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 AC oscillation frequency.
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 of radar stations, satellite communication stations, and other special systems (for example, GLANASS, GPS) fluctuate at 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). The angle of rotation of the radius vector at any given moment relative to its initial position 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.
Resonant frequency measurement method.
Frequency comparison method;
The discrete counting method is based on counting pulses of the required frequency for a specific period of time. It is most often used by digital frequency counters, and it is thanks to this simple method that fairly accurate data can be obtained.
You can learn more about AC frequency from the video:
The method of recharging a capacitor also does not involve complex calculations. In this case, the average value of the overcharge current is proportional to the frequency, and is measured using a magnetoelectric ammeter. The scale of the device, in this case, is graduated in Hertz.
The error of such frequency meters is within 2%, and therefore such measurements are quite suitable for domestic use.
The measurement method is based on electrical resonance that occurs in a circuit with adjustable elements. The frequency to be measured is determined by a special scale of the tuning mechanism itself.
This method gives a very low error, but only applies to frequencies above 50 kHz.
The frequency comparison method is used in oscilloscopes, and is based on mixing the reference frequency with the measured one. In this case, beats of a certain frequency occur. When these beats reaches zero, then the measured becomes equal to the reference. Further, according to the figure obtained on the screen, using the formulas, you can calculate the desired frequency electric current.
Another interesting video about AC frequency:
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
- State primary standard of units of time, frequency and 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
Wikimedia Foundation. 2010 .
Synonyms: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
Ionic 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, 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 ... Explanatory Dictionary of Ushakov
s; frequencies; and. 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) 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
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
Frequency- oscillations, the number of complete periods (cycles) of the oscillatory process occurring per unit of time. The unit of frequency is the hertz (Hz), corresponding to one complete cycle in 1 second. Frequency f=1/T, where T is the oscillation period, but often... ... Illustrated Encyclopedic Dictionary
(lat. amplitude- magnitude) - this is the largest deviation of the oscillating body from the equilibrium position.
For a pendulum, this is the maximum distance that the ball moves from its equilibrium position (figure below). For oscillations with small amplitudes, this distance can be taken as the length of the arc 01 or 02, as well as the lengths of these segments.
The oscillation amplitude is measured in units of length - meters, centimeters, etc. On the oscillation graph, the amplitude is defined as the maximum (modulo) ordinate of the sinusoidal curve, (see figure below).
Oscillation period.
Oscillation period- this is the smallest period of time after which the system, making oscillations, again returns to the same state in which it was at the initial moment of time, chosen arbitrarily.
In other words, the oscillation period ( T) is the time for which one complete oscillation takes place. For example, in the figure below, this is the time it takes for the weight of the pendulum to move from the rightmost point through the equilibrium point O to the leftmost point and back through the point O again to the far right.
For a full period of oscillation, therefore, the body travels a path equal to four amplitudes. The oscillation period is measured in units of time - seconds, minutes, etc. The oscillation period can be determined from the well-known oscillation graph, (see figure below).
The concept of “oscillation period”, strictly speaking, is valid only when the values of the oscillating quantity are exactly repeated after a certain period of time, that is, for harmonic oscillations. However, this concept is also applied to cases of approximately repeating quantities, for example, for damped oscillations.
Oscillation frequency.
Oscillation frequency is the number of oscillations per unit of time, for example, in 1 s.
The SI unit of frequency is named hertz(Hz) in honor of the German physicist G. Hertz (1857-1894). If the oscillation frequency ( v) is equal to 1 Hz, then this means that one oscillation is made for every second. The frequency and period of oscillations are related by the relations:
In the theory of oscillations, the concept is also used cyclical, or circular frequency ω . It is related to the normal frequency v and oscillation period T ratios:
.
Cyclic frequency is the number of oscillations per 2π seconds.
So, before determining what frequency is measured in, it is important to understand what it is? We will not delve into complex physical terms, but we will still need some concepts from this discipline. Firstly, the concept of "frequency" - can only refer to any periodic process. That is, it is an action that is constantly repeated over time. The rotation of the Earth around the Sun, the contraction of the heart, the change of day and night - all this happens with a certain frequency. Secondly, phenomena or objects that we, people, may seem quite static and motionless, have their own frequency, or periodicity of oscillations. A good example of this is ordinary daylight. We do not notice any change or flicker, but it still has its own oscillation frequency, since it is a high-frequency electromagnetic wave.
Units
How is frequency measured and in what units? There are separate units for low-frequency processes. For example, on a cosmic scale - a galactic year (the revolution of the Sun around the center of the Galaxy), an earthly year, a day, etc. It is clear that to measure smaller quantities, it is inconvenient to use such units, therefore, in physics, the more universal value "second to the minus first degree" (s -1) is used. Perhaps you have never heard of such a measure, and this is not surprising - it is usually used only in scientific or technical literature.
Luckily for us, in 1960, the measure of oscillation frequency was named after the German physicist Heinrich Hertz. This value (hertz, abbr. Hz) is what we use today. It denotes the number of vibrations (impulses, actions) performed by an object in 1 second. In fact, 1 Hz = 1 s -1. The human heart, for example, has an oscillation frequency of approximately 1 Hz, i.e. shrinks once per second. The frequency of the processor of your computer, maybe, say, 1 gigahertz (1 billion hertz) - this means that 1 billion of some actions take place in it per second.
How to measure frequency?
If we talk about measuring the frequencies of electrical vibrations, then the first device that each of us is familiar with is our own eyes. Due to the fact that our eyes are able to measure frequency, we distinguish colors (recall that light is electromagnetic waves) - we see the lowest frequencies as red, high frequencies - this is closer to purple. To measure lower (or higher) frequencies, people have invented many instruments.
In general, there are two main methods for measuring frequency: direct counting of pulses per second, and a comparative method. The first method is implemented in frequency counters (digital and analog). The second is in frequency comparators. The measurement method with a frequency counter is simpler, while the measurement with a comparator is more accurate. One of the varieties of the comparative method is the frequency measurement using an oscilloscope (we are familiar with physics classrooms since school) and the so-called. "Lissajous figures". The disadvantage of the comparative method is that two sources of oscillations are needed for measurement, and one of them must have a frequency already known to us. We hope you enjoyed our little exploration!