The characteristic of a periodic process, equal to the number of complete cycles of the process, performed per unit of time. Standard notation in formulas is,, or. The unit of frequency in the International System of Units (SI) is generally the hertz ( Hz, Hz). The reciprocal of the frequency is called the period. Frequency, like time, is one of the most accurately measured physical quantities: up to a relative accuracy of 10 −17.
In nature, periodic processes are known with frequencies from ~ 10-16 Hz (the frequency of the Sun's revolution around the center of the Galaxy) to ~ 10 35 Hz (the frequency of field oscillations characteristic of the most high-energy cosmic rays).
Cyclic frequency
Discrete event rate
The frequency of discrete events (pulse frequency) is a physical quantity equal to the number of discrete events occurring per unit of time. The unit of the frequency of discrete events is the second in the minus of the first power ( s −1, s −1), but in practice, hertz is usually used to express the pulse frequency.
Rotation frequency
Rotational speed is a physical quantity equal to the number of full revolutions per unit of time. The unit of rotation frequency is a second to the minus degree ( s −1, s −1), revolution per second. Units such as rpm, rpm, etc. are often used.
Other quantities related to frequency
Metrological aspects
Measurements
- Frequency meters are used to measure frequency different types, including: for measuring the frequency of pulses - electronic-counting and capacitor, for determining the frequencies of spectral components - resonant and heterodyne frequency meters, as well as spectrum analyzers.
- To reproduce the frequency with a given accuracy, various measures are used - frequency standards (high accuracy), frequency synthesizers, signal generators, etc.
- Frequencies are compared with a frequency comparator or with an oscilloscope according to Lissajous figures.
Standards
- State primary standard of units of time, frequency and national time scale GET 1-98 - located in VNIIFTRI
- Secondary standard of the unit of time and frequency VET 1-10-82 - located in SNIIM (Novosibirsk)
see also
Notes
Literature
- Fink L.M. Signals, interference, errors ... - M .: Radio and communication, 1984
- Physical units... Burdun G. D., Bazakutsa V. A. - Kharkov: Vishcha school,
- Physics reference... Yavorsky B.M., Detlaf A.A. - Moscow: Nauka,
Links
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Synonyms:- Authorization
- Chemical physics
See what "Frequency" is in other dictionaries:
FREQUENCY - (1) the number of repetitions of a periodic phenomenon per unit of time; (2) Ch. Side frequency, greater or less than the carrier frequency of the high-frequency generator, arising at (see); (3) The number of rotation is a value equal to the ratio of the number of revolutions ... ... Big Polytechnic Encyclopedia
Frequency - ion plasma frequency - the frequency of electrostatic oscillations that can be observed in plasma, the electron temperature of which is significantly higher than the temperature of the ions; this frequency depends on the concentration, charge and mass of plasma ions. ... ... Nuclear power terms
FREQUENCY - FREQUENCY, frequencies, pl. (special) frequencies, frequencies, women. (book). 1.units only. distract. noun to frequent. Frequency of occurrence. Rhythm frequency. Increased heart rate. Current frequency. 2. A quantity that expresses a certain degree of some frequent movement ... Dictionary Ushakova
frequency - s; frequency; g. 1. to Frequent (1 character). Monitor the repetition rate of moves. Required h. Planting potatoes. Pay attention to your heart rate. 2. The number of repetitions of the same movements, fluctuations in what l. unit of time. Ch. Wheel rotation. H ... encyclopedic Dictionary
FREQUENCY - (Frequency) number of periods per second. Frequency is the reciprocal of the oscillation period; ex. if the frequency of the alternating current is f \u003d 50 oscillations per second. (50 N), then the period T \u003d 1/50 sec. Frequency is measured in hertz. When characterizing radiation ... ... Marine dictionary
frequency - harmonica, vibration Dictionary of Russian synonyms. frequency n. density density (about vegetation)) Dictionary of Russian synonyms. Context 5.0 Informatics. 2012 ... Synonym dictionary
frequency - the occurrence of a random event is the ratio m / n of the number m of occurrences of this event in a given sequence of tests (its occurrence) to the total n tests. The term frequency is also used to mean occurrence. In an old book ... ... Dictionary of Sociological Statistics
Frequency - oscillations, the number of complete periods (cycles) of the oscillatory process, occurring per unit of time. The unit of frequency is hertz (Hz), which corresponds to one complete cycle in 1 s. Frequency f \u003d 1 / T, where T is the oscillation period, but often ... ... Illustrated Encyclopedic Dictionary
A quantum mechanical state has the physical meaning of the energy of this state, and therefore the system of units is often chosen in such a way that frequency and energy are expressed in the same units (in other words, the conversion factor between frequency and energy is Planck's constant in the formula E = hν - is chosen equal to 1).
The human eye is sensitive to electromagnetic waves with frequencies from 4⋅10 14 to 8⋅10 14 Hz (visible light); the vibration frequency determines the color of the observed light. The human hearing analyzer perceives acoustic waves with frequencies from 20 Hz to 20 kHz. In different animals, the frequency ranges of sensitivity to optical and acoustic vibrations are different.
The frequency ratios of sound vibrations are expressed in terms of musical intervals, such as an octave, fifth, third, etc. An interval of one octave between the frequencies of sounds means that these frequencies differ by 2 times, an interval of a pure fifth means the ratio of frequencies 3 ⁄ 2 ... In addition, a decade is used to describe frequency intervals - the interval between frequencies that differ by a factor of 10. Thus, the range of human sound sensitivity is 3 decades (20 Hz - 20,000 Hz). To measure the ratio of very close sound frequencies, units such as cent (frequency ratio equal to 2 1/1200) and millioctave (frequency ratio equal to 2 1/1000) are used.
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Instantaneous frequency and spectral frequencies
A periodic signal is characterized by an instantaneous frequency, which is (up to a factor) the rate of phase change, but the same signal can be represented as a sum of harmonic spectral components that have their own (constant) frequencies. The properties of the instantaneous frequency and the frequency of the spectral component are different.
Cyclic frequency
In the case of using degrees per second as the unit of angular frequency, the relationship with the usual frequency will be as follows: ω \u003d 360 ° ν.
Numerically, the cyclic frequency is equal to the number of cycles (oscillations, revolutions) in 2π seconds. The introduction of the cyclic frequency (in its basic dimension - radians per second) makes it possible to simplify many formulas in theoretical physics and electronics. So, the resonant cyclic frequency of the oscillatory LC-circuit is ω L C \u003d 1 / L C, (\\ displaystyle \\ omega _ (LC) \u003d 1 / (\\ sqrt (LC)),) whereas the usual resonant frequency ν L C \u003d 1 / (2 π L C). (\\ displaystyle \\ nu _ (LC) \u003d 1 / (2 \\ pi (\\ sqrt (LC))).) At the same time, a number of other formulas are getting more complicated. The decisive consideration in favor of the cyclic frequency was that the factors 2π and 1 / (2π), which appear in many formulas when using radians to measure angles and phases, disappear when the cyclic frequency is introduced.
In mechanics, when considering rotational motion, the analogue of the cyclic frequency is the angular velocity.
Discrete event rate
The frequency of discrete events (pulse frequency) is a physical quantity equal to the number of discrete events occurring per unit of time. The unit of the frequency of discrete events is a second to the minus first power (Russian designation: s −1; international: s −1). The frequency of 1 s −1 is equal to the frequency of discrete events at which one event occurs during 1 s.
Rotation frequency
Rotational speed is a physical quantity equal to the number of full revolutions per unit of time. The unit of rotation frequency is a second to the minus degree ( s −1, s −1), revolution per second. Units such as rpm, rpm, etc. are often used.
Other quantities related to frequency
Units
The SI unit of measurement is hertz. The unit was originally introduced in 1930 by the International Electrotechnical Commission, and was adopted for general use by the 11th General Conference on Weights and Measures as the SI unit in 1960. Before that, the unit of frequency was cycle per second (1 cycle per second \u003d 1 Hz) and derivatives (kilocycle per second, megacycle per second, kilomegacycle per second, equal to kilohertz, megahertz and gigahertz, respectively).
Metrological aspects
Frequency meters of various types are used to measure frequency, including: to measure the frequency of pulses - electronic counting and capacitor ones, to determine the frequencies of spectral components - resonant and heterodyne frequency meters, as well as spectrum analyzers. To reproduce the frequency with a given accuracy, various measures are used - frequency standards (high accuracy), frequency synthesizers, signal generators, etc. Frequencies are compared with a frequency comparator or using an oscilloscope according to Lissajous figures.
Standards
For the verification of frequency measuring instruments, national frequency standards are used. In Russia, national frequency standards include:
- The state primary standard of units of time, frequency and national time scale GET 1-98 is located in VNIIFTRI.
- Secondary standard of the unit of time and frequency VET 1-10-82 - located in SNIIM (Novosibirsk).
Calculations
The calculation of the frequency of a recurring event is performed by taking into account the number of occurrences of that event during a given period of time. The received amount is divided by the duration of the corresponding time interval. For example, if 71 homogeneous events occurred within 15 seconds, then the frequency will be
ν \u003d 71 15 s ≈ 4.7 Hz (\\ displaystyle \\ nu \u003d (\\ frac (71) (15 \\, (\\ mbox (s)))) \\ approx 4.7 \\, (\\ mbox (Hz)))If the received number of samples is small, then a more accurate technique is to measure the time interval for a given number of occurrences of the event in question, rather than finding the number of events within a given time interval. The use of the latter method introduces a random error between zero and the first sample, averaging half of the sample; this can lead to the appearance of an average error in the calculated frequency Δν \u003d 1 / (2 T m), or the relative error Δ ν /ν = 1/(2vT m ) whereT m is the time interval, and ν is the measured frequency. The error decreases with increasing frequency, therefore this problem is most significant for low frequencies, where the number of samplesN few.
Measurement methods
Stroboscopic method
The use of a special device - a stroboscope - is one of the historically earliest methods of measuring the frequency of rotation or vibration of various objects. During the measurement process, a stroboscopic light source (usually a bright lamp, periodically giving short light flashes) is used, the frequency of which is adjusted using a pre-calibrated timing circuit. A light source is directed at a rotating object, and then the frequency of the flashes gradually changes. When the frequency of the flashes equals the frequency of rotation or vibration of the object, the latter manages to complete a full oscillatory cycle and return to its original position in the interval between two flashes, so that when illuminated by a stroboscopic lamp, this object will appear stationary. Have this method, however, there is a drawback: if the object rotation frequency ( x ) is not equal to the strobe frequency ( y ), but proportional to it with an integer coefficient (2 x , 3x etc.), then the object will still appear motionless when illuminated.
The stroboscopic method is also used to fine-tune the rotational speed (vibration). In this case, the frequency of the flashes is fixed, and the frequency of the periodic movement of the object changes until it begins to seem stationary.
Beat method
All these waves, from the lowest frequencies of radio waves to the highest frequencies of gamma rays, are fundamentally the same, and they are all called electromagnetic radiation... They all travel in a vacuum at the speed of light.
Another characteristic of electromagnetic waves is wavelength. Wavelength is inversely proportional to frequency, so higher frequency electromagnetic waves have a shorter wavelength, and vice versa. In vacuum the wavelength
λ \u003d c / ν, (\\ displaystyle \\ lambda \u003d c / \\ nu,)where from is the speed of light in a vacuum. In a medium in which the phase velocity of propagation of an electromagnetic wave c′ Differs from the speed of light in vacuum ( c′ = c / n where n is the refractive index), the relationship between wavelength and frequency will be as follows:
λ \u003d c n ν. (\\ displaystyle \\ lambda \u003d (\\ frac (c) (n \\ nu)).)Another frequently used characteristic of a wave is the wavenumber (spatial frequency), which is equal to the number of waves per unit length: k \u003d 1 / λ. Sometimes this value is used with a factor of 2π, by analogy with normal and circular frequencies. k s \u003d 2π / λ. In the case of an electromagnetic wave in a medium
k \u003d 1 / λ \u003d n ν c. (\\ displaystyle k \u003d 1 / \\ lambda \u003d (\\ frac (n \\ nu) (c)).) k s \u003d 2 π / λ \u003d 2 π n ν c \u003d n ω c. (\\ displaystyle k_ (s) \u003d 2 \\ pi / \\ lambda \u003d (\\ frac (2 \\ pi n \\ nu) (c)) \u003d (\\ frac (n \\ omega) (c)).)Sound
The properties of sound (mechanical elastic vibrations of the medium) depend on frequency. A person can hear vibrations with a frequency of 20 Hz falls within the range of 50 Hz... In North America (USA, Canada, Mexico), Central and in some countries in northern South America (Brazil, Venezuela, Colombia, Peru), as well as in some Asian countries (in southwestern Japan, in South Korea, Saudi Arabia, the Philippines and Taiwan) use 60 Hz. Refer to the Standards for plugs, voltages and frequencies of the power supply in different countries. Almost all household electrical appliances work equally well in networks with a frequency of 50 and 60 Hz, subject to the same mains voltage. At the end of the XIX - first half of the XX century, before standardization, frequencies from 16 , although it increases transmission losses over long distances - due to capacitive losses, growth inductive resistance lines and losses on
The concept of frequency and period of a periodic signal. Units. (10+)
Signal frequency and period. Concept. Units
The material is an explanation and addition to the article:
Units of measurement of physical quantities in radio electronics
Units and ratios of physical quantities used in radio engineering.
In nature, periodic processes are often found. This means that some parameter characterizing the process changes according to a periodic law, that is, the equality is true:
Determination of frequency and period
F (t) \u003d F (t + T) (relation 1), where t is time, F (t) is the value of the parameter at time t, and T is some constant.
It is clear that if the previous equality is true, then the following is also true:
F (t) \u003d F (t + 2T) So, if T is the minimum value of a constant at which relation 1 is satisfied, then we will call T period
In electronics, we study the strength of current and voltage, so that periodic signals will be considered signals for voltage or current in which relation 1 is true.
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Everything on the planet has its own frequency. According to one version, it even forms the basis of our world. Alas, the theory is very difficult to present it within the framework of one publication, so we will consider exclusively the vibration frequency as an independent action. Within the framework of the article, a definition will be given to this physical process, its units of measurement and metrological component. And finally, an example of the importance of ordinary sound in ordinary life will be considered. We will find out what he is and what his nature is.
What is called the vibration frequency?
By this is meant a physical quantity that is used to characterize a periodic process, which is equal to the number of repetitions or occurrences of certain events per unit of time. This indicator is calculated as the ratio of the number of these incidents to the time period for which they were committed. Every element of the world has its own vibration frequency. The body, atom, road bridge, train, plane - they all perform certain movements, which are called so. Even if these processes are not visible to the eye, they are. The units of measurement in which the vibration frequency is considered are hertz. They got their name in honor of the physicist of German origin Heinrich Hertz.
Instantaneous frequency
A periodic signal can be characterized by an instantaneous frequency, which is, up to a factor, the rate of phase change. It can be represented as the sum of harmonic spectral components, which have their own constant oscillations.
Cyclic vibration frequency
It is convenient to use in theoretical physics, especially in the section on electromagnetism. Cyclic frequency (also called radial, circular, angular) is a physical quantity that is used to indicate the intensity of origin of oscillatory or rotational motion. The first is expressed in revolutions or oscillations per second. During rotational motion, the frequency is equal to the modulus of the angular velocity vector.
This indicator is expressed in radians per second. Cyclic frequency is the reciprocal of time. In numerical terms, it is equal to the number of oscillations or revolutions that occurred in 2π seconds. Its introduction for use makes it possible to significantly simplify the various spectrum of formulas in electronics and theoretical physics. The most popular use case is calculating the resonant cyclic frequency of an oscillating LC circuit. Other formulas can get quite complicated.
Discrete event rate
By this value is meant a value that is equal to the number of discrete events that occur in one unit of time. In theory, an indicator is usually used - a second to the minus of the first degree. In practice, the hertz is usually used to express the pulse frequency.
Rotation frequency
It is understood as a physical quantity that is equal to the number of complete revolutions that occur in one unit of time. The indicator is also used here - a second to the minus of the first degree. To indicate the work done, phrases such as revolution per minute, hour, day, month, year and others can be used.
Units
How is the vibration frequency measured? If we take into account the SI system, then the unit of measurement here is hertz. It was originally introduced by the International Electrotechnical Commission back in 1930. And the 11th General Conference on Weights and Measures in 1960 consolidated the use of this indicator as an SI unit. What has been put forward as the "ideal"? It was the frequency when one cycle occurs in one second.
But what about production? For them, arbitrary values \u200b\u200bwere fixed: kilocycle, megacycle per second, and so on. Therefore, picking up a device that operates with an indicator in GHz (like a computer processor), you can roughly imagine how many actions it performs. It would seem how slowly time passes for a person. But technology in the same period manages to perform millions and even billions of operations per second. In one hour, the computer is already doing so many actions that most people cannot even imagine them in numerical terms.
Metrological aspects
The vibration frequency has found its application even in metrology. Various devices have many functions:
- The pulse frequency is measured. They are represented by electronic counting and capacitor types.
- Determine the frequency of the spectral components. There are heterodyne and resonant types.
- Spectrum analysis is performed.
- They reproduce the required frequency with the specified accuracy. In this case, various measures can be applied: standards, synthesizers, signal generators and other equipment in this direction.
- The indicators of the obtained oscillations are compared; for this purpose, a comparator or an oscilloscope is used.
Example of work: sound
All of the above can be quite difficult to understand, since we used the dry language of physics. To understand the information given, you can give an example. Everything will be detailed in it, based on an analysis of cases from modern life... To do this, consider the most famous example of vibration - sound. Its properties, as well as the features of the implementation of mechanical elastic vibrations in a medium, are in direct proportion to the frequency.
Human hearing organs can pick up vibrations that range from 20 Hz to 20 kHz. Moreover, with age, the upper limit will gradually decrease. If the frequency of sound vibrations falls below 20 Hz (which corresponds to the subcontroctave), then infrasound will be generated. This type, which in most cases is not heard by us, people can still feel tactilely. When the limit of 20 kilohertz is exceeded, oscillations are generated, which are called ultrasound. If the frequency exceeds 1 GHz, then in this case we will be dealing with hypersound. If we consider such a musical instrument as a piano, then it can create vibrations in the range from 27.5 Hz to 4186 Hz. It should be borne in mind that the musical sound does not consist only of the fundamental frequency - overtones and harmonics are also mixed with it. This all together determines the timbre.
Conclusion
As you may have learned, vibration frequency is an extremely important component that allows our world to function. Thanks to her, we can hear, with her assistance, computers work and many other useful things are done. But if the oscillation frequency exceeds the optimal limit, then certain destruction may begin. So, if you influence the processor so that its crystal works at twice the rate, then it will quickly fail.
The same can be done with human life, when at high frequency, his eardrums burst. Other negative changes in the body will also occur, which will entail certain problems, up to and including death. Moreover, due to the peculiarity of the physical nature, this process will stretch for a rather long period of time. By the way, taking this factor into account, the military is considering new opportunities for developing weapons of the future.
This term "alternating electric current" should be understood as a current that changes in time in any way, in accordance with the concept of "variable quantity" introduced into mathematics. However, in electrical engineering, the term "alternating electric current" has entered the meaning electric current, imputed in direction (as opposed to), and, consequently, in magnitude, since it is physically impossible to imagine changes in the electric current in the direction without corresponding changes in magnitude.
The movement of electrons in a wire, first in one direction and then in the other, is called one alternating current oscillation. The first oscillation is followed by the second, then the third, etc. When the current in the wire oscillates around it, a corresponding oscillation of the magnetic field occurs.
The time of one oscillation is called a period and is denoted by the letter T. The period is expressed in seconds or in units of fractions of a second. These include: thousandth of a second - millisecond (ms) equal to 10 -3 s, millionth of a second - microsecond (μs) equal to 10 -6 s, and billionth of a second - nanosecond (ns) equal to 10 -9 s.
An important quantity that characterizes is frequency. It represents the number of oscillations or the number of periods per second and is denoted by the letter f or F. The unit of frequency is the hertz, named after the German scientist G. Hertz and abbreviated by the letters Hz (or Hz). If one full oscillation occurs in one second, then the frequency is equal to one hertz. When ten vibrations occur within a second, the frequency is 10 Hz. Frequency and period are reciprocals:
and
At a frequency of 10 Hz, the period is 0.1 s. And if the period is 0.01 s, then the frequency is 100 Hz.
Frequency - essential characteristic alternating current.Electrical machines and AC apparatus can only operate normally at the frequency for which they are designed. Parallel operation of electric generators and power stations common network is only possible on the same frequency. Therefore, in all countries, the frequency of alternating current produced by power plants is standardized by law.
IN electrical network alternating current frequency is 50 Hz. The current goes fifty times a second in one direction and fifty times in the opposite direction. It reaches its amplitude value a hundred times per second and becomes equal to zero a hundred times, that is, it changes its direction a hundred times when crossing the zero value. Lamps connected to the network go out a hundred times per second and flash brighter the same number of times, but the eye does not notice this, thanks to visual inertia, that is, the ability to retain received impressions for about 0.1 s.
When calculating with alternating currents, the angular frequency is also used, it is equal to 2pif or 6.28f. It should not be expressed in hertz, but in radians per second.
With the accepted industrial current frequency of 50 Hz, the maximum possible generator speed is 50 r / s (p \u003d 1). Turbine generators are built for this number of revolutions, i.e. generators driven by steam turbines. The number of revolutions of hydraulic turbines and the hydro generators driven by them depends on natural conditions (primarily on the pressure) and fluctuates within wide limits, sometimes decreasing to 0.35 - 0.50 rev / sec.
The number of revolutions has a great influence on the economic performance of the machine - dimensions and weight. Hydrogenerators with several revolutions per second have an outer diameter 3 - 5 times larger and their weight is many times greater than turbine generators of the same power with n \u003d 50 rps. In modern alternators, their magnetic system rotates, and the conductors in which the emf is induced are placed in the stationary part of the machine.
Alternating currents are usually divided by frequency. Currents with a frequency of less than 10000 Hz are called low frequency currents (LF currents). For these currents, the frequency corresponds to the frequency of various sounds of the human voice or musical instruments, and therefore they are otherwise called audio-frequency currents (with the exception of currents with a frequency below 20 Hz, which do not correspond to audio frequencies). In radio engineering, LF currents are widely used, especially in radiotelephone transmission.
However main role in radio communication perform alternating currents with a frequency of more than 10,000 Hz, called high frequency currents, or radio frequencies (high frequency currents). To measure the frequency of these currents, units are used: kilohertz (kHz), equal to one thousand hertz, megahertz (MHz), equal to one million hertz, and gigahertz (GHz), equal to a billion hertz. Otherwise, kilohertz, megahertz and gigahertz denote kHz, MHz, GHz. Currents with a frequency of hundreds of megahertz and above are called ultra-high or ultra-high frequency currents (microwave and UHF).
Radio stations operate using HF alternating currents with a frequency of hundreds of kilohertz and above. In modern radio engineering, currents with a frequency of billions of hertz are used for special purposes, and there are devices that can accurately measure such ultra-high frequencies.
