Frequency is the number of occurrences of a repeating event per unit time Time has been defined as the continuum in which events occur in succession from the past to the present and on to the future. Time has also been defined as a one-dimensional quantity used to sequence events, to quantify the durations of events and the intervals between them, and to quantify and measure the motions of objects and other changes. It is also referred to as temporal frequency. The period is the duration of one cycle in a repeating event, so the period is the reciprocal In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1⁄x or x −1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a⁄b is b⁄a. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one of the frequency. Loosely speaking, 1 year A year is the orbital period of the Earth moving around the Sun. For an observer on Earth, this corresponds to the period it takes the Sun to complete one course throughout the zodiac along the ecliptic is the period Copernicus devised a mathematical formula to calculate a planet's sidereal period from its synodic period of the Earth Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets. It is sometimes referred to as the World, the Blue Planet,[note 6] or by its Latin name, Terra.[note 7]'s orbit around the Sun The Sun is the star at the center of the Solar System. It has a diameter of about 1,392,000 kilometers , about 109 times that of Earth, and its mass (about 2 × 1030 kilograms, 330,000 times that of Earth) accounts for about 99.86% of the total mass of the Solar System. About three quarters of the Sun's mass consists of hydrogen, while the rest is^[1], and the Earth's rotation Earth's rotation is the rotation of the solid Earth around its own axis. The Earth rotates towards the east. As viewed from the North Star Polaris, the Earth turns counter-clockwise on its axis has a frequency of 1 rotation per day.^[2]

The SI unit The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science of frequency is the hertz The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of sine wave, particularly those used in radio and audio applications (Hz), defined as one cycle per second.

Definitions and units

For cyclical processes, such as rotation A rotation is a movement of an object in a circular motion. An object rotates around a center of rotation. A three-dimensional object rotates always around an imaginary line called an axis as the Euler's rotation theorem shows. If the axis of rotation is within the body, the body is said to rotate upon itself, or spin—which implies relative, oscillations Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes is used to be synonymous with "oscillation.&, or waves In mathematics and science, a wave is a disturbance that travels through space and time, usually by the transfer of energy. Waves are described by a wave equation that can take on many forms depending on the type of wave. A mechanical wave is a wave that propagates through a medium owing to restoring forces resulting from its deformation. For, frequency is defined as a number of cycles per unit time. In physics Physics is a natural science that involves the study of matter and its motion through space-time, as well as all applicable concepts, including energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves and engineering Engineering is the discipline, art and profession of acquiring and applying technical, scientific, and mathematical knowledge to design and implement materials, structures, machines, devices, systems, and processes that safely realize a desired objective or invention disciplines, such as optics Optics is the branch of physics which studies the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation, acoustics Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics technology may be called an acoustical or audio engineer, and radio Radio is the transmission of signals by modulation of electromagnetic waves with frequencies below those of visible light. Electromagnetic radiation travels by means of oscillating electromagnetic fields that pass through the air and the vacuum of space. Information is carried by systematically changing some property of the radiated waves, such as, frequency is usually denoted by a Latin letter f or by a Greek letter ν (nu) The name of the letter is written νῦ in in Ancient Greek and traditional Modern Greek polytonic orthography, while in Modern Greek it is sometimes written νι [ni]. In English, the name of the letter is pronounced /ˈnuː/ or /ˈnjuː/.

In SI The International System of Units specifies a set of seven base units from which all other units of measurement are formed. These other units are called SI derived units and are also considered part of the standard units, the unit of frequency is the hertz (Hz) The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of sine wave, particularly those used in radio and audio applications, named after the German physicist Heinrich Hertz Heinrich Rudolf Hertz was a German physicist who clarified and expanded the electromagnetic theory of light that had been put forth by Maxwell. He was the first to satisfactorily demonstrate the existence of electromagnetic waves by building an apparatus to produce and detect VHF or UHF radio waves. 1 Hz means that an event repeats once per second The second , sometimes abbreviated sec., is the name of a unit of time, and is the International System of Units (SI) base unit of time. It may be measured using a clock. A previous name for this unit was cycles per second.

A traditional unit of measure used with rotating mechanical devices is revolutions per minute Revolutions per minute is a unit of frequency of rotation: the number of full rotations completed in one minute around a fixed axis. It is used as a measure of rotational speed of a mechanical component, abbreviated RPM. 60 RPM equals one hertz.^[3]

The period, usually denoted by T, is the length of time taken by one cycle, and is the reciprocal In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1⁄x or x −1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a⁄b is b⁄a. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one of the frequency f:

The SI The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science unit for period is the second.

Measurement

By counting

Calculating the frequency of a repeating event is accomplished by counting the number of times that event occurs within a specific time interval, then dividing the count by the length of the time interval. For example, if 71 events occur within 15 seconds, the frequency is:

If the number of counts is not very large, it is more accurate to measure the time interval for a predetermined number of occurrences, rather than the number of occurrences within a specified time.^[4] The latter method introduces a random error Random errors are errors in measurement that lead to measured values being inconsistent when repeated measures of a constant attribute or quantity are taken. The word random indicates that they are inherently unpredictable, and have null expected value, namely, they are scattered about the true value, and tend to have null arithmetic mean when a into the count of between zero and one count, so on average In mathematics, an average, or central tendency of a data set is a measure of the "middle" value of the data set half a count. This is called gating error and causes an average error in the calculated frequency of Δf = 1/(2 T_m), or a fractional error of Δf / f = 1/(2 f T_m) where T_m is the timing interval and f is the measured frequency. This error decreases with frequency, so it is a problem at low frequencies where the number of counts N is small.

By stroboscope

An older method of measuring the frequency of rotating or vibrating objects is to use a stroboscope A stroboscope, also known as a strobe, is an instrument used to make a cyclically moving object appear to be slow-moving, or stationary. The principle is used for the study of rotating, reciprocating, oscillating or vibrating objects. Machine parts and vibrating strings are common examples. This is an intense repetitively flashing light (strobe light Strobe light or stroboscopic lamp, commonly called a strobe, is a device used to produce regular flashes of light. It is one of a number of devices that can be used as a stroboscope. The word originated from the Greek strobos, meaning "act of whirling.") whose frequency can be adjusted with a calibrated timing circuit. The strobe light is pointed at the rotating object and the frequency adjusted up and down. When the frequency of the strobe equals the frequency of the rotating or vibrating object, the object completes one cycle of oscillation and returns to its original position between the flashes of light, so when illuminated by the strobe the object appears stationary. Then the frequency can be read from the calibrated readout on the stroboscope. A downside of this method is that an object rotating at a multiple of the strobing frequency will also appear stationary.

By frequency counter

Higher frequencies are usually measured with a frequency counter A frequency counter is an electronic instrument, or component of one, that is used for measuring frequency. Frequency is defined as the number of events of a particular sort occurring in a set period of time. Frequency counters usually measure the number of oscillations or pulses per second in a repetitive electronic signal. This is an electronic instrument An electronic musical instrument is a musical instrument that produces its sounds using electronics. Such an instrument sounds by outputting an electrical audio signal that ultimately drives a loudspeaker which measures the frequency of an applied repetitive electronic signal In the fields of communications, signal processing, and in electrical engineering more generally, a signal is any time-varying or spatial-varying quantity and displays the result in hertz on a digital display. It uses digital logic Digital electronics are systems that represent signals as discrete levels, rather than as a continuous range. In most cases the number of states is two, and these states are represented by two voltage levels: one near to zero volts and one at a higher level depending on the supply voltage in use. These two levels are often represented as "Low& to count the number of cycles during a time interval established by a precision quartz A quartz clock is a clock that uses an electronic oscillator that is regulated by a quartz crystal to keep time. This crystal oscillator creates a signal with very precise frequency, so that quartz clocks are at least an order of magnitude more accurate than good mechanical clocks. Generally, some form of digital logic counts the cycles of this time base. Cyclic processes that are not electrical in nature, such as the rotation rate of a shaft, mechanical vibrations, or sound waves Sound is a travelling wave which is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations, can be converted to a repetitive electronic signal by transducers A transducer is a device that converts one type of energy to another. The conversion can be to/from electrical, electro-mechanical, electromagnetic, photonic, photovoltaic, or any other form of energy. While the term transducer commonly implies use as a sensor/detector, any device which converts energy can be considered a transducer and the signal applied to a frequency counter. Frequency counters can currently cover the range up to about 100 GHz. This represents the limit of direct counting methods; frequencies above this must be measured by indirect methods.

Heterodyne methods

Above the range of frequency counters, frequencies of electromagnetic signals are often measured indirectly by means of heterodyning (frequency conversion). A reference signal of a known frequency near the unknown frequency is mixed with the unknown frequency in a nonlinear mixing device such as a diode In electronics, a diode is a two-terminal electronic component that conducts electric current in only one direction. The term usually refers to a semiconductor diode, the most common type today. This is a crystalline piece of semiconductor material connected to two electrical terminals. A vacuum tube diode is a vacuum tube with two electrodes: a. This creates a heterodyne In radio and signal processing, heterodyning is the generation of new frequencies by mixing , two oscillating waveforms. It is useful for placing information of interest into a useful frequency range following modulation or prior to demodulation. The two frequencies are mixed in a vacuum tube, transistor, diode, or other signal processing device or "beat" signal at the difference between the two frequencies, which is low enough to be measured by a frequency counter. Of course, this process just measures the unknown frequency by its offset from the reference frequency, which must be determined by some other method. To reach higher frequencies, several stages of heterodyning can be used. Current research is extending this method to infrared and light frequencies (optical heterodyne detection).

Frequency of waves

Frequency has an inverse relationship to the concept of wavelength In physics, the wavelength of a sinusoidal wave is the spatial period of the wave – the distance over which the wave's shape repeats. It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a characteristic of both traveling waves and, simply, frequency is inversely proportional to wavelength λ (lambda Lambda is the 11th letter of the Greek alphabet. In the system of Greek numerals lambda has a value of 30. Lambda is related to the Phoenician letter Lamed . Letters in other alphabets that stemmed from lambda include the Roman L and the Cyrillic letter El (Л, л). The ancient grammarians and dramatists give evidence to the pronunciation as /laː). The frequency f is equal to the phase velocity The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity. The phase speed is given in terms of the v of the wave In mathematics and science, a wave is a disturbance that travels through space and time, usually by the transfer of energy. Waves are described by a wave equation that can take on many forms depending on the type of wave. A mechanical wave is a wave that propagates through a medium owing to restoring forces resulting from its deformation. For divided In mathematics, especially in elementary arithmetic, division is the arithmetic operation that is the inverse of multiplication by the wavelength λ of the wave:

In the special case of electromagnetic waves moving through a vacuum In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". Even putting aside the complexities of the quantum vacuum, the classical notion of a perfect vacuum with gaseous pressure of exactly, then v = c , where c is the speed of light The speed of light, usually denoted by c, is a physical constant important in many areas of physics. Light and all other electromagnetic radiation always travel at this speed in empty space , regardless of the motion of the source or the inertial frame of the observer. Its value is exactly 299,792,458 metres per second (approximately 186,282 miles in a vacuum, and this expression becomes:

When waves In mathematics and science, a wave is a disturbance that travels through space and time, usually by the transfer of energy. Waves are described by a wave equation that can take on many forms depending on the type of wave. A mechanical wave is a wave that propagates through a medium owing to restoring forces resulting from its deformation. For from a monochromatic Monochrome describes paintings, drawings, design, or photographs in one color or shades of one color. A monochromatic object or image has colors in shades of limited colors or hues. Monochrome images in neutral colors are called grayscale or black-and-white. "Monochromatic light" refers to light of a narrow frequency source travel from one medium An optical medium is material through which electromagnetic waves propagate. It is a form of transmission medium. The permittivity and permeability of the medium define how electromagnetic waves propagate in it. The medium has an intrinsic impedance, given by to another, their frequency remains exactly the same — only their wavelength In physics, the wavelength of a sinusoidal wave is the spatial period of the wave – the distance over which the wave's shape repeats. It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a characteristic of both traveling waves and and speed The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity. The phase speed is given in terms of the change.

Examples

Physics of light

Radiant energy is energy which is propagated in the form of electromagnetic waves. Most people think of natural sunlight or electrical light, when considering this form of energy. The type of light which we perceive through our optical sensors (eyes) is classified as white light, and is composed of a range of colors (red, orange, yellow, green, blue, indigo, violet) over a range of wavelengths, or frequencies.

Visible (white) light is only a small fraction of the entire spectrum of electromagnetic radiation. At the short end of that wavelength scale is ultraviolet (UV) light from the sun, which cannot be seen. At the longer end of that spectrum is infrared (IR) light (perceived as heat), which is used for night vision and other heat-seeking devices. At even shorter wavelengths than UV are X-rays and Gamma-rays. At longer wavelengths than IR are microwaves, radio waves, electromagnetic waves in megahertz and kHz range, as well as natural waves with frequencies in the millihertz and microhertz range. A 2 millihertz wave has a wavelength approximately equal to the distance from the earth to the sun. A microhertz wave would extend 0.0317 light years. A nanohertz wave would extend 31.6881 light years.

Electromagnetic radiation is classified according to the frequency (or wavelength) of the light wave. This includes (in order of increasing frequency): natural electromagnetic waves, radio waves, microwaves, terahertz radiation, infrared (IR) radiation, visible light, ultraviolet (UV) radiation, X-rays and gamma rays. Of these, natural electromagnetic waves have the longest wavelengths and gamma rays have the shortest. A small window of frequencies, called the visible spectrum or light, is sensed by the eye of various organisms, with variations of the limits of this narrow spectrum.

Physics of sound

Sound is vibration transmitted through a solid, liquid, or gas; particularly, sound means those vibrations composed of frequencies capable of being detected by ears. For humans, hearing is limited to frequencies between about 20 Hz and 20,000 Hz (20 kHz), with the upper limit generally decreasing with age. Other species have a different range of hearing. For example, some dog breeds can perceive vibrations up to 60,000 Hz.^[5] As a signal perceived by one of the major senses, sound is used by many species for detecting danger, navigation, predation, and communication.

The mechanical vibrations that can be interpreted as sound are able to travel through all forms of matter: gases, liquids, solids, and plasmas. The matter that supports the sound is called the medium. Sound cannot travel through vacuum.

Other examples

In Europe, Africa, Australia, Southern South America, most of Asia, and Russia, the frequency of the alternating current in household electrical outlets is 50 Hz (close to the tone G), whereas in North America and Northern South America, the frequency of the alternating current is 60 Hz (between the tones B♭ and B — that is, a minor third above the European frequency). The frequency of the 'hum' in an audio recording can show where the recording was made — in countries utilizing the European, or the American grid frequency.

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