As denotes the period and frequency in physics. Frequency formula. Other frequency associated

Definition

Frequency - This is a physical parameter that is used to characterize periodic processes. The frequency is equal to the number of repetitions or accomplishment of events per unit of time.

Most often in physics, the frequency is indicated by the letter $ \\ Nu, $ sometimes there are other frequency designations, such as $ F $ or $ F $.

The frequency (along with time) is the most accurately measured value.

Formula Frequency of oscillations

With the help of frequency characterize oscillations. In this case, the frequency is the physical value of the reverse period of oscillations $ (t). $

\\ [\\ Nu \u003d \\ FRAC (1) (T) \\ Left (1 \\ Right). \\]

Frequency, in this case, is the number of full oscillations ($ n $) per unit of time:

\\ [\\ Nu \u003d \\ FRAC (N) (\\ Delta T) \\ Left (2 \\ Right), \\]

where $ \\ Delta T $ is the time for which $ n $ oscillations occurs.

The frequency measurement unit in the international system of units (C) serve in Hertz or reverse seconds:

\\ [\\ left [\\ nu \\ right] \u003d s ^ (- 1) \u003d Hz. \\]

Hertz is a unit of measurement of the frequency of the periodic process, in which one cycle of the process occurs during equal one second. The unit of measurement of the frequency of the periodic process received its name in honor of the German scientist G. Hertz.

The frequency of the beats that occur when the addition of two oscillations occurring on one straight line with different, but close by the magnitude of the frequencies ($ (\\ nu) _1 \\ and \\ (\\ nu) _2 $) is equal to:

\\ [(\\ Nu \u003d \\ Nu) _1- \\ (\\ Nu) _2 \\ left (3 \\ Right). \\]

Another quantity characterizing the oscillatory process is a cyclic frequency ($ (\\ omega) _0 $), associated with frequency as:

\\ [(\\ Omega) _0 \u003d 2 \\ pi \\ nu \\ left (4 \\ right). \\]

Cyclic frequency is measured in radians divided for a second:

\\ [\\ Left [(\\ Omega) _0 \\ Right] \u003d \\ FRAC (Running) (C). \\]

The fluctuation frequency of the body having a mass of $ \\ m, $ suspended on a spring with a coefficient of elasticity $ k $ is:

\\ [\\ Nu \u003d \\ FRAC (1) (2 \\ pi \\ sqrt ((m) / (k))) \\ left (5 \\ Right). \\]

Formula (4) is true for elastic, small oscillations. In addition, the mass of the spring should be small compared to a mass of the body attached to this spring.

For a mathematical pendulum, the frequency of oscillations are calculated as: the length of the thread:

\\ [\\ Nu \u003d \\ FRAC (1) (2 \\ pi \\ sqrt ((l) / (g))) \\ left (6 \\ right), \\]

where $ G $ is to accelerate the free fall; $ \\ l $ - the length of the thread (suspension length) of the pendulum.

Physical pendulum performs fluctuations with frequency:

\\ [\\ Nu \u003d \\ FRAC (1) (2 \\ pi \\ sqrt ((j) / (mgd))) \\ left (7 \\ Right), \\]

where $ j $ is the moment of inertia of the body that makes the oscillations relative to the axis; $ D $ - the distance from the center of masses of the pendulum to the oscillation axis.

Formulas (4) - (6) are approximate. The smaller the amplitude of the oscillations, the more accurate the value of the oscillation frequency calculated with their help.

Formulas for calculating the frequency of discrete events, rotational speed

discrete oscillations ($ n $) - call a physical value equal to the number of action (events) per unit of time. If the time that takes one event to designate as $ \\ tau $, then the frequency of discrete events is:

The unit of measurement of the frequency of discrete events is the reverse second:

\\ [\\ left \u003d \\ FRAC (1) (C). \\]

Soon in minus the first degree is equal to the frequency of discrete events, if one event occurs in a time equal to one second.

The frequency of rotation ($ n $) is called a value equal to the number of complete revolutions that makes the body per unit of time. If $ \\ Tau $ is the time spent on one full revolution, then:

Examples of tasks with the solution

Example 1.

The task. The oscillatory system made a single minute ($ \\ delta t \u003d 1 / min $) 600 oscillations. What is the frequency of these oscillations?

Decision. To solve the problem, we use the determination of the frequency of oscillations: the frequency in this case is the number of full oscillations per unit time.

\\ [\\ Nu \u003d \\ FRAC (N) (\\ Delta T) \\ Left (1.1 \\ Right). \\]

Before switching to computations, we translate the time in the SI system: $ \\ delta t \u003d 1 / min \u003d 60 \\ C $. We calculate the frequency:

\\ [\\ Nu \u003d \\ FRAC (600) (60) \u003d 10 \\ \\ LEFT (Hz \\ Right). \\]

Answer. $ \\ nu \u003d 10gz $

Example 2.

The task. Figure 1 shows a chart of oscillations of a certain parameter $ \\ xi \\ (t) $, what is the amplitude and frequency of oscillations of this magnitude?

Decision. Figure 1 shows that the amplitude of the value of $ \\ xi \\ \\ left (t \\ right) \u003d (\\ xi) _ (max) \u003d 5 \\ (m) $. From the schedule we obtain that one complete oscillation occurs in a time equal to 2 s, therefore, the period of oscillations is:

Frequency - the reverse period of oscillations, it means:

\\ [\\ Nu \u003d \\ FRAC (1) (T) \u003d 0.5 \\ \\ LEFT (Hz \\ Right). \\]

Answer. 1) $ (\\ xi) _ (max) \u003d 5 \\ (m) $. 2) $ \\ nu \u003d 0.5 $ Hz

The time during which one complete change in EMF is performed, that is, one cycle of oscillations or one full turnover of the radius-vector is called alternating current fluctuations (picture 1).

Picture 1. The period and amplitude of sinusoidal oscillations. The period is the time of one oscillation; Applite - its greatest instantaneous meaning.

The period is expressed in seconds and denote the letter T..

Also used smaller units of measurement of the period. This is millisecond (MS) - one thousandth second and microsecond (ISS) is one million seconds.

1 ms \u003d 0.001sek \u003d 10 -3 sec.

1 μs \u003d 0.001 ms \u003d 0.000001sec \u003d 10 -6 sec.

1000 μs \u003d 1 ms.

The number of complete changes in EDF or the number of revolutions of the radius-vector, that is, in other words, the number of total oscillation cycles performed by alternating current for one second, called aC fluctuations frequency.

The frequency is indicated by the letter f. And expressed in periods per second or in Hertz.

One thousand hertz is called Kilohertz (kHz), and Million Hertz - Meghertz (MHz). There is also a unit of gigahertz (GHz) equal to one thousand megahertz.

1000 Hz \u003d 10 3 Hz \u003d 1 kHz;

1000 000 Hz \u003d 10 6 Hz \u003d 1000 kHz \u003d 1 MHz;

1000 000 000 Hz \u003d 10 9 Hz \u003d 1000,000 kHz \u003d 1000 MHz \u003d 1 GHz;

The faster the emf change occurs, that is, the faster the radius-vector rotates, the less period of oscillations the faster the radius-vector rotates, the higher the frequency. Thus, the frequency and period of alternating current are values \u200b\u200binversely proportional to each other. The more one of them, the smaller the other.

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

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

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

And vice versa, if it is known that the current period is 0.02 seconds, (t \u003d 0.02 seconds), the frequency will be equal to:

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 equal to 50 Hz.

Frequencies from 20 to 20,000 Hz are called sound frequencies. The currents in the radio station antennas oscillate with frequencies of 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, currents in the antennas of radar stations, satellite stations, other special systems (for example, Glanss, GPS) fluctuate with frequencies up to 40,000 MHz (40 GHz) and higher.

AC amplitude

The greatest value that the EDC is reaches or the current of the current in one period is called amplitude EMF or AC power. It is easy to notice that the amplitude on the scale is equal to the length of the radius-vector. The amplitudes of the current, EMF and voltage are indicated by letters accordingly IM, EM and UM (picture 1).

Angle (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 an angular (cyclic) frequency of alternating current and is indicated by the Greek letter ? (Omega). The angle of rotation of the radius-vector at any given moment relative to its initial position is usually not measured in degrees, but in special units - radians.

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

Figure 2.

1rad \u003d 360 ° / 2

Consequently, the end of the radius-vector for one period runs through the path equal to 6.28 radians (2). Since for one second, the radius-vector performs the number of revolutions equal to the frequency of alternating current f., in one second, its end runs the way equal to 6.28 * F. radian. This expression characterizing the rotational speed of the radius-vector, and is the angular frequency of alternating current -? .

? \u003d 6.28 * F \u003d 2F

The angle of rotation of the radius-vector in any given moment about its initial position is called phase of alternating current. The phase characterizes the value of the EMF (or current) to this moment or, as they say the instantaneous value of the EMF, its direction in the chain and the direction of its change; Phase shows whether EDC decreases or increases.

Figure 3.

The total turnover of the radius-vector is 360 °. With the beginning of the new turnover of the radius-vector, the change in EMF occurs in the same manner as during the first turnover. Consequently, all phases of EDC will be repeated in the same order. For example, the EDC phase when turning the radius-vector at 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 \u200b\u200bof the EMF will be the same in the same phase in both of these cases.

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

Frequency and signal period. Concept. Units

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

In nature, periodic processes are often found. This means that some parameter characterizing the process varies in a periodic law, that is, the equality is true:

Frequency definition and period

F (t) \u003d f (t + t) (ratio 1), where t - time, f (t) - the value of the parameter at time t, and T is some constant.

It is clear that if the previous equality is true, then it is true:

F (t) \u003d f (t + 2t) so if T is the minimum value of the constant at which the ratio 1 is made, then we will call T period

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

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So, before you determine what frequency is measured, it is important to understand what it is? We will not deepen into complex physical terms, but some concepts from this discipline will still be needed. First, the concept of "frequency" - may only apply to any periodic process. That is, this is an action that is constantly repeated in time. The rotation of the Earth around the Sun, the reduction of the heart, the change of day and night - all this happens with a certain frequency. Secondly, its frequency, or the frequency of oscillations have phenomena, or items that we, people, may seem completely static and fixed. A good example of this is an ordinary daylight. We do not notice what either his change, or flicker, but he, all the same, has its own frequency of oscillations, since it is high-frequency electromagnetic waves.

Units

What is the frequency in which units? For low-frequency processes, individual units exist. For example, in a space scale - a galactic year (the conversion of the Sun around the center of the Galaxy), the earthly year, day, etc. It is clear that to measure smaller values, it is inconvenient to measure such units, therefore the physics uses a more universal value "second in minus the first degree" (C -1). Perhaps you never heard about the same extent, and it is not surprising - it is usually applied only in scientific, or technical literature.

Fortunately for us, in the 1960s, the mode of frequency of oscillations was named after the German physics of Henry Hertz. This value (Hertz, Sokr. Hz) and we are used today. It denotes the number of oscillations (pulses, actions) performed by an object in 1 second. In essence, 1 Hz \u003d 1 s -1. The human heart, for example, has a frequency of oscillations of approximately 1 Hz, i.e. Reduced once per second. The frequency of the processor of your computer may be, let's say, 1 Gigahertz (1 billion hertz) means that 1 billion some actions take place in it.

How to measure the frequency?

If we talk about measuring the frequencies of electrical oscillations, then the first device with which each of us is familiar is our own eyes. Due to the fact that our eyes know how to measure the frequency, we will distinguish colors (we will remind that the light is electromagnetic waves) - the lowest frequency we see like red, high-frequency - it's closer to violet. To measure lower (or higher frequencies), people invented many devices.

In general, there are two main ways to measure frequency: direct counting pulses per second, and a comparative method. The first method is implemented in frequency meters (digital and analog). The second is in frequency comparators. The measurement method with the frequency meter is easier, while the measurement of the comparator is more accurate. One of the varieties of the comparative method is the measurement of the frequency with the help of an oscilloscope (familiar to us at physics cabinets from school) and so-called. "Figures Lissazu". The lack of a comparative method - for measurement you need two oscillation sources, and one of them must have a frequency already known to us. We hope our small study was interesting to you!

The characteristic of the periodic process equal to the number of complete cycles of the process performed per unit of time. Standard designations in formulas -, or. The unit of frequency in the international system of units (s) is generally hertz ( Hz, Hz.). The value, inverse frequency, is called a period. The frequency, like time, is one of the most precisely measured physical quantities: to relative accuracy of 10 -17.

In nature, periodic processes with frequencies from ~ 10 -16 Hz are known (the frequency of the sun circulation around the center of the galaxy) to ~ 10 35 Hz (the frequency of field oscillations characteristic of the most highly powerful cosmic rays).

Cyclic frequency

Frequency of discrete events

The frequency of discrete events (pulse frequency) is a physical value equal to the number of discrete events occurring per unit of time. Unit of the frequency of discrete events of second in minus of the first degree ( c -1, s -1) However, in practice, the hertz is usually used to express the pulse frequency.

Rotation frequency

Rotation frequency is a physical value equal to the number of total revolutions per unit of time. The unit of rotation frequency is second in minus the first degree ( c -1, s -1), turnover per second. Frequently used such units as turnover per minute, turnover per hour, etc.

Other frequency associated

Metrological aspects

Measurements

Frequency measurements are used for different types, including: to measure pulse frequency - electronic accounting and condenser, to determine the frequencies of spectral components - resonant and heterodyne frameworks, as well as spectrum analyzers.
To play a 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 using an oscilloscope according to the figures of Lissen.

Standards

State primary standard of time units, frequency and national time scale GET 1-98 - located in VNIIFTRI
Secondary standard of time and frequency of WET 1-10-82 - Located in Sniem (Novosibirsk)

Notes

Literature

Fink L. M. Signals, interference, mistakes ... - M.: Radio and Communication, 1984
Units of physical quantities. Burdun G. D., Bazaktsa V. A. - Kharkov: Vice school,
Handbook of physics. Yavorsky B. M., Detlaf A. A. - M.: Science,

Links

Wikimedia Foundation. 2010.

Synonyms:

Authorization
Chemical physics

Watch what is "frequency" in other dictionaries:

FREQUENCY - (1) the number of repetitions of a periodic phenomenon per unit of time; (2) C. Side frequency, large or smaller carrier frequency of the high-frequency generator, occurring at (see); (3) Ch. Rotation The value equal to the ratio of the number of revolutions ... ... Large polytechnic encyclopedia

Frequency - ion plasma frequency - the frequency of electrostatic oscillations that can be observed in plasma, the electron temperature of which significantly exceeds the temperature of the ions; This frequency depends on the concentration, charge and mass of plasma ions. ... ... Terms of atomic energy

FREQUENCY - frequency, frequency, mn. (Spec.) Frequency, frequencies, wives. (Book.). 1. Only units. Distractors. SUD To frequent. Frequency of cases. Rhythm frequency. Increase pulse rate. Current frequency. 2. The value expressesing one or another degree of some frequent movement ... Explanatory Dictionary Ushakov

frequency - s; frequencies; g. 1. To frequent (1 zn). Follow the frequency of repetition of moves. Necessary parting of potatoes. Pay attention to the pulse frequency. 2. The number of repetitions of the same movements, oscillations in which l. Unit of time. C. Wheel rotation. H ... encyclopedic Dictionary

FREQUENCY - (Frequency) the number of periods in one second. Frequency value, reverse period of oscillations; eg If the frequency of the alternating current F \u003d 50 oscillations in sec. (50 H), then the period T \u003d 1/50 seconds. Frequency is measured in hertz. When the radiation characteristic ... ... Sea dictionary

frequency - Harmonic, fluctuate dictionary of Russian synonyms. Frequency of land. Delicious density (about vegetation)) Dictionary of Russian Synonyms. Context 5.0 informatrary. 2012 ... Synonym dictionary

frequency - The appearance of a random event is the ratio M / N of the number M appearances of this event in this test sequence (its occurrence) to the total number of N tests. The term frequency is also used in the meaning. In an old book ... ... Dictionary of sociological statistics

Frequency - oscillations, the number of total periods (cycles) of the oscillatory process occurring per unit of time. The frequency unit is the hertz (Hz) corresponding to one full cycle in 1 seconds. Frequency F \u003d 1 / T, where t period of oscillations, but often ... ... Illustrated Encyclopedic Dictionary