The time during which one complete change in the EMF occurs, that is, one cycle of oscillation or one complete revolution of the radius vector, is called alternating current oscillation period(picture 1).

Picture 1. Period and amplitude of a sinusoidal oscillation. Period - the time of one oscillation; The amplitude is its largest instantaneous value.

The period is expressed in seconds and denoted by the letter T.

Smaller units of period are also used, these are millisecond (ms) - one thousandth of a second and microsecond (μs) - one millionth of a second.

1 ms = 0.001 sec = 10 -3 sec.

1 µs = 0.001 ms = 0.000001 sec = 10 -6 sec.

1000 µs = 1 ms.

The number of complete changes in the EMF or the number of revolutions of the radius vector, that is, in other words, the number of complete cycles of oscillations performed by alternating current in one second, is called oscillation frequency alternating current .

The frequency is indicated by the letter f and is expressed in periods per second or hertz.

One thousand hertz is called a kilohertz (kHz), and one million hertz is called a megahertz (MHz). There is also a unit gigahertz (GHz) equal to one thousand megahertz.

1000 Hz = 10 3 Hz = 1 kHz;

1000,000 Hz = 10 6 Hz = 1000 kHz = 1 MHz;

1000,000,000 Hz = 109 Hz = 1000,000 kHz = 1000 MHz = 1 GHz;

The faster the EMF changes, that is, the faster the radius vector rotates, the shorter the oscillation period. The faster the radius vector rotates, the higher the frequency. Thus, the frequency and period of an alternating current are inversely proportional to each other. The larger one of them, the smaller the other.

The mathematical relationship between the period and frequency of alternating current and voltage is expressed by the formulas

For example, if the frequency of the current is 50 Hz, then the period will be equal to:

T \u003d 1 / f \u003d 1/50 \u003d 0.02 sec.

Conversely, if it is known that the period of the current is 0.02 sec, (T=0.02 sec), then the frequency will be:

f \u003d 1 / T \u003d 1 / 0.02 \u003d 100/2 \u003d 50 Hz

The frequency of alternating current used for lighting and industrial purposes is exactly 50 Hz.

Frequencies from 20 to 20,000 Hz are called audio frequencies. The currents in the antennas of radio stations fluctuate with frequencies up to 1,500,000,000 Hz, or, in other words, up to 1,500 MHz or 1.5 GHz. Such high frequencies are called radio frequencies or high frequency oscillations.

Finally, the currents in the antennas radar stations, stations satellite communications, other special systems (for example, GLANASS, GPS) fluctuate with frequencies up to 40,000 MHz (40 GHz) and higher.

AC amplitude

The highest value that the EMF or current strength reaches in one period is called amplitude of the emf or alternating current. It is easy to see that the scaled amplitude is equal to the length of the radius vector. Amplitudes of current, EMF and voltage are indicated respectively by letters Im, Em and Um (picture 1).

Angular (cyclic) frequency of alternating current.

The speed of rotation of the radius vector, i.e., the change in the value of the angle of rotation for one second, is called the angular (cyclic) frequency of the alternating current and is denoted by the Greek letter ? (omega). Rotation angle of the radius vector in any this moment relative to its initial position, it is usually measured not in degrees, but in special units - radians.

The radian is the angular value of the arc of a circle, the length of which is equal to the radius of this circle (Figure 2). The whole circle that is 360° is equal to 6.28 radians, which is 2.

Figure 2.

1rad = 360°/2

Therefore, the end of the radius vector during one period runs a path equal to 6.28 radians (2). Since for one second the radius vector makes a number of revolutions equal to the frequency of the alternating current f, then in one second its end runs a path equal to 6.28*f radian. This expression, which characterizes the speed of rotation of the radius vector, will be the angular frequency of the alternating current - ? .

? = 6.28*f = 2f

The angle of rotation of the radius vector at any given moment relative to its initial position is called AC phase. The phase characterizes the magnitude of the EMF (or current) at a given moment, or, as they say, the instantaneous value of the EMF, its direction in the circuit and the direction of its change; phase shows whether the emf is decreasing or increasing.

Figure 3

A complete rotation of the radius vector is 360°. With the beginning of a new revolution of the radius vector, the change in the EMF occurs in the same order as during the first revolution. Therefore, all phases of the EMF will be repeated in the same order. For example, the phase of the EMF when the radius vector is rotated through an angle of 370 ° will be the same as when it is rotated by 10 °. In both of these cases, the radius vector occupies the same position, and, therefore, the instantaneous values ​​​​of the emf will be the same in phase in both of these cases.

The 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 the frequency and energy are expressed in the same units (in other words, the conversion factor between frequency and energy is the Planck 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 oscillation frequency determines the color of the observed light. The human auditory analyzer perceives acoustic waves with frequencies from 20 Hz to 20 kHz. Different animals have different frequency ranges of sensitivity to optical and acoustic vibrations.

The ratios of the frequencies of sound vibrations are expressed using musical intervals, such as 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 10 times. So, the range of human sound sensitivity is 3 decades (20 Hz - 20,000 Hz). To measure the ratio of very close audio frequencies, units such as cent (frequency ratio equal to 2 1/1200) and millioctave (frequency ratio 2 1/1000) are used.

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Instantaneous frequency and frequencies of spectral components

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. Introduction cyclic frequency(in its basic dimension - radians per second) allows you to simplify many formulas in theoretical physics and electronics. So, the resonant cyclic frequency of the oscillatory LC circuit is equal to ω L C = 1 / L C , (\displaystyle \omega _(LC)=1/(\sqrt (LC)),) while the normal resonant frequency ν L C = 1 / (2 π L C) . (\displaystyle \nu _(LC)=1/(2\pi (\sqrt (LC))).) At the same time, a number of other formulas become more complicated. The decisive consideration in favor of 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 cyclic frequency is introduced.

In mechanics, when considering rotational motion, the analogue of cyclic frequency is the angular velocity.

Discrete event frequency

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 frequency of discrete events is a second to the minus one degree (Russian designation: s −1; international: s−1). The frequency 1 s −1 is equal to the frequency of discrete events at which one event occurs in 1 s.

Rotation frequency

The rotational speed is a physical quantity equal to the number of full revolutions per unit of time. The unit of rotational speed is a second to the minus first power ( s −1, s−1), revolution per second. Units often used are revolutions per minute, revolutions per hour, etc.

Other quantities related to frequency

Units

In the SI system, the unit of measure is hertz. The unit was originally introduced in 1930 by the International Electrotechnical Commission, and in 1960 adopted for general use by the 11th General Conference on Weights and Measures as the SI unit. 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 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. The frequencies are compared with a frequency comparator or using an oscilloscope using Lissajous figures.

Standards

National frequency standards are used to calibrate frequency measuring instruments. In Russia, the national frequency standards include:

• The state primary standard of time, frequency and national scale time GET 1-98 is located at VNIIFTRI.
• Secondary standard of the unit of time and frequency VET 1-10-82- located in SNIIM (Novosibirsk).

Computing

The calculation of the frequency of a recurring event is carried out by taking into account the number of occurrences of this event during a given period of time. The resulting amount is divided by the duration of the corresponding time period. For example, if 71 homogeneous events occurred within 15 seconds, then the frequency will be

ν = 71 15 s ≈ 4.7 Hz (\displaystyle \nu =(\frac (71)(15\,(\mbox(s))))\approx 4.7\,(\mbox(Hz)))

If the number of samples obtained 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 the zero and the first count, averaging half the count; this can lead to the appearance of an average error in the calculated frequency Δν = 1/(2 Tm) , or the relative error Δ ν /ν = 1/(2v Tm ) , where Tm is the time interval and ν is the measured frequency. The error decreases as the frequency increases, so this problem is the most important for low frequencies, where the number of samples N few.

Measurement methods

Stroboscopic method

The use of a special device - a stroboscope - is one of the historically early methods for measuring the rotational speed or vibration of various objects. During the measurement, a stroboscopic light source is used (usually bright lamp, periodically giving short light flashes), the frequency of which is adjusted using a pre-calibrated timing circuit. A light source is directed at a rotating object, and then the flash rate gradually changes. When the frequency of the flashes equalizes with the frequency of rotation or vibration of the object, the latter has time to complete a complete oscillatory cycle and return to its original position in the interval between two flashes, so that when illuminated by a strobe lamp, this object will appear to be stationary. At this method, however, there is a drawback: if the rotation frequency of the object ( 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 look stationary when illuminated.

The stroboscopic method is also used to fine-tune the speed (oscillations). 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 appear stationary.

beat method

All of these waves, from the lowest frequencies of radio waves to the high frequencies of gamma rays, are fundamentally the same, and they are all called electromagnetic radiation. All of them propagate in vacuum at the speed of light.

Another characteristic of electromagnetic waves is the wavelength wave. Wavelength is inversely proportional to frequency, so an electromagnetic wave with a higher frequency has a shorter wavelength, and vice versa. In a vacuum, the wavelength

λ = c / ν , (\displaystyle \lambda =c/\nu ,)

where from is the speed of light in 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- refractive index), the relationship between wavelength and frequency will be as follows:

λ = c n ν . (\displaystyle \lambda =(\frac (c)(n\nu )).)

Another frequently used characteristic of a wave is the wave number (spatial frequency), equal to the number of waves that fit per unit length: k= 1/λ . Sometimes this value is used with a factor of 2π, by analogy with the usual and circular frequency k s = 2π/λ . In the case of an electromagnetic wave in a medium

k = 1 / λ = n ν c . (\displaystyle k=1/\lambda =(\frac (n\nu )(c)).) k s = 2 π / λ = 2 π n ν c = n ω c . (\displaystyle k_(s)=2\pi /\lambda =(\frac (2\pi n\nu )(c))=(\frac (n\omega )(c)).)

Sound

The properties of sound (mechanical elastic vibrations of the medium) depend on the frequency. A person can hear vibrations with a frequency of 20 Hz fit within the range of 50 Hz notes. In North America (USA, Canada, Mexico), Central and in some countries of the northern part of South America (Brazil, Venezuela, Colombia, Peru), as well as in some Asian countries (in the southwestern part of Japan, in South Korea, Saudi Arabia, the Philippines and Taiwan) use 60 Hz. See Standards connectors, voltages and frequency wire in country . Almost all household electrical appliances work equally well in networks with a frequency of 50 and 60 Hz, provided that the mains voltage is the same. At the end of the 19th - the first half of the 20th century, before standardization, frequencies from 16 , although it increases losses during transmission over long distances - due to capacitive losses, an increase in the inductive resistance of the line and losses on

Everything on the planet has its frequency. According to one version, it is even the basis of our world. Alas, the theory is very complicated to present it within the framework of one publication, so we will consider only the frequency of oscillations as an independent action. Within the framework of the article, this physical process, its units of measurement and the metrological component will be defined. And in the end, an example of the importance of an ordinary sound in ordinary life will be considered. We learn what it is and what its nature is.

What is the oscillation 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 in one unit of time. This indicator is calculated as the ratio of the number of these incidents to the period of time during which they were committed. Each element of the world has its own oscillation frequency. A body, an atom, a road bridge, a train, an airplane - they all make certain movements, which are called so. Let these processes are not visible to the eye, they are. The units of measurement in which the oscillation frequency is considered are hertz. They got their name in honor of the German-born physicist Heinrich Hertz.

Instantaneous frequency

A periodic signal can be characterized by an instantaneous frequency, which, up to a factor, is the rate of phase change. It can be represented as the sum of harmonic spectral components that have their own constant oscillations.

Cyclic oscillation frequency

It is convenient to apply it 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 the origin of an 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. The dimension of cyclic frequency is the reciprocal of time. In numerical terms, it is equal to the number of oscillations or revolutions that occurred in the number of seconds 2π. Its introduction for use makes it possible to significantly simplify the various range of formulas in electronics and theoretical physics. The most popular use case is the calculation of the resonant cyclic frequency of an oscillating LC circuit. Other formulas can become much more complicated.

Discrete event frequency

This value means the value, which is equal to the number of discrete events that occur in one unit of time. In theory, the indicator is usually used - a second to the minus first degree. In practice, hertz is usually used to express the frequency of pulses.

Rotation frequency

It is understood as a physical quantity, which 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 first degree. To indicate the work done, phrases such as revolution per minute, hour, day, month, year and others can be used.

Units

What is the frequency of oscillations measured in? If we take into account the SI system, then here the unit of measurement 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 a unit of SI. What was put forward as the "ideal"? They were the frequency when one cycle is completed in one second.

But what about production? Arbitrary values ​​were fixed for them: kilocycle, megacycle per second, and so on. Therefore, picking up a device that works 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 over the same period manages to perform millions and even billions of operations per second. In one hour, the computer is already doing so many things that most people can't even imagine them in numerical terms.

Metrological aspects

The oscillation frequency has found its application even in metrology. Various devices have many functions:

1. Measure the pulse frequency. They are represented by electronic counting and capacitor types.
2. Determine the frequency of the spectral components. There are heterodyne and resonant types.
3. Perform spectrum analysis.
4. Reproduce the required frequency with a given accuracy. In this case, various measures can be applied: standards, synthesizers, signal generators and other equipment in this area.
5. The indicators of the received oscillations are compared; for this purpose, a comparator or an oscilloscope is used.

Work example: sound

Everything written above can be quite difficult to understand, since we used the dry language of physics. To understand the above information, 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 vibrations - sound. Its properties, as well as the features of the implementation of mechanical elastic oscillations in a medium, are directly dependent on frequency.

Human hearing organs can pick up vibrations that are in the range from 20 Hz to 20 kHz. Moreover, with age, the upper limit will gradually decrease. If the frequency of sound oscillations falls below 20 Hz (which corresponds to mi subcontra-octave), then infrasound will be created. This type, which in most cases is not audible to 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. At the same time, it should be borne in mind that the musical sound does not consist only of the fundamental frequency - overtones and harmonics are also added to it. It all together determines the timbre.

Conclusion

As you have had the opportunity to learn, the frequency of oscillation 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 carried out. 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 with twice as much performance, then it will quickly fail.

The same can be said about human life, when at a high frequency, his eardrums burst. Other negative changes will also occur with the body, which will entail certain problems, up to and including death. Moreover, due to the peculiarities 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.

The concept of frequency and period of a periodic signal. Units. (10+)

The frequency and period of the signal. Concept. Units

The material is an explanation and addition to the article:
Units of measurement of physical quantities in radio electronics
Units of measurement and ratios of physical quantities used in radio engineering.

Periodic processes are often encountered in nature. This means that some parameter characterizing the process changes according to a periodic law, that is, the equality is true:

Definition of frequency and period

F(t) = 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 this is also true:

F(t) = F(t + 2T) So, if T is the minimum value of the constant for which relation 1 holds, then we will call T period

In radio electronics, we study the strength of current and voltage, so that periodic signals will be considered signals for voltage or current in which the ratio 1 is true.

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A characteristic of a periodic process, equal to the number of complete cycles of the process completed per unit of time. The 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 frequency is called period. Frequency, like time , is one of the most accurately measured physical quantities: up to a relative accuracy of 10 −17 .

Periodic processes are known in nature with frequencies ranging from ~10 −16 Hz (the frequency of revolution of the Sun around the center of the Galaxy) to ~1035 Hz (the frequency of field oscillations characteristic of the most high-energy cosmic rays).

Cyclic frequency

Discrete event frequency

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 frequency of discrete events is a second to the minus first power ( s −1, s−1), but in practice, hertz is usually used to express the pulse frequency.

Rotation frequency

The rotational speed is a physical quantity equal to the number of full revolutions per unit of time. The unit of rotational speed is a second to the minus first power ( s −1, s−1), revolution per second. Units often used are revolutions per minute, revolutions per hour, etc.

Other quantities related to frequency

Metrological aspects

measurements

• To measure the frequency, various types of frequency meters are used, including: to measure the frequency of pulses - electronic counting and capacitor, to determine the frequencies of the 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.
• Compare frequencies with a frequency comparator or with an oscilloscope using Lissajous figures.

Standards

• The state primary standard of units of time, frequency and the national time scale GET 1-98 - located at 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
• Units of physical quantities. Burdun G. D., Bazakutsa V. A. - Kharkiv: Vishcha school,
• Handbook of physics. Yavorsky B. M., Detlaf A. A. - M .: 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) H. lateral frequency, greater or lesser carrier frequency of the high-frequency generator that occurs when (see); (3) N. of rotation is a value equal to the ratio of the number of revolutions ... ... Great Polytechnic Encyclopedia

Frequency- ion plasma frequency - the frequency of electrostatic oscillations that can be observed in plasma, the electron temperature of which is much higher than the temperature of 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. only units distraction noun to frequent. Case frequency. rhythm frequency. Increased heart rate. Current frequency. 2. A value expressing one or another degree of some kind of frequent movement ... Dictionary Ushakov

frequency- s; frequencies; well. 1. to Frequent (1 digit). Keep track of the frequency of repetition of moves. Necessary hours of planting potatoes. Pay attention to the pulse rate. 2. The number of repetitions of the same movements, fluctuations in what l. unit of time. H. wheel rotation. Ch... encyclopedic Dictionary

FREQUENCY- (Frequency) number of periods per second. Frequency is the reciprocal of the oscillation period; e.g. if the frequency of the alternating current f \u003d 50 oscillations per second. (50 N), then the period T = 1/50 sec. The frequency is measured in hertz. When characterizing radiation ... ... Marine Dictionary

frequency- harmonica, oscillation Dictionary of Russian synonyms. noun frequency 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 trials (its occurrence) to the total number n of trials. The term frequency is also used in the meaning of occurrence. In an old book... Dictionary of Sociological Statistics