertz range[14] and beyond.[15]

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.[16] 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

Submultiples Multiples Value SI symbol Name Value 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.

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").[17]

• U+3390 SQUARE HZ
• U+3391 SQUARE KHZ
• U+3392 SQUARE MHZ
• U+3393 SQUARE GHZ
• U+3394 SQUARE THZ

Notes and references

1. ^ "hertz". (1992). American Heritage Dictionary of the English Language (3rd ed.), Boston: Houghton Mifflin.
2. ^
3. ^
4. ^ "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.
5. ^ "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.
6. ^ NIST Guide to SI Units – 9 Rules and Style Conventions for Spelling Unit Names, National Institute of Standards and Technology
7. ^ "(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.
8. ^ "SI brochure, Section 2.2.2, paragraph 6". Archived from the original on 1 October 2009.
9. ^ "IEC History". Iec.ch. Archived from the original on 19 May 2013. Retrieved 6 January 2021.
10. ^ Cartwright, Rufus (March 1967). Beason, Robert G. (ed.). "Will Success Spoil Heinrich Hertz?" (PDF). Electronics Illustrated. Fawcett Publications, Inc. pp. 98–99.
11. ^ 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.
12. ^ 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.
13. ^ "Black Hole Sound Waves – Science Mission Directorate". science.nasa.go.
14. ^ Atomic vibrations are typically on the order of tens of terahertz
15. ^ "Black Hole Sound Waves – Science Mission Directorate". science.nasa.go.
16. ^ Asaravala, Amit (30 March 2004). "Good Riddance, Gigahertz". Wired. Retrieved 28 April 2012.
17. ^ Unicode Consortium (2019). "The Unicode Standard 12.0 – CJK Compatibility ❰ Range: 3300—33FF ❱" (PDF). Unicode.org. Retrieved 24 May 2019.