hertz

The hertz (symbol: Hz) is a unit of frequency. It is defined as the number of complete cycles per second. It is the basic unit of frequency in the International System of Units (SI), and is used worldwide in both general-purpose and scientific contexts. Hertz can be used to measure any periodic event; the most common uses for hertz are to describe radio and audio frequencies, more or less sinusoidal contexts in which case a frequency of 1 Hz is equal to one cycle per second.

The unit hertz is defined by the International System of Units (SI) such 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.^[1] Equivalently, 1 Hz = ¹⁄_{9,192,631,770} ν (hfs Cs). This definition is derived from the SI definition of the second. Hertz are inverse, s⁻¹. In practice, the hertz simply replaced the older cycle per second.

In English, hertz is used as both singular and 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 cycle per second and the hertz are, however, not regularly used in nonsinusoidal contexts. The "frequency" (activity) of aperiodic or stochastic events, especially radioactive decay, is expressed in becquerels.

To avoid confusion, periodically varying angles are typically not expressed in hertz^[2], but rather in an appropriate angular unit such as radians per second. A disc rotating at 60 revolutions per minute (RPM) can thus be said to be rotating at ≈6.283 rad/s or 1 Hz, where the latter reflects the number of complete revolutions per second. The conversion between a frequency f measured in hertz and an angular frequency ω measured in radians/s are:

ω = 2πf and .

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 electromagnetism. The name was established by the International Electrotechnical Commission (IEC) in 1930.^[3] 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 speed and radio frequency (RF) applications, can be pronounced either /ˈɡɪɡəhɜrts/, with a hard /ɡ/ sound, or /ˈdʒɪɡəhɜrts/, with a soft /dʒ/. 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 16 Hz to 20,000 Hz; the average human can hear sounds between 20 Hz and 16,000 Hz.^[4] 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 speed expressed in megahertz or gigahertz (10⁹ hertz). This number refers to the frequency of the CPU's master clock signal ("clock speed"). This signal is simply an electrical voltage which changes from low to high and back again at regular intervals. Hertz has become the primary unit of measurement accepted by the general populace to determine the speed of a CPU, but many experts have criticized this approach, which they claim is an easily manipulable benchmark.^[5] For home-based personal computers, the CPU has ranged from approximately 1 megahertz in the late 1970s (Atari, Commodore, Apple computers) to nearly 4 GHz in the present. This can be increased even further by increasing the frequency of the CPU (overclocking) in the BIOS or other software. (Likewise, speed can also be decreased, or underclocked.)

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).

SI multiples

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

References

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
• One Hertz in Radians per Second (Google). Note, as of 06 May 2009 there is an error of 2π.