Hertz

This article is about the unit measure. For other uses, see Hertz (disambiguation).

"Hz" and "Megahertz" redirect here. For other uses, see Hz (disambiguation) and Megahertz (disambiguation).

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. 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 equivalent to cycles per second, i.e., "1/second" or ${\text{s}}^{-1}$. 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" and then adds the obvious conclusion: "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."

In English, "hertz" is also used as the plural form. 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. 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, 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

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

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 1930. 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.

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. The range of ultrasound, infrasound and other physical vibrations such as molecular and atomic vibrations extends from a few femtoHz into the terahertz range 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

Further information on why the frequency, including for gigahertz (GHz) etc., is a flawed speed indicator for computers: Megahertz myth

In computers, most central processing units (CPU) are labeled in terms of their clock rate expressed in megahertz or gigahertz (10⁶ or 10⁹ hertz, respectively). This number refers to the frequency of the CPU's master clock signal ("clock rate"). This signal is a square wave, which is an electrical voltage that switches between low and high values at regular intervals. 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 as some processors use multiple clock periods to perform a single operation, while others can perform multiple operations in a single cycle. For home-based 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.

The "speed" or the more correct term bandwidth of networks, including wireless, such as Wi-Fi, 3G, 4G, LTE, etc. is not affected by the myth described above. In general, higher frequency allows for higher possible bandwidth or bit rates, and lowers the time it takes to download large files. In general, however, higher frequencies do not pass through walls, making lower frequencies an advantage indoors. Most common equipment reports the highest frequency available, but usually also works at lower ones. Bandwidth is often equated with "speed", while latency ("lag") is the perceived problem (and is a measure distinct from bandwidth); higher bandwidth has an influence on latency.

SI multiples

SI multiples of hertz (Hz)

Submultiples			Multiples
Value	SI symbol	Name	Value	SI 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
10−27 Hz	rHz	rontohertz	1027 Hz	RHz	ronnahertz
10−30 Hz	qHz	quectohertz	1030 Hz	QHz	quettahertz
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.

See also

• Alternating current
• Bandwidth (signal processing)
• Electronic tuner
• FLOPS
• Frequency changer
• Normalized frequency
• Orders of magnitude (frequency)
• Periodic function
• Radian per second
• Rate

External links

• BIPM Cesium ion f_Cs definition
• 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