- a physical quantity, which is the main characteristic of periodic processes or processes occurring according to certain patterns. Shows the number of complete oscillations (cycles) per unit of time.
fluctuations- physical processes that repeat exactly or approximately at regular intervals. Oscillations, depending on the physical nature, are of two main types: mechanical, electromagnetic. Sometimes a mixed type is also distinguished, which is a combination of the main types.
Oscillation types
Mechanical vibrations- such movements of bodies in which, at regular intervals, the coordinates of the moving body, its speed and acceleration take on the original values.
electromagnetic- interconnected fluctuations of magnetic and electric fields. Occurs in various electrical circuits. They are manifested by a periodic change in time of one of the electrodynamic quantities: electric charge, current, voltage, electric field strength, induction magnetic field. They are described by the same laws as mechanical vibrations. Get this species oscillations experimentally possible using the simplest oscillatory circuit, which includes an inductor and a capacitor.
According to the nature of interaction with the environment, vibrations are divided into
Free- vibrations occurring in a mechanical system under the action of internal forces of the system after a short-term exposure to an external force. Such oscillations are called damped.
Forced- vibrations arising under the action of external forces that change with time in magnitude and direction. Such oscillations are called undamped.
Self-oscillations- the system initially has a reserve of potential energy, which is used to make oscillations. Moreover, the amplitude (the value of the maximum deviation from the equilibrium point) does not depend on initial conditions, but is determined by the properties of the system. Example: the oscillatory movement of the clock pendulum under the action of the weight of a weight or spring, the oscillations of leaves, tree branches under the influence of a constant air flow. Parametric oscillations are also determined (occur when one of the system parameters changes) and random.
Quantities characterizing fluctuations
The concept of "oscillations" is closely related to waves. But with oscillatory motion, unlike wave motion, there is no process of energy transfer from one point of space to another.
The main characteristics of oscillatory motion, as well as wave motion, are period (T), amplitude (A) and frequency ( v Sometimes f). Moreover, the period and frequency are reciprocal values - the greater the frequency, the shorter the period: T=1/v. A period is a period of time during which one complete oscillation (cycle) takes place, measured in seconds. Accordingly, the frequency is measured in ( 1/sec).
Since 1933, the unit of frequency in the international metric system of units C is hertz. The unit of measurement is named after the German physics professor Heinrich Rudolf Hertz (1858-1894), who empirically confirmed the existence of electromagnetic waves by studying diffraction, interference, polarization and reflection. He proved that light is a kind of electromagnetic waves, which substantiated the existing electromagnetic theory of light by Maxwell. Hertz also studied the electric fields that arise around moving bodies. On the basis of observations, he created a theory, but it did not receive experimental confirmation. The studies of the external photoelectric effect, carried out by Hertz, formed the basis for further scientific research. Also, cyclic frequency and phase are used to describe oscillatory and wave processes. The cyclic frequency shows the number of complete oscillations per unit of time, equal to 2P (where P = 3.14), and the phase is the amount of displacement at any given time.
It should also be noted that if the oscillations can be described according to the law of sine or cosine, then they are harmonic. Accordingly, in the equation for mathematical description there must be a sin or cos function.
Definition
Frequency- This physical parameter, which are used to characterize periodic processes. The frequency is equal to the number of repetitions or accomplishments of events per unit of time.
Most often in physics, the frequency is denoted by the letter $\nu$, sometimes there are other frequency designations, such as $f$ or $F$.
Frequency (along with time) is the most accurately measured quantity.
Oscillation frequency formula
Frequency is used to characterize vibrations. In this case, the frequency is a physical quantity inverse to the oscillation period $(T).$
\[\nu=\frac(1)(T)\left(1\right).\]
Frequency, in this case, is the number of complete oscillations ($N$) that occur per unit of time:
\[\nu =\frac(N)(\Delta t)\left(2\right),\]
where $\Delta t$ is the time during which $N$ oscillations occur.
The unit of frequency in the International System of Units (SI) is hertz or reciprocal seconds:
\[\left[\nu \right]=c^(-1)=Hz.\]
Hertz is a unit of measurement of the frequency of a periodic process, at which one cycle of the process occurs in a time equal to one second. The unit for measuring the frequency of a periodic process got its name in honor of the German scientist G. Hertz.
The beat frequency that occurs when adding two oscillations that occur along the same straight line with different, but close in magnitude frequencies ($(\nu )_1\ and\ (\nu )_2$) is equal to:
\[(\nu =\nu )_1-\ (\nu )_2\left(3\right).\]
Another quantity characterizing the oscillatory process is the cyclic frequency ($(\omega )_0$), related to the frequency as:
\[(\omega )_0=2\pi \nu \left(4\right).\]
Cyclic frequency is measured in radians per second:
\[\left[(\omega )_0\right]=\frac(rad)(s).\]
The oscillation frequency of a body with a mass $\ m,$ suspended on a spring with a coefficient of elasticity $k$ is equal to:
\[\nu =\frac(1)(2\pi \sqrt((m)/(k)))\left(5\right).\]
Formula (4) is true for elastic, small oscillations. In addition, the mass of the spring must be small compared to the mass of the body attached to this spring.
For a mathematical pendulum, the oscillation frequency is calculated as: thread length:
\[\nu =\frac(1)(2\pi \sqrt((l)/(g)))\left(6\right),\]
where $g$ - free fall acceleration; $\ l$ - the length of the thread (the length of the suspension) of the pendulum.
A physical pendulum oscillates with a frequency:
\[\nu =\frac(1)(2\pi \sqrt((J)/(mgd)))\left(7\right),\]
where $J$ is the moment of inertia of the body oscillating about the axis; $d$ - distance from the center of mass of the pendulum to the axis of oscillation.
Formulas (4) - (6) are approximate. The smaller the oscillation amplitude, 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 ($n$) - they call a physical quantity equal to the number of actions (events) per unit time. If the time that one event takes is denoted as $\tau $, then the frequency of discrete events is equal to:
The unit of measure for the frequency of discrete events is the reciprocal second:
\[\left=\frac(1)(c).\]
A second to the minus one power is equal to the frequency of discrete events if one event occurs in a time equal to one second.
Frequency of rotation ($n$) - is called a value equal to the number of full revolutions that the body makes per unit time. If $\tau $ is the time taken for one complete revolution, then:
Examples of problems with a solution
Example 1
Exercise. The oscillatory system made 600 oscillations in a time equal to one minute ($\Delta t=1\min$). What is the frequency of these oscillations?
Solution. To solve the problem, we use the definition of the oscillation frequency: Frequency, in this case, is the number of complete oscillations that occur per unit of time.
\[\nu =\frac(N)(\Delta t)\left(1.1\right).\]
Before proceeding to the calculations, let's convert the time to SI units: $\Delta t=1\ min=60\ s$. Let's calculate the frequency:
\[\nu =\frac(600)(60)=10\ \left(Hz\right).\]
Answer.$\nu =10Hz$
Example 2
Exercise. Figure 1 shows a graph of oscillations of some parameter $\xi \ (t)$. What is the amplitude and frequency of oscillations of this quantity?
Solution. Figure 1 shows that the amplitude of the value $\xi \ \left(t\right)=(\xi )_(max)=5\ (m)$. From the graph we get that one complete oscillation occurs in a time equal to 2 s, therefore, the oscillation period is:
Frequency is the reciprocal of the oscillation period, which means:
\[\nu =\frac(1)(T)=0.5\ \left(Hz\right).\]
Answer. 1) $(\xi )_(max)=5\ (m)$. 2) $\nu =0.5$ Hz
Characteristic of a periodic process, equal to the number full cycles processes 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
- 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.
- 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:- 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; 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- (Frequency) number of periods per second. Frequency is the reciprocal of the oscillation period; e.g. if frequency alternating current f = 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
Consider the following figure:
It features two identical pendulums. As can be seen from the figure, the first pendulum oscillates with a larger swing than the second. That is, in other words, the extreme positions that the first pendulum occupies are at a greater distance from each other than that of the second pendulum.
Amplitude
- Oscillation amplitude- the largest deviation of the oscillating body from the equilibrium position in absolute value.
Usually, the letter A is used to denote the amplitude of vibrations. The units of measurement of the amplitude are the same as the units of length, that is, they are meters, centimeters, etc. In principle, the amplitude can be written in units of a plane angle, since each arc of a circle will correspond to a single central angle.
It is said that an oscillating body makes one complete oscillation when it travels a path equal to four amplitudes.
Oscillation period
- Oscillation period is the time it takes for the body to make one complete oscillation.
The oscillation period is denoted by the letter T. The units of the oscillation period T are seconds.
If we hang two identical balls on threads of different lengths, and bring them into oscillatory motion, we will notice that in the same intervals of time, they will make a different number of oscillations. A ball suspended from a short string will oscillate more than a ball suspended from a long string.
Oscillation frequency
- Oscillation frequency called the number of oscillations that were made in a unit of time.
The oscillation frequency is denoted by the letter ν (read as "nu"). The units of oscillation frequency are called Hertz. One hertz means one oscillation per second.
The period and frequency of oscillations are interconnected by the following relationship:
Frequency free vibrations is called the natural frequency of the oscillatory system. Each system has its own oscillation frequency.
Oscillation phase
There is also such a thing as the phase of oscillations. Two pendulums can have the same oscillation frequency, but at the same time they can oscillate in different phases, that is, their speeds at any time will be directed in opposite directions.
- If the speeds of the pendulums at any moment of time are directed in the same direction, then they say that the pendulums oscillate in the same phases of oscillation.
Pendulums can also oscillate with a certain phase difference, in which case at some points in time the direction of their velocities will coincide, and at others not.
The quantum mechanical state has physical meaning energy of this state, in connection with which 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 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 relationship of very close audio frequencies units such as the cent (a frequency ratio of 2 1/1200) and the millioctave (a frequency ratio of 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. The introduction of a cyclic frequency (in its main 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 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 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 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
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. 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 most significant 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. The measurement process uses a stroboscopic light source (usually a bright lamp that periodically gives short flashes of light), the frequency of which is adjusted using a pre-calibrated timing chain. 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 stroboscopic 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 for fine tuning frequency of rotation (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 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 electromagnetic waves with more high frequency has a shorter wavelength, and vice versa. In a vacuum, the wavelength
λ = c / ν , (\displaystyle \lambda =c/\nu ,)Where With is the speed of light in vacuum. In a medium in which the phase velocity of propagation 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
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