A characteristic of a periodic process, equal to the number of complete cycles of the process completed per unit of time. Standard notations in formulas are , , 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 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 frequency of discrete events is the second to the minus first power ( s −1, s−1), however in practice the hertz is usually used to express the pulse frequency.
Rotation frequency
Rotation frequency is a physical quantity equal to the number of full revolutions per unit of time. The unit of rotation speed is the second minus the first power ( s −1, s−1), revolutions per second. Units often used are revolutions per minute, revolutions per hour, etc.
Other quantities related to frequency
Metrological aspects
Measurements
- To measure frequency, different types of frequency meters are used, 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.
- Compare frequencies using a frequency comparator or using an oscilloscope using Lissajous patterns.
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 Communications, 1984
- Units of physical quantities. Burdun G. D., Bazakutsa V. A. - Kharkov: Vishcha school,
- Physics Handbook. Yavorsky B. M., Detlaf A. A. - M.: Science,
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) Ch. side frequency, greater or less than the carrier frequency of the high-frequency generator, occurring when (see); (3) Number of rotations is a value equal to the ratio of the number of revolutions... ... Big Polytechnic Encyclopedia
Ion plasma frequency is the frequency of electrostatic oscillations that can be observed in a plasma whose electron temperature significantly exceeds the temperature of the ions; this frequency depends on the concentration, charge and mass of plasma ions.... ... Nuclear energy terms
FREQUENCY, frequencies, plural. (special) frequencies, frequencies, women. (book). 1. units only distracted noun to frequent. Frequency of cases. Rhythm frequency. Increased heart rate. Current frequency. 2. A quantity expressing one or another degree of some frequent movement... Dictionary Ushakova
Y; frequencies; and. 1. to Frequent (1 digit). Monitor the frequency of repetition of moves. Required part of planting potatoes. Pay attention to your pulse rate. 2. The number of repetitions of identical movements, oscillations in what direction. unit of time. Hours of wheel rotation. H... encyclopedic Dictionary
- (Frequency) number of periods per second. Frequency is the reciprocal of the oscillation period; eg if frequency alternating current f = 50 oscillations per second. (50 N), then the period T = 1/50 sec. Frequency is measured in hertz. When characterizing radiation... ... Marine Dictionary
Harmonics, vibration Dictionary of Russian synonyms. frequency noun density density (about vegetation)) Dictionary of Russian synonyms. Context 5.0 Informatics. 2012… Synonym dictionary
frequency- occurrence of a random event is the ratio m/n of the number m occurrences of this event in a given sequence of tests (its occurrence) to the total number n of tests. The term frequency is also used to mean occurrence. In an old book... ... Dictionary of Sociological Statistics
>>Physics: Period and frequency of revolution
Uniform circular motion is characterized by the period and frequency of revolution.
Circulation period- this is the time it takes to complete one revolution.
If, for example, during a time t = 4 s a body, moving in a circle, made n = 2 revolutions, then it is easy to understand that one revolution lasted 2 s. This is the period of circulation. It is designated by the letter T and is determined by the formula:
So, to find the period of revolution, you need to divide the time during which n revolutions are made by the number of revolutions.
Another characteristic of uniform circular motion is the rotation frequency.
Frequency- this is the number of revolutions made in 1 s. If, for example, in a time t = 2 s the body made n = 10 revolutions, then it is easy to understand that in 1 s it managed to make 5 revolutions. This number expresses the frequency of circulation. It is denoted by the Greek letter V(read: nude) and is determined by the formula:
So, To find the rotation frequency, you need to divide the number of revolutions by the time during which they occurred.
The SI unit of revolution frequency is the frequency of revolution at which a body makes one revolution every second. This unit is designated as follows: 1/s or s -1 (read: second minus the first power). This unit used to be called "revolutions per second", but this name is now considered obsolete.
Comparing formulas (6.1) and (6.2), one can notice that period and frequency are mutually inverse quantities. That's why
Formulas (6.1) and (6.3) allow us to find the revolution period T if the number n and the revolution time t or the revolution frequency are known V. However, it can also be found in the case when none of these quantities are known. Instead, it is enough to know the speed of the body V and the radius of the circle along which it moves.
To derive the new formula, let us remember that the period of revolution is the time during which the body makes one revolution, i.e., it travels a path equal to the length of the circle ( l env = 2 P r, where P≈3.14 is the number “pi”, known from the mathematics course). But we know that with uniform motion, time is found by dividing the distance traveled by the speed of movement. Thus,
So, To find the period of revolution of a body, you need to divide the length of the circle along which it moves by the speed of its movement.
??? 1. What is the circulation period? 2. How can you find the period of revolution, knowing the time and number of revolutions? 3. What is the frequency of circulation? 4. How is the unit of frequency designated? 5. How can you find the frequency of circulation, knowing the time and number of revolutions? 6. How are period and frequency of circulation related? 7. How can you find the period of revolution, knowing the radius of the circle and the speed of the body?
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Frequency is a physical parameter that is used to characterize periodic processes. Frequency is equal to the number of repetitions or occurrences of events per unit of time.
Most often in physics, frequency is denoted by the letter $\nu ,$ sometimes other frequency designations are found, for example $f$ or $F$.
Frequency (along with time) is the most accurately measured quantity.
Vibration frequency formula
Frequency is used to characterize vibrations. In this case, the frequency is a physical quantity reciprocal to the oscillation period $(T).$
\[\nu =\frac(1)(T)\left(1\right).\]
Frequency, in this case, is the number of complete oscillations ($N$) occurring 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:
\[\left[\nu \right]=с^(-1)=Hz.\]
Hertz is a unit of measurement of the frequency of a periodic process, at which one process cycle occurs in a time equal to one second. The unit for measuring the frequency of a periodic process received its name in honor of the German scientist G. Hertz.
The frequency of beats that arise when adding two oscillations occurring along one straight line with different but similar 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 ($(\omega )_0$), associated with frequency as:
\[(\omega )_0=2\pi \nu \left(4\right).\]
Cyclic frequency is measured in radians divided per second:
\[\left[(\omega )_0\right]=\frac(rad)(s).\]
The oscillation frequency of a body having a mass $\ m,$ suspended on a spring with an elasticity coefficient $k$ is equal to:
\[\nu =\frac(1)(2\pi \sqrt((m)/(k)))\left(5\right).\]
Formula (4) is true for elastic, small vibrations. 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: length of the thread:
\[\nu =\frac(1)(2\pi \sqrt((l)/(g)))\left(6\right),\]
where $g$ is the acceleration of free fall; $\l$ is the length of the thread (length of the suspension) of the pendulum.
A physical pendulum oscillates with the frequency:
\[\nu =\frac(1)(2\pi \sqrt((J)/(mgd)))\left(7\right),\]
where $J$ is the moment of inertia of a body oscillating about the axis; $d$ is the distance from the center of mass of the pendulum to the axis of oscillation.
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 frequency of discrete events, rotation speed
discrete oscillations ($n$) - called a physical quantity equal to the number of actions (events) per unit of time. If the time that one event takes is denoted as $\tau $, then the frequency of discrete events is equal to:
The unit of measurement for discrete event frequency is the reciprocal second:
\[\left=\frac(1)(с).\]
A second to the minus first power is equal to the frequency of discrete events if one event occurs in a time equal to one second.
Rotation frequency ($n$) is a value equal to the number of full revolutions a body makes per unit time. If $\tau$ is the time spent on one full revolution, then:
Examples of problems with solutions
Example 1
Exercise. The oscillatory system performed 600 oscillations in a time equal to one minute ($\Delta t=1\min$). What is the frequency of these vibrations?
Solution. To solve the problem, we will use the definition of oscillation frequency: Frequency, in this case, is the number of complete oscillations occurring per unit of time.
\[\nu =\frac(N)(\Delta t)\left(1.1\right).\]
Before moving on to calculations, let's convert time into 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 a certain parameter $\xi \ (t)$. What is the amplitude and frequency of oscillations of this value?
Solution. From Fig. 1 it is clear that the amplitude of the value $\xi \ \left(t\right)=(\xi )_(max)=5\ (m)$. From the graph we find that one complete oscillation occurs in a time equal to 2 s, therefore, the period of oscillation is equal to:
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
(lat. amplitude- magnitude) is the greatest deviation of an oscillating body from its equilibrium position.
For a pendulum, this is the maximum distance that the ball moves away from its equilibrium position (figure below). For oscillations with small amplitudes, such a distance can be taken as the length of the arc 01 or 02, and the lengths of these segments.
The amplitude of oscillations 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 shortest period of time through which a system oscillating returns again 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 during which one complete oscillation occurs. For example, in the figure below, this is the time it takes for the pendulum bob to move from the rightmost point through the equilibrium point ABOUT to the far left point and back through the point ABOUT again to the far right.
Over a full period of oscillation, the body thus travels a path equal to four amplitudes. The period of oscillation is measured in units of time - seconds, minutes, etc. The period of oscillation can be determined from a well-known graph of oscillations (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, i.e. for harmonic oscillations. However, this concept also applies to cases of approximately repeating quantities, for example, for damped oscillations.
Oscillation frequency.
Oscillation frequency- this is the number of oscillations performed 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, this means that every second there is one oscillation. The frequency and period of oscillations are related by the relations:
In the theory of oscillations they also use the concept 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 performed per 2π seconds
Resonance method for measuring frequencies.
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 due to this simple method You can get fairly accurate data.
You can learn more about the frequency of alternating current from the video:
The method of recharging a capacitor also does not involve complex calculations. In this case, the average value of the recharge current is proportional to the frequency, and is measured using a magnetoelectric ammeter. The instrument scale, in this case, is calibrated 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 that needs to be measured is determined by a special scale of the adjustment mechanism itself.
This method gives a very low error, but is only used for 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 reach zero, the measured one becomes equal to the reference one. Next, using the figure obtained on the screen using formulas, you can calculate the desired frequency electric current.
Another interesting video about AC frequency:
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