Holomorphic function

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Lights flash at frequency f = 0.5 Hz (Hz = hertz), 1.0 Hz or 2.0 Hz, where Template:J means $x$ flashes per second. T is the period and T = Template:J (s = seconds) means that $y$ is the number of seconds per flash. T and f are each other's reciprocal: Template:J and Template:J.

The hertz (symbol Hz) is the unit of frequency in the International System of Units (SI). It is defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications, such as the frequency of musical tones. The unit is named for Heinrich Rudolf Hertz, who was the first to conclusively prove the existence of electromagnetic waves.

Definition

The hertz is equivalent to cycles per second. 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 2S_1/2 of the cesium 133 atom, unperturbed by external fields, and that the frequency of this transition is assigned the value 9 192 631 770 hertz" thereby effectively defining the hertz and the second simultaneously.

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 "frequency" or activity of aperiodic or stochastic events, such as radioactive decay, is expressed in becquerels, not hertz.

Even though angular velocity, angular frequency and the unit hertz all have the dimension 1/s (reciprocal second), 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 $f={\frac {\omega }{2\pi }}\,$.

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.

Applications

Sine wave with varying frequency.

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.

Vibration

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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, high-intensity 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 (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.)

Computing

In computing, 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. For home-based personal computers, CPU clock speeds have ranged from approximately 1 megahertz in the late 1970s (Atari, Commodore, Apple computers) to up to 6 GHz in IBM POWER processors.

Various computer buses, such as the front-side bus connecting the CPU and northbridge, also operate at various frequencies in the megahertz range.

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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. 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.

Notes and references

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External links

• BIPM Cesium ion f_Cs definition
• National Research Council of Canada: Generation of the Hz
• 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