Energy of resonance. Some examples of the manifestation and application of resonance in nature and technology. What is resonance? Useful manifestation of resonance

March 02 2016

Resonance is a sharp increase in the amplitude of forced oscillations, which occurs when the frequency of the external influence approaches certain values (resonance frequencies) determined by the properties of the oscillatory system. An increase in amplitude occurs when the external (exciting) frequency coincides with the internal (natural) frequency of the oscillatory system. With the help of resonant phenomena, even very weak harmonic vibrations can be isolated and/or amplified. Resonance is a phenomenon in which the oscillatory system is particularly responsive to the influence of a certain frequency of the driving force.

There are quite a few situations in our lives in which resonance manifests itself. For example, if you bring a ringing tuning fork to a stringed musical instrument, the acoustic wave emanating from the tuning fork will cause vibration of the string tuned to the frequency of the tuning fork, and it will sound itself.

Another example, the well-known experiment with a thin-walled glass. If you measure the frequency of sound at which a glass rings, and apply sound with the same frequency from a frequency generator, but with a larger amplitude, through an amplifier and speaker back to the glass, its walls resonate with the frequency of the sound coming from the speaker and begin to vibrate. Increasing the amplitude of this sound to a certain level leads to the destruction of the glass.

Bioresonance: from Ancient Rus' to the present day

Our Orthodox ancestors, tens of thousands of years before the arrival of Christianity in Rus', knew well about the power of bell ringing and tried to install a bell tower in every village! Due to this, in the Middle Ages, Rus', rich in church bells, avoided the devastating plague epidemics, unlike Europe (Gaul), in which the holy inquisitors burned at the stake not only all scientists and knowledgeable people, but also all the ancient “heretical” books written in Glagolitic alphabet, which were kept unique knowledge of our ancestors, including the power of resonance!

Thus, all Orthodox knowledge accumulated over centuries was prohibited, destroyed and replaced by the new Christian faith. However, to this day, data on bioresonance are prohibited. Even after centuries, any information about treatment methods that do not bring profit to the pharmaceutical industry is kept silent. While the annual multi-billion dollar turnover of pharmaceuticals is growing every year.

A striking example of the use of resonant frequencies in Rus', and this is a fact that cannot be avoided. When a plague epidemic broke out in Moscow in 1771 (1771), Catherine II sent Count Orlov from St. Petersburg with four Life Guards and a huge staff of doctors. All life in Moscow was paralyzed. In order to ward off the “pestilence”, the laity fumigated their homes, lit huge fires in the streets, and all of Moscow was shrouded in black smoke, since it was then believed that the plague spread through the air, but this did not help much. They also rang the alarm (the largest bell) and all the smaller bells with all their might for 3 days in a row, as they firmly believed that the ringing of the bells would ward off terrible misfortune from the city. A few days later the epidemic began to recede. "What's the secret?" - you ask. In fact, the answer lies on the surface.

Now let’s look at a well-known example of the use of bioresonance in our time. In order to maintain the purity of the experiment, doctors placed metal plates in the ward with cancer patients, similar to those used in ancient monasteries, so that the patients could not associate the bells with the church, and self-hypnosis, born involuntarily, could not significantly affect the results of the research. When selecting individual frequencies for each patient, many titanium plates of various sizes were used. The result exceeded all expectations!

After exposure to acoustic waves of a certain frequency on the biologically active points of the patients, 30% of the patients stopped having pain and were able to fall asleep, and another 30% of the patients stopped having pain that was not relieved by the strongest narcotic anesthetics!

Currently, to achieve the resonance effect, there is no need to use huge bells, but there is a unique opportunity to use the achievements of science and technology, created electronic devices based on frequency resonance, in other words, Smart Life bioresonance therapy devices.

The resonance effect in biological structures can be caused by:

Acoustic waves

Mechanical impact

Electromagnetic waves in the visible and radio frequency ranges

Magnetic field pulses

Pulses of weak electric current

Pulsed thermal effects

That is, the resonance effect in biological structures can be caused by external influences and any physical phenomena that arise during biochemical reactions inside a living cell. Moreover, each biological structure has its own unique frequency spectrum that accompanies biochemical processes and responds to external influences, both the main resonant frequency and higher or lower harmonics from the main frequency, with an amplitude as many times greater as these harmonics are distant from the frequency of the main resonance .

How can you use the power of resonance in everyday life, and what method of influence should you choose?

Acoustic waves

Guess what happens to tartar when it is removed, using ultrasound in the dentist's office or when breaking up kidney stones? The answer is obvious. And without a doubt, acoustic exposure is an excellent opportunity for healing the body, if not for one “but”. Bells weigh a lot, are expensive, create a lot of noise, and can only be used permanently.

A magnetic field

To cause at least any noticeable effect from the influence of a pulsating magnetic field on the entire body, it is necessary to make an electromagnet of enormous size and weighing a couple of tons; it will occupy half the room and consume a lot of electricity. The inertia of the system will not allow its use at high frequencies. Small electromagnets can only be used locally due to their short range. You also need to know exactly the areas on the body and the frequency of exposure. The conclusion is disappointing: using a magnetic field to treat diseases is not economically feasible at home.

Electricity Electromagnetic waves
For the frequency resonance method, you can use radio waves with a carrier frequency from 10 kHz to 300 MHz, since this range has the lowest absorption coefficient of electromagnetic waves by our body and it is transparent to them, as well as electromagnetic waves in the visible and infrared spectrum. Visible red light with a wavelength from 630 nm to 700 nm penetrates tissue to a depth of 10 mm, and infrared light from 800 nm to 1000 nm penetrates to a depth of 40 mm and deeper, also causing some thermal effects when braking in tissue. To influence biologically active zones on the surface of the skin, you can use radio waves with a carrier frequency of up to ~ 50 GHz

Resonance phenomena are associated with the periodic oscillatory movement of electrons in a circuit and consist in the fact that electrons in a given oscillatory circuit most easily “swing” with a certain frequency, which we call resonant. We encounter periodic oscillatory motion everywhere. The oscillation of a pendulum, the vibration of a string, the movement of a swing - all these are examples of oscillatory motion.

For example, consider the oscillatory system shown in Figure 1. This system, as we will see later, has much in common with an electrical oscillatory circuit. It consists of a spring and a massive ball attached to a rod.

Picture 1. Mechanical model of an oscillatory circuit.Mass-inductance, flexibility-capacitance, friction-resistance.

If we pull the ball down from its equilibrium position, then under the action of the spring it will immediately rush back; however, having acquired a certain speed, the ball will not stop at the equilibrium point, but by inertia will jump further, which will cause new deformation (compression) of the spring. Then this process will be repeated in the opposite direction, etc. The ball will oscillate in one direction and the other until the entire supply of energy imparted to the spring when the ball is deflected is spent on friction.

It is easy to notice that when the ball oscillates, the energy imparted to the system constantly transfers from the energy of deformation (compression and extension) of the spring into the energy of motion of the ball and back. In mechanics, the first type of energy is called potential energy, and the second type is called kinetic energy.

While the ball is in one of its extreme positions, it stops for a moment. At this moment, the energy of its movement is zero. But the spring at this moment is very strongly deformed: either compressed or stretched; it therefore contains the greatest amount of energy. At the same moment when the ball passes through the equilibrium position with the greatest speed, it has the greatest energy, but the energy of the spring at this moment is zero, since it is not compressed or stretched.

By deflecting the ball at various distances and observing each time the frequency of subsequent free oscillations of the system, we will notice that the frequency of oscillations of the system remains the same all the time. In other words, it does not depend on the magnitude of the initial deviation. We will call this frequency natural frequency systems.

If we had at our disposal not one such system, but several, then we could be convinced that the natural frequency of free oscillations of the system decreases with increasing mass of the ball and increases with increasing elasticity, i.e., with decreasing flexibility of the spring. This dependence can also be detected using a simpler example with vibrating strings of various thicknesses and varying degrees of tension.

If we want to swing the ball with the least amount of effort, then we will, of course, try, firstly, to establish a strict periodicity of our pushes, that is, we will try to ensure that the pushes follow each other after a certain time, and secondly, we will try, so that the time interval between shocks is equal to the period of natural oscillations of the system (Figure 2).

Figure 2. Mechanical model of an oscillatory circuit with undamped oscillations.The frequency of the forced force is equal to the natural frequency of the system (resonance).

In order to swing the oscillatory system with the least amount of effort, it is necessary to make the frequency of the driving force equal to the natural frequency of oscillation of the system. This rule is very well known to all of us since childhood, when we used it while swinging on a swing.

Figure 3. The phenomenon of resonance using the example of a swing.

So, when the frequency of the driving force coincides with the natural frequency of oscillations of the system, the amplitude of the oscillations becomes greatest.

Thus, it must be said that the coincidence of the frequency of the driving force with the natural frequency of oscillations of the system is resonance.

You don't have to look far for examples of resonance. Window glass that shakes with a certain frequency every time a tram or truck passes by; the trembling of a string of a musical instrument after we touch an adjacent string tuned in unison with the first, etc. - all these are resonance phenomena.

Let's charge the capacitor with some amount of electricity (Fig. 4, a) and then close it to the inductor (Fig. 4, b). The capacitor will begin to discharge immediately. A discharge current will flow through the inductor, and the appearance of current in the coil will lead to the appearance of a magnetic field around it. In this case, a self-induction emf will arise in the coil, which will delay the discharge of the capacitor. When the capacitor is discharged, the current in the coil will not stop, since it will now be supported by the self-induction emf due to the energy stored in the magnetic field of the coil during the discharge of the capacitor. This continuing current will recharge the capacitor in the opposite direction, that is, the plate that was previously positive will become negative, and vice versa (Fig. 4, c).

Figure 4. At the top - electrical, at the bottom - mechanical.

After this, the capacitor will again begin to discharge, recharge again (Fig. 4, d, e), etc. The current oscillations in the circuit will continue until all the electrical energy imparted to the circuit when charging the capacitor is converted into thermal energy. This will happen the sooner, the greater the active resistance of the circuit.

So, the discharge of a capacitor through an inductor is an oscillatory process. During this process, the capacitor is charged and discharged several times, energy alternately transfers from the electric field of the capacitor to the magnetic field of the coil and vice versa.

Figure 5. Oscillations in an oscillatory circuit.

The current fluctuations that occur during this discharge are of a damped nature (Fig. 6).

Figure 6. Damped oscillations in the circuit.

The oscillation frequency for the selected values of capacitance and inductance is a completely definite value and is called the natural frequency of the circuit. The circuit's natural frequency will be greater, the smaller the capacitance and inductance of the circuit.

If an alternating current source is introduced into the oscillatory circuit, the frequency of which coincides with the natural frequency of the circuit, then the oscillations in the circuit will reach the greatest value, i.e., the phenomenon of resonance will occur.

A far-reaching parallel can be drawn between electrical and mechanical vibrations.

In table 1 on the left are electrical quantities and phenomena, and on the right are similar quantities and phenomena from the field of mechanics in relation to our mechanical model of the oscillatory circuit.

Analogy of electrical and mechanical quantities

Electrical quantities	Mechanical quantities
Oscillatory circuit inductance	Ball mass;
Oscillatory circuit capacitance	Spring flexibility
Loop resistance	Mechanical friction
Capacitor plates	Springs
Capacitor charge	Deformation (compression and extension) of springs
Positive plate charge	Spring compression
Negative plate charge	Spring stretch
Current strength	Ball speed
Current direction	Ball movement direction
Electromotive force of self-induction	Ball inertia force
Amplitude (largest instantaneous current value)	Amplitude (the largest deviation of the ball from the equilibrium position)
Frequency (cycles per second)	Frequency (number of oscillations per second)
Resonance (coincidence of the frequency of the external EMF with the natural frequency of the horn)	Resonance (coincidence of the frequency of the driving force shocks with the natural frequency of oscillations of the ball)

The various moments of electrical oscillation and the corresponding moments of oscillation of our mechanical model of the oscillatory circuit are depicted in Fig. 4.

Before you begin to get acquainted with the phenomena of resonance, you should study the physical terms associated with it. There are not many of them, so it will not be difficult to remember and understand their meaning. So, first things first.

What is the amplitude and frequency of movement?

Imagine an ordinary yard where a child sits on a swing and waves his legs to swing. At the moment when he manages to swing the swing and it reaches from one side to the other, the amplitude and frequency of the movement can be calculated.

Amplitude is the greatest length of deviation from the point where the body was in the equilibrium position. If we take our example of a swing, then the amplitude can be considered the highest point to which the child swings.

And frequency is the number of oscillations or oscillatory movements per unit time. Frequency is measured in Hertz (1 Hz = 1 cycle per second). Let's return to our swing: if a child passes only half the entire length of the swing in 1 second, then its frequency will be equal to 0.5 Hz.

How is frequency related to the phenomenon of resonance?

We have already found out that frequency characterizes the number of vibrations of an object in one second. Imagine now that an adult helps a weakly swinging child to swing, pushing the swing over and over again. Moreover, these shocks also have their own frequency, which will increase or decrease the swing amplitude of the “swing-child” system.

Let's say an adult pushes a swing while it is moving towards him, in this case the frequency will not increase the amplitude of the movement. That is, an external force (in this case, pushes) will not increase the oscillation of the system.

If the frequency with which an adult swings a child is numerically equal to the swing frequency itself, resonance may occur. In other words, an example of resonance is the coincidence of the frequency of the system itself with the frequency of forced oscillations. It is logical to imagine that frequency and resonance are interrelated.

Where can you see an example of resonance?

It is important to understand that examples of resonance are found in almost all areas of physics, from sound waves to electricity. The meaning of resonance is that when the frequency of the driving force is equal to the natural frequency of the system, then at that moment it reaches its highest value.

The following example of resonance will give insight. Let's say you are walking on a thin board thrown across a river. When the frequency of your steps coincides with the frequency or period of the entire system (board-person), the board begins to oscillate strongly (bend up and down). If you continue to move in the same steps, the resonance will cause a strong vibration amplitude of the board, which goes beyond the permissible value of the system and this will ultimately lead to inevitable failure of the bridge.

There are also areas of physics where it is possible to use such a phenomenon as useful resonance. The examples may surprise you, because we usually use it intuitively, without even realizing the scientific side of the issue. So, for example, we use resonance when we try to pull a car out of a hole. Remember, it is easiest to achieve results only when you push the car as it moves forward. This example of resonance increases the range of motion, thereby helping to pull the car.

Examples of harmful resonance

It is difficult to say which resonance is more common in our lives: good or harmful to us. History knows a considerable number of terrifying consequences of the resonance phenomenon. Here are the most famous events where an example of resonance can be observed.

In France, in the city of Angers, in 1750, a detachment of soldiers walked in step across a chain bridge. When the frequency of their steps coincided with the frequency of the bridge, the range of vibrations (amplitude) increased sharply. There was a resonance, and the chains broke, and the bridge collapsed into the river.
There have been cases when in villages a house was destroyed due to a truck driving along the main road.

As you can see, resonance can have very dangerous consequences, which is why engineers should carefully study the properties of construction objects and correctly calculate their vibration frequencies.

Beneficial Resonance

The resonance is not limited to dire consequences. By carefully studying the world around us, one can observe many good and beneficial results of resonance for humans. Here is one striking example of resonance that allows people to receive aesthetic pleasure.

The design of many musical instruments operates on the principle of resonance. Let's take a violin: the body and the string form a single oscillatory system, inside of which there is a pin. It is through it that vibration frequencies are transmitted from the upper deck to the lower one. When the luthier moves the bow along the string, the latter, like an arrow, overcomes the friction of the rosin surface and flies in the opposite direction (begins to move in the opposite area). A resonance occurs, which is transmitted to the housing. And inside it there are special holes - f-holes, through which the resonance is brought out. This is how it is controlled in many stringed instruments (guitar, harp, cello, etc.).

The phenomenon of resonance is understood as an instantaneous increase in the amplitude of vibrations of an object under the influence of an external energy source of a periodic nature of influence with a similar frequency value.

In the article we will consider the nature of the occurrence of resonance using the example of a mechanical (mathematical) pendulum, an electric oscillatory circuit and a nuclear magnetic resonator. In order to more easily present physical processes, the article is accompanied by numerous inserts in the form of practical examples. The purpose of the article is to explain at a primitive level the phenomenon of resonance in different areas of its occurrence without mathematical formulas.

The simplest model that can clearly show oscillations is the simplest pendulum, or rather a mathematical pendulum. Oscillations are divided into free and forced. Initially, the energy acting on the pendulum provides free oscillations in the body without the presence of an external source of variable impact energy. This energy can be either kinetic or potential.

Here it does not matter how strongly or not the pendulum itself swings - the time spent on traveling its path in the forward and reverse directions remains unchanged. To avoid misunderstandings with the damping of oscillations due to friction with air, it is worth highlighting that for free oscillations the conditions for the pendulum to return to the point of equilibrium and the absence of friction must be met.

But the frequency, in turn, directly depends on the length of the pendulum thread. The shorter the thread, the higher the frequency and vice versa.

The natural frequency of a body that arises under the influence of an initially applied force is called the resonant frequency.

All bodies that are characterized by vibrations perform them with a given frequency. To maintain undamped vibrations in the body, it is necessary to provide constant periodic energy “feeding”. This is achieved by exposure to a simultaneous vibration of the body of a constant force with a certain period. Thus, the vibrations that arise in the body under the influence of a periodic force from the outside are called forced.

At some point in the external influences, a sharp jump in amplitude occurs. This effect occurs if the periods of internal vibrations of the body coincide with the periods of external force and is called resonance. For resonance to occur, very small values of external sources of influence are sufficient, but with the obligatory condition of repetition in time. Naturally, when making actual calculations under terrestrial conditions, one should not forget about the action of friction forces and air resistance on the surface of the body.

Simple examples of resonance from life

Let's start with an example of the occurrence of resonance that each of us has encountered - this is an ordinary swing on a playground.

Resonance of the swing

In the situation with a children's swing, at the moment the hand applies force while passing one of the two symmetrical highest points, a jump in amplitude occurs with a corresponding increase in the vibration energy. In everyday life, vocal lovers could observe the phenomenon of resonance in the bathroom.

Sound acoustic resonance when singing in the bathroom

Anyone who sings in a tiled bathroom has probably noticed how the sound changes. Sound waves reflected on the tiles in the enclosed space of the bathroom become louder and longer lasting. But not all notes of the vocalist’s song are affected by this effect, but only those that resonate in one beat with the sound resonant frequency of the air.

For each of the above cases of resonance occurrence, there is external exciting energy: in the case of a swing, an elementary push by hand, coinciding with the swing phase of oscillation, and in the case of an acoustic effect in the bathroom, a person’s voice, the individual frequencies of which coincided with certain frequencies of the air.

Sound resonance of a glass - experience at home

This experiment can be done at home. It requires a crystal glass and a closed room without extraneous noise for a sensitive perception of the acoustic effect. We move the finger moistened with water along the edge of the glass with “ragged” periodic accelerations. During such movements, you can observe the occurrence of a ringing sound. This effect occurs due to the transfer of motion energy, the vibration frequency of which coincides with the natural vibration frequency of the glass.

Bridge failure due to resonance - the case of the Tacoma Bridge

Everyone who served in the army remembers how, when passing in formation across a bridge, the command was heard from the commander: “Keep in step!” Why was it impossible to march in lockstep across the bridge? It turns out that when passing in formation across a bridge and simultaneously raising their straightened leg to knee level, servicemen lower the plane of the sole in one beat with an effort that is accompanied by a characteristic slap.

The step of the military personnel merges into one single beat, creating an abrupt external applied energy for the bridge with a certain amount of vibration. If the natural frequency of the bridge’s vibrations coincides with the vibration of the soldiers’ step “in step,” a resonance will occur, the energy of which can lead to destructive effects on the bridge structure.

Although cases of complete destruction of the bridge have not been recorded when soldiers passed in lockstep, the most famous case is the destruction of the Tacoma Bridge over the Tacoma Narrows in Washington State, USA in 1940.

One of the probable reasons for the destruction is mechanical resonance, which arose due to the coincidence of the frequency of the wind flow with the internal natural frequency of the bridge.

Current resonance in electrical circuits

If in mechanics the phenomenon of resonance can be explained relatively simply, then in electricity everything cannot be explained with one’s fingers. To understand, basic knowledge of the physics of electricity is required. Resonance created in an electrical circuit can occur if there is an oscillating circuit. What elements are needed to create an oscillatory circuit in an electrical network? First of all, the circuit must be connected to a source of electrical energy.

In an electrical network, the simplest oscillatory circuit consists of a capacitor and an inductor.

A capacitor, consisting inside of two metal plates separated by dielectric insulators, is capable of storing electrical energy. An inductance coil made in the form of spiral-shaped turns of an electrical conductor has a similar property.

The mutual connection of a capacitor and an inductor in an electrical network, forming an oscillatory circuit, can be either parallel or series. In the following video tutorial, an example of a sequential switching method is given to demonstrate resonance.

Fluctuations in the electric current inside the circuit occur under the influence of electricity. However, not all incoming signals, or rather their frequencies, serve as a source of resonance, but only those whose frequency coincides with the resonant frequency of the circuit. The rest, not participating in the process, are suppressed in the general signal flow. It is possible to regulate the resonant frequency by changing the values of the capacitor capacitance and the inductance of the coil.

Returning to the physics of resonance in mechanical vibrations, it is especially pronounced at minimal values of friction forces. The friction indicator is compared in an electrical circuit to resistance, an increase in which leads to heating of the conductor due to the conversion of electrical energy into the internal energy of the conductor. Therefore, as in the case of mechanics, in an oscillatory electrical circuit the resonance is clearly expressed at low active resistance.

An example of electrical resonance during tuning of TV and radio receivers

Unlike resonance in mechanics, which can negatively affect structural materials up to the point of destruction, for electrical purposes it is widely used for useful functional purposes. One example of application is tuning TV and radio programs in receivers.

Radio waves of the appropriate frequency reach the receiving antennas and cause small electrical fluctuations. Next, the signal, including the entire pool of broadcast programs, enters the amplifier. Tuned to a specific frequency in accordance with the value of the adjustable capacitance of the capacitor, the oscillatory circuit receives only that signal whose frequency coincides with its own.

An oscillating circuit is installed in the radio receiver. To tune to a station, rotate the handle of the variable capacitor, changing the position of its plates and accordingly changing the resonant frequency of the circuit.

Remember the analog radio receiver “Ocean” from the times of the USSR, the channel tuning knob in which is nothing more than a regulator for changing the capacitance of a capacitor, the position of which changes the resonant frequency of the circuit.

Nuclear magnetic resonance

Certain types of atoms contain nuclei that can be compared to miniature magnets. Under the influence of a powerful external magnetic field, the nuclei of atoms change their orientation in accordance with the relative position of their own magnetic field in relation to the external one. An external strong electromagnetic pulse is absorbed by the atom, resulting in its reorientation. As soon as the source of the impulse ceases its action, the nuclei return to their original positions.

Nuclei, depending on their belonging to a particular atom, are capable of receiving energy in a certain frequency range. The change in the position of the nucleus occurs in one step with external oscillations of the electromagnetic field, which is the reason for the occurrence of the so-called nuclear magnetic resonance (abbreviated NMR). In the scientific world, this type of resonance is used to study atomic bonds within complex molecules. The magnetic resonance imaging (MRI) method used in medicine allows the results of scanning of internal human organs to be displayed on a display for diagnosis and treatment.

The magnetic field of the OMR scanner, formed using inductance coils, creates high-frequency radiation under the influence of which hydrogen changes its orientation, provided that its own frequencies coincide with the external one. As a result of the data received from the sensors, a graphic image is formed on the monitor.

If we compare the NMR and OMR methods with respect to radiation, then scanning with a nuclear magnetic resonator is less harmful than OMR. Also, in the study of soft tissues, NMR technology has shown greater efficiency in reflecting the detail of the tissue area under study.

What is spectrography

The mutual bond between atoms in a molecule is not strictly rigid; when it changes, the molecule goes into a state of vibration. The vibrational frequency of the mutual bonds of atoms changes the resonant frequency of the molecules accordingly. Using the radiation of electromagnetic waves in the IR spectrum, the above vibrations of atomic bonds can be caused. This method, called infrared spectrography, is used in scientific laboratories to study the composition of the material under study.

resonance

Dictionary of medical terms

Explanatory Dictionary of the Living Great Russian Language, Dal Vladimir

resonance

m. French sound, hum, paradise, echo, leave, hum, return, voice; the sonority of the voice, by location, by the size of the room; sonority, sonority of a musical instrument, according to its design.

In grand piano, piano, gusli: deck, deck, old. shelf, board along which strings are stretched.

Explanatory dictionary of the Russian language. D.N. Ushakov

resonance

resonance, plural no, m. (from Latin resonans - giving Echo).

The response sound of one of two bodies tuned in unison (physical).

The ability to increase the strength and duration of sound, characteristic of rooms, the inner surface of which can reflect sound waves. There is a good resonance in the concert hall. There is poor resonance in the room.

Excitation of vibration of a body caused by vibrations of another body of the same frequency and transmitted by an elastic medium located between them (mechanical).

The relationship between self-induction and capacitance in an alternating current circuit that causes maximum electromagnetic oscillations of a given frequency (physical, radio).

Explanatory dictionary of the Russian language. S.I.Ozhegov, N.Yu.Shvedova.

resonance

Excitation of vibrations of one body by vibrations of another of the same frequency, as well as the response sound of one of two bodies tuned in unison (special).

The ability to amplify sound, characteristic of resonators or rooms whose walls reflect sound waves well. R. violins.

adj. resonant, -th, -oe (to 1 and 2 values). Resonance spruce (for making musical instruments; special).

New explanatory dictionary of the Russian language, T. F. Efremova.

resonance

Excitation of vibrations of one body by vibrations of another of the same frequency, as well as the response sound of one of two bodies tuned in unison.

Encyclopedic Dictionary, 1998

resonance

RESONANCE (French resonance, from Latin resono - I respond) is a sharp increase in the amplitude of steady-state forced oscillations as the frequency of an external harmonic influence approaches the frequency of one of the natural oscillations of the system.

Resonance

(French resonance, from Latin resono ≈ I sound in response, I respond), the phenomenon of a sharp increase in the amplitude of forced oscillations in any oscillatory system, which occurs when the frequency of a periodic external influence approaches certain values determined by the properties of the system itself. In the simplest cases, R. occurs when the frequency of the external influence approaches one of those frequencies with which natural oscillations occur in the system, arising as a result of the initial shock. The nature of the R. phenomenon depends significantly on the properties of the oscillatory system. Regeneration occurs most simply in cases where a system with parameters that do not depend on the state of the system itself (so-called linear systems) is subjected to periodic action. Typical features of R. can be clarified by considering the case of harmonic action on a system with one degree of freedom: for example, on a mass m suspended on a spring under the action of a harmonic force F = F0 coswt ( rice. 1), or an electrical circuit consisting of series-connected inductance L, capacitance C, resistance R and a source of electromotive force E, varying according to a harmonic law ( rice. 2). For definiteness, the first of these models is considered below, but everything said below can be extended to the second model. Let us assume that the spring obeys Hooke's law (this assumption is necessary for the system to be linear), i.e., that the force acting on the mass m from the spring is equal to kx, where x ≈ displacement of the mass from the equilibrium position, k ≈ elasticity coefficient (gravity is not taken into account for simplicity). Further, let the mass, when moving, experience resistance from the environment that is proportional to its speed and the coefficient of friction b, i.e., equal to k (this is necessary for the system to remain linear). Then the equation of motion of mass m in the presence of a harmonic external force F has the form: ═══(

where F0≈ oscillation amplitude, w ≈ cyclic frequency equal to 2p/T, T ≈ period of external influence, ═≈ mass acceleration m. The solution to this equation can be represented as the sum of two solutions. The first of these solutions corresponds to free oscillations of the system arising under the influence of the initial push, and the second ≈ forced oscillations. Due to the presence of friction and resistance of the medium, natural oscillations in the system always dampen, therefore, after a sufficient period of time (the longer, the less the damping of natural oscillations), only forced oscillations will remain in the system. The solution corresponding to forced oscillations has the form:

and tgj = . Thus, forced oscillations are harmonic oscillations with a frequency equal to the frequency of the external influence; the amplitude and phase of forced oscillations depend on the relationship between the frequency of the external influence and the parameters of the system.

The dependence of the amplitude of displacements during forced vibrations on the relationship between the values of mass m and elasticity k is most easily traced, assuming that m and k remain unchanged, and the frequency of the external influence changes. With a very slow action (w ╝ 0), the displacement amplitude x0 »F0/k. With increasing frequency w, the amplitude x0 increases, since the denominator in expression (2) decreases. When w approaches the value ═ (i.e., the value of the frequency of natural oscillations with low damping), the amplitude of forced oscillations reaches a maximum ≈ P occurs. Then, with an increase in w, the amplitude of oscillations monotonically decreases and at w ╝ ¥ tends to zero.

The amplitude of oscillations during R. can be approximately determined by setting w = . Then x0 = F0/bw, i.e., the amplitude of oscillations during R. is greater, the lower the damping b in the system ( rice. 3). On the contrary, as the attenuation of the system increases, the radiation becomes less and less sharp, and if b is very large, then the radiation ceases to be noticeable at all. From an energy point of view, R. is explained by the fact that such phase relationships are established between the external force and forced oscillations in which the greatest power enters the system (since the speed of the system is in phase with the external force and the most favorable conditions are created for the excitation of forced oscillations ).

If a linear system is subject to a periodic, but not harmonic, external influence, then R. will occur only when the external influence contains harmonic components with a frequency close to the natural frequency of the system. In this case, for each individual component the phenomenon will proceed in the same way as discussed above. And if there are several of these harmonic components with frequencies close to the natural frequency of the system, then each of them will cause resonant phenomena, and the overall effect, according to the superposition principle, will be equal to the sum of the effects from individual harmonic influences. If the external influence does not contain harmonic components with frequencies close to the natural frequency of the system, then R. does not occur at all. Thus, the linear system responds, “resonates” only to harmonic external influences.

In electrical oscillatory systems consisting of a series-connected capacitance C and inductance L ( rice. 2), R. is that when the frequencies of the external emf approach the natural frequency of the oscillatory system, the amplitudes of the emf on the coil and the voltage on the capacitor separately turn out to be much greater than the amplitude of the emf created by the source, but they are equal in magnitude and opposite in phase. In the case of a harmonic emf acting on a circuit consisting of capacitance and inductance connected in parallel ( rice. 4), there is a special case of R. (anti-resonance). As the frequency of the external emf approaches the natural frequency of the LC circuit, there is not an increase in the amplitude of forced oscillations in the circuit, but, on the contrary, a sharp decrease in the amplitude of the current in the external circuit feeding the circuit. In electrical engineering, this phenomenon is called R. currents or parallel R. This phenomenon is explained by the fact that at a frequency of external influence close to the natural frequency of the circuit, the reactances of both parallel branches (capacitive and inductive) turn out to be the same in value and therefore flow in both branches of the circuit currents are approximately the same amplitude, but almost opposite in phase. As a result, the amplitude of the current in the external circuit (equal to the algebraic sum of the currents in the individual branches) turns out to be much smaller than the amplitude of the current in the individual branches, which, with parallel flow, reach their greatest value. Parallel R., as well as serial R., is expressed the more sharply, the lower the active resistance of the branches of the R. circuit. Serial and parallel R. are called voltage R. and current R., respectively.

In a linear system with two degrees of freedom, in particular in two coupled systems (for example, in two coupled electrical circuits; rice. 5), the phenomenon of R. retains the main features indicated above. However, since in a system with two degrees of freedom, natural oscillations can occur with two different frequencies (the so-called normal frequencies, see Normal oscillations), then R. occurs when the frequency of a harmonic external influence coincides with both one and the other. with a different normal system frequency. Therefore, if the normal frequencies of the system are not very close to each other, then with a smooth change in the frequency of the external influence, two maximum amplitudes of forced oscillations are observed ( rice. 6). But if the normal frequencies of the system are close to each other and the attenuation in the system is sufficiently large, so that the R. at each of the normal frequencies is “dull,” then it may happen that both maxima merge. In this case, the R. curve for a system with two degrees of freedom loses its “double-humped” character and in appearance differs only slightly from the R. curve for a linear contour with one degree of freedom. Thus, in a system with two degrees of freedom, the shape of the R curve depends not only on the damping of the contour (as in the case of a system with one degree of freedom), but also on the degree of connection between the contours.

In coupled systems there is also a phenomenon that is to a certain extent similar to the phenomenon of antiresonance in a system with one degree of freedom. If, in the case of two connected circuits with different natural frequencies, adjust the secondary circuit L2C2 to the frequency of the external emf included in the primary circuit L1C1 ( rice. 5), then the current strength in the primary circuit drops sharply and the more sharply, the less attenuation of the circuits. This phenomenon is explained by the fact that when the secondary circuit is tuned to the frequency of the external emf, just such a current arises in this circuit that induces an induction emf in the primary circuit, approximately equal to the external emf in amplitude and opposite to it in phase.

In linear systems with many degrees of freedom and in continuous systems, control retains the same basic features as in a system with two degrees of freedom. However, in this case, unlike systems with one degree of freedom, the distribution of external influence along individual coordinates plays a significant role. In this case, such special cases of distribution of external influence are possible in which, despite the coincidence of the frequency of the external influence with one of the normal frequencies of the system, R. still does not occur. From an energy point of view, this is explained by the fact that such phase relationships are established between the external force and forced oscillations in which the power supplied to the system from the excitation source along one coordinate is equal to the power given by the system to the source along the other coordinate. An example of this is the excitation of forced vibrations in a string, when an external force coinciding in frequency with one of the normal frequencies of the string is applied at a point that corresponds to the velocity node for a given normal vibration (for example, a force coinciding in frequency with the fundamental tone of the string is applied at the very end of the string). Under these conditions (due to the fact that the external force is applied to a fixed point of the string), this force does not do any work, power from the source of the external force does not enter the system, and no noticeable excitation of string oscillations occurs, i.e., no vibration is observed. .

R. in oscillatory systems, the parameters of which depend on the state of the system, that is, in nonlinear systems, has a more complex character than in linear systems. R. curves in nonlinear systems can become sharply asymmetrical, and the phenomenon of R. can be observed at different ratios of the frequencies of influence and the frequencies of natural small oscillations of the system (the so-called fractional, multiple, and combination R.). An example of R. in nonlinear systems is the so-called. ferroresonance, i.e., resonance in an electrical circuit containing inductance with a ferromagnetic core, or ferromagnetic resonance, which is a phenomenon associated with the reaction of elementary (atomic) magnets of a substance when a high-frequency magnetic field is applied (see Radio spectroscopy).

If an external influence produces periodic changes in the energy-intensive parameters of an oscillatory system (for example, capacitance in an electrical circuit), then at certain ratios of the frequencies of changes in the parameter and the natural frequency of free oscillations of the system, parametric excitation of oscillations, or parametric R, is possible.

R. is very often observed in nature and plays a huge role in technology. Most structures and machines are capable of performing their own vibrations, so periodic external influences can cause them to vibrate; for example, the movement of a bridge under the influence of periodic shocks when a train passes along the joints of rails, the movement of the foundation of a structure or the machine itself under the influence of not completely balanced rotating parts of the machines, etc. There are known cases when entire ships entered into the movement at certain numbers of propeller revolutions shaft In all cases, R. leads to a sharp increase in the amplitude of forced vibrations of the entire structure and can even lead to the destruction of the structure. This is a harmful role of R., and to eliminate it, the properties of the system are selected so that its normal frequencies are far from the possible frequencies of external influence, or the phenomenon of anti-resonance is used in one form or another (so-called vibration absorbers, or dampers, are used). In other cases, radio plays a positive role, for example: in radio engineering, radio is almost the only method that allows you to separate the signals of one (desired) radio station from the signals of all other (interfering) stations.

Lit.: Strelkov S.P., Introduction to the theory of oscillations, 2nd ed., M., 1964; Gorelik G.S., Oscillations and waves, Introduction to acoustics, radiophysics and optics, 2nd ed. M., 1959.

Wikipedia

Resonance

Resonance- a phenomenon in which the amplitude of forced oscillations has a maximum at a certain value of the frequency of the driving force. Often this value is close to the frequency of natural oscillations, in fact it may coincide, but this is not always the case and is not the cause of resonance.

As a result of resonance at a certain frequency of the driving force, the oscillatory system turns out to be especially responsive to the action of this force. The degree of responsiveness in the theory of oscillations is described by a quantity called the quality factor. With the help of resonance, even very weak periodic oscillations can be isolated and/or amplified.

The phenomenon of resonance was first described by Galileo Galilei in 1602 in works devoted to the study of pendulums and musical strings.

Examples of the use of the word resonance in literature.

The instability of the universe can excite self-oscillations of nearby plot lines, which arises resonance, then the system collapses and.

There he continued his work on the study of physical phenomena known in science as the Saebeck and Peltier effects, under conditions of double in-phase piezoelectric resonance, discovered by him during his postgraduate studies and described in detail in his Ph.D. thesis.

If from resonance If the building collapses, then this five-beat gait can destroy Style.

The stock market crash immediately had an international impact resonance: Within a few days, most European markets, including the usually resilient Swiss market, suffered even greater losses than Wall Street.

The structure is swarming with electricians who watch as mechanics spray a layer of conductive fiber onto the shiny walls of the tower from the inside, installing insulating tubes, waveguides, frequency converters, luminous flux meters, optical communications equipment, focal plane locators, neutron activation rods, Mössbauer absorbers, multichannel pulse amplitude analyzers, nuclear amplifiers, voltage converters, cryostats, pulse repeaters, resistance bridges, optical prisms, torsion testers, all kinds of sensors, demagnetizers, collimators, magnetic cells resonance, thermocouple amplifiers, reflector accelerators, proton storage devices and much, much more, in strict accordance with the plan located in the computer memory and including for each device the floor number and coordinates on the block diagram.

Special radiations penetrating the baths cause resonance vibrations of deuterium atoms and body microstructures, ensuring the preservation of all body functions.

I believe that these books will continue to carry us along in mysterious ways. resonance with the works of Klossowski - another major and exceptional name.

There is no benefit from a discovered agent, but many obstacles are foreseen, and it is easier to get rid of him, if only to avoid possible incriminating conversations with the general public. resonance.

The divine gift of a deep and powerful mind, the awareness of whose presence came in youth, endowed with the genius of spiritual guidance, in resonance with whom the whole world found itself, and an artistic genius, for which you probably can’t even find words to define - incomparable, and at the same time - external everyday prosperity, a talented and worthy family, numerous - and all this is rare majestic, exhaustive, and in this in the sense that it is also harmonious.

Tangled in a web of wires, like a pin in a woman’s loose hair, a new paramagnetic installation swayed rhythmically in the wind. resonance.

Copwillem and others acoustic electronic and nuclear magnetic resonances have now been discovered in many crystals containing paramagnetic impurities.

Proximity to the stern teacher occupying the top position and the correct complete resonance in a beneficial second position makes this position quite happy.

Of course, the relationship with Mikhail, like all polygamous sexual desires, was resonance meetings in a past life with different persons, lost and met again in the current reality.

Even the character of my book, which is now coming to an end, changed as a result of the fascinating adventure of trying to divert a lava flow: fascinating technical details, huge social resonance this operation, finally, the incredible interest that this project aroused in me personally, all this has not gone anywhere over the past five months, while I was writing the second half of my book, and what I had previously intended to talk about in the last six chapters has melted away behind the bluish haze curling over the lava flows.

The desire of a noble driller got so noisy resonance, that it was decided to arrange a public display of her labor achievements.