Hertz

Hertz
Unit system: SI derived unit
Unit of... Frequency
Symbol: Hz
Named after: Heinrich Hertz
Unit conversions
1 Hz in... is equal to...
   SI base units    1/s

The hertz (symbol: Hz) is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon.[1] One of its most common uses is the description of sine wave, particularly those used in radio and audio applications.

Contents

Definition

Details of a heartbeat as an example of a non-sinusoidal periodic phenomenon that can be described in terms of hertz. Two complete cycles are illustrated.

The hertz is equivalent to cycles per second.[2] In defining the second the CIPM declared that "the standard to be employed is the transition between the hyperfine levels F = 4, M =  0 and F = 3, M = 0 of the ground state 2S1/2 of the caesium 133 atom, unperturbed by external fields, and that the frequency of this transition is assigned the value 9 192 631 770 hertz"[3] thereby effectively defining the hertz and the second simultaneously.

In English, hertz is used as plural. 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 "frequency" (activity) of aperiodic or stochastic events, such as radioactive decay, is expressed in becquerels.

Even though angular velocity, angular frequency and hertz all have the dimensions of 1/s, angular velocity and angular frequency are not expressed in hertz [4], 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 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 are:

\omega = 2\pi f and f = \omega/(2\pi) \, .
This SI unit is named after Heinrich Hertz. As with every SI unit whose name is derived from the proper name of a person, the first letter of its symbol is uppercase (Hz). When an SI unit is spelled out in English, it should always begin with a lowercase letter (hertz), except where any word would be capitalized, such as at the beginning of a sentence or in capitalized material such as a title. Note that "degree Celsius" conforms to this rule because the "d" is lowercase.
—Based on The International System of Units, section 5.2.

History

The hertz is named after the German physicist Heinrich Hertz, who made important scientific contributions to the study of electromagnetism. The name was established by the International Electrotechnical Commission (IEC) in 1930.[5] 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.

The term "gigahertz", most commonly used in computer processor clock rates and radio frequency (RF) applications, can be pronounced either /ˈɡɪɡəhɜrts/, with a hard /ɡ/ sound, or /ˈdʒɪɡəhɜrts/, with a soft /dʒ/.[6] The prefix "giga-" is derived directly from the Greek "γιγας."

Applications

Vibration

Sound is a traveling 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 human can hear sounds between 20 Hz and 16,000 Hz.[7] The range of ultrasound, infrasound and other physical vibrations such as molecular vibrations extends into the megahertz range and well 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, megahertz, or gigahertz; this is why radio dials are commonly labeled with kHz, MHz, and 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.)

Computing

In computing, most central processing units (CPU) are labeled in terms of their clock rate expressed in megahertz or gigahertz (109 hertz). This number refers to the frequency of the CPU's master clock signal ("Clock rate"). This signal is simply an electrical voltage which changes from low to high and back again at regular intervals. This signal is also referred to as a square wave. Hertz has become the primary unit of measurement accepted by the general populace to determine the performance of a CPU, but many experts have criticized this approach, which they claim is an easily manipulable benchmark.[8] For home-based personal computers, the CPU has ranged from approximately 1 megahertz in the late 1970s (Atari, Commodore, Apple computers) to up to 6 GHz in the present (IBM POWER processors).

Various computer buses, such as the front-side bus connecting the CPU and northbridge, also operate at different frequencies in the megahertz range (for modern products).

CRT television and monitor refresh rates are measured in hertz.

SI multiples

SI multiples for hertz (Hz)
Submultiples Multiples
Value Symbol Name Value Symbol Name
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.

Frequencies not expressed in hertz

Even higher frequencies are believed to occur naturally, in the frequencies of the quantum-mechanical wave functions of high-energy (or, equivalently, massive) particles, although these are not directly observable, and must be inferred from their interactions with other phenomena. For practical reasons, 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.

See also
  • Orders of magnitude (frequency)
  • Radian per second
  • Signal bandwidth

References

  1. ↑ "hertz". (1992). American Heritage Dictionary of the English Language, 3rded. Boston: Houghton Mifflin.
  2. ↑ "SI brochure: Table 3. Coherent derived units in the SI with special names and symbols". http://www.bipm.org/en/si/si_brochure/chapter2/2-1/second.html. Retrieved 20102025. 
  3. ↑ "[Resolutions of the CIPM, 1964 - Atomic and molecular frequency standards"]. http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf. Retrieved 2010-20-26. 
  4. ↑ "SI brochure, Section 2.2.2, paragraph 6". http://www.bipm.org/en/si/derived_units/2-2-2.html. 
  5. ↑ IEC History
  6. ↑ "Gigahertz" in Dictionary.com Unabridged. Dictionary.
  7. ↑ Dominant spectral region
  8. ↑ Good Riddance, Gigahertz

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