What sign represents frequency in physics? Frequency, signal period, voltage changes, current
The time during which one complete change in the emf occurs, that is, one cycle of oscillation or one full revolution of the radius vector, is called period of alternating current oscillation(Figure 1).
Figure 1. Period and amplitude of a sinusoidal oscillation. Period is the time of one oscillation; Amplitude is its greatest instantaneous value.
The period is expressed in seconds and denoted by the letter T.
Smaller units of measurement of period are also used: 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 within one second, is called AC oscillation frequency.
The frequency is indicated by the letter f and is expressed in cycles per second or hertz.
One thousand hertz is called a kilohertz (kHz), and a million hertz is called a megahertz (MHz). There is also a unit of 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 = 10 9 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 alternating current are quantities 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 current frequency is 50 Hz, then the period will be equal to:
T = 1/f = 1/50 = 0.02 sec.
And vice versa, if it is known that the period of the current is 0.02 sec, (T = 0.02 sec.), then the frequency will be equal to:
f = 1/T=1/0.02 = 100/2 = 50 Hz
The frequency of alternating current used for lighting and industrial purposes is exactly 50 Hz.
Frequencies between 20 and 20,000 Hz are called audio frequencies. Currents in radio station antennas fluctuate with frequencies up to 1,500,000,000 Hz or, in other words, up to 1,500 MHz or 1.5 GHz. These high frequencies are called radio frequencies or high frequency vibrations.
Finally, currents in the antennas of radar stations, satellite communication stations, and other special systems (for example, GLANASS, GPS) fluctuate with frequencies of up to 40,000 MHz (40 GHz) and higher.
AC current amplitude
The greatest value that the emf or current reaches in one period is called amplitude of emf or alternating current. It is easy to notice that the amplitude on the scale is equal to the length of the radius vector. The amplitudes of current, EMF and voltage are designated by letters respectively Im, Em and Um (Figure 1).
Angular (cyclic) frequency of alternating current.
The rotation speed of the radius vector, i.e. the change in the rotation angle within one second, is called the angular (cyclic) frequency of 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.
A radian is the angular value of an arc of a circle, the length of which is equal to the radius of this circle (Figure 2). The entire circle that makes up 360° is equal to 6.28 radians, that is, 2.
Figure 2.
1rad = 360°/2
Consequently, the end of the radius vector during one period covers a path equal to 6.28 radians (2). Since within one second the radius vector makes a number of revolutions, equal to frequency AC f, then in one second its end covers a path equal to 6.28*f radian. This expression characterizing the rotation speed 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 instant relative to its initial position is called AC phase. The phase characterizes the magnitude of the EMF (or current) at a given instant or, as they say, the instantaneous value of the EMF, its direction in the circuit and the direction of its change; phase indicates whether the emf is decreasing or increasing.
Figure 3.
A full rotation of the radius vector is 360°. With the beginning of a new revolution of the radius vector, the EMF changes in the same order as during the first revolution. Consequently, 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 by an angle of 370° will be the same as when 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.
Resonance method for measuring frequencies.
Frequency comparison method;
The discrete counting method is based on pulse counting 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.
One more thing interesting video About AC frequency:
Consider the following figure:
It shows 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 occupied by the first pendulum are at a greater distance from each other than those of the second pendulum.
Amplitude
- Oscillation amplitude– the largest deviation in magnitude of the oscillating body from the equilibrium position.
Typically, the letter A is used to denote the amplitude of oscillations. The units of amplitude are the same as the units of length, that is, meters, centimeters, etc. In principle, the amplitude can be written in terms of plane angle, since each arc of a circle will have a single central angle.
An oscillating body is said to complete one complete oscillation when it travels a path equal to four amplitudes.
Oscillation period
- Oscillation period- the period of time during which the body makes one complete oscillation.
The period of oscillation is denoted by the letter T. The units of measurement for the period of oscillation T are seconds.
If we hang two identical balls on threads of different lengths and set them in oscillatory motion, we will notice that over the same periods of time, they will perform a different number of oscillations. A ball suspended on a short thread will vibrate more than a ball suspended on a long thread.
Oscillation frequency
- Oscillation frequency is the number of oscillations that were completed per unit of time.
The oscillation frequency is designated by the letter ν (read as “nu”). The units of vibration frequency are called Hertz. One hertz means one vibration per second.
The period and frequency of oscillations are related to each other by the following relationship:
The frequency of 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 oscillation phase. Two pendulums can have the same frequency of oscillation, but they can oscillate in different phases, that is, their speeds at any given time will be directed in opposite directions.
- If the speeds of the pendulums at any moment of time are in the same direction, then the pendulums are said to 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 concept of frequency and period of a periodic signal. Units of measurement. (10+)
Frequency and period of the signal. Concept. Units of measurement
The material is an explanation and addition to the article:
Units of measurement of physical quantities in radio electronics
Units of measurement and relationships of physical quantities used in radio engineering.
Periodic processes often occur in nature. This means that some parameter characterizing the process changes according to a periodic law, that is, the equality is true:
Determining 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 a certain constant.
It is clear that if the previous equality is true, then the following is true:
F(t) = F(t + 2T) So, if T is the minimum value of the constant at which relation 1 holds, then we will call T period
In radio electronics, we study current and voltage, so we will consider periodic signals to be signals for which the voltage or current ratio is true: 1.
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Definition
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 the frequency of discrete events, rotational 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
