The definition of the concept of resonance (response) in physics is entrusted to special technicians who have statistics graphs who often encounter this phenomenon. Today, resonance is a frequency-selective response, where a vibration system or a sharp increase external force causes another system to oscillate with greater amplitude at certain frequencies.
Operating principle
This phenomenon is observed, when a system is capable of storing and easily transferring energy between two or more different storage modes, such as kinetic and potential energy. However, there is some loss from cycle to cycle, called attenuation. When the damping is negligible, the resonant frequency is approximately equal to the natural frequency of the system, which is the frequency of unforced oscillation.
These phenomena occur with all types of oscillations or waves: mechanical, acoustic, electromagnetic, nuclear magnetic (NMR), electron spin (ESR), and quantum wave function resonance. Such systems can be used to generate vibrations of a certain frequency (for example, musical instruments).
The term "resonance" (from the Latin resonantia, "echo") comes from the field of acoustics, especially seen in musical instruments, such as when strings begin to vibrate and produce sound without direct input from the player.
Pushing a man on a swing is a common example of this phenomenon. A loaded swing, a pendulum, has a natural vibration frequency and a resonant frequency that resists being pushed faster or slower.
An example is the oscillation of projectiles on a playground, which acts like a pendulum. A person's push while swinging at a natural swing interval causes the swing to go higher and higher (maximum amplitude), while attempting to swing at a faster or slower pace creates smaller arcs. This is because the energy absorbed by vibrations increases when the shocks correspond to natural vibrations.
The response occurs widely in nature and is used in many artificial devices. This is the mechanism by which virtually all sine waves and vibrations are generated. Many of the sounds we hear, such as when hard objects made of metal, glass or wood hit, are caused by short vibrations in the object. Light and other short-wave electromagnetic radiation is created by resonance on the atomic scale, such as electrons in atoms. Other terms and conditions that may apply beneficial features this phenomenon:
- Timekeeping mechanisms of modern watches, a balance wheel in a mechanical watch and a quartz crystal in a watch.
- Tidal response of the Bay of Fundy.
- Acoustic resonances of musical instruments and the human vocal tract.
- Destruction of a crystal glass under the influence of a musical right tone.
- Frictional idiophones, such as making a glass object (glass, bottle, vase), vibrate when rubbed around its edge with a fingertip.
- The electrical response of tuned circuits in radios and televisions that allow selective reception of radio frequencies.
- Creation of coherent light by optical resonance in a laser cavity.
- Orbital response, exemplified by some of the gas giant moons of the Solar System.
Material resonances on the atomic scale are the basis of several spectroscopic methods that are used in condensed matter physics, for example:
- Electronic spin.
- Mossbauer effect.
- Nuclear magnetic.
Types of phenomenon
In describing resonance, G. Galileo drew attention to the most essential thing - the ability of a mechanical oscillatory system (heavy pendulum) to accumulate energy, which is supplied from an external source with a certain frequency. Manifestations of resonance have certain characteristics in different systems and therefore different types are distinguished.
Mechanical and acoustic
Electrical resonance
Occurs in an electrical circuit at a certain resonant frequency when the circuit impedance is minimum in a series circuit or maximum in a parallel circuit. Resonance in circuits is used to transmit and receive wireless communications such as television, cellular, or radio.
Optical resonance
An optical cavity, also called an optical cavity, is a special arrangement of mirrors that forms standing wave resonator for light waves. Optical cavities are the main component of lasers, surrounding the amplification medium and providing feedback to the laser radiation. They are also used in optical parametric oscillators and some interferometers.
Light confined within the cavity produces standing waves repeatedly for specific resonant frequencies. The resulting standing wave patterns are called "modes". Longitudinal modes differ only in frequency, while transverse modes differ for different frequencies and have different intensity patterns across the beam cross section. Ring resonators and whispering galleries are examples of optical resonators that do not produce standing waves.
Orbital wobble
In space mechanics, an orbital response arises, when two orbital bodies exert a regular, periodic gravitational influence on each other. This is usually because their orbital periods are related by the ratio of two small integers. Orbital resonances significantly enhance the mutual gravitational influence of bodies. In most cases, this results in an unstable interaction in which the bodies exchange momentum and displacement until resonance no longer exists.
Under some circumstances, a resonant system can be stable and self-correcting to keep bodies in resonance. Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io and the 2:3 resonance between Pluto and Neptune. Unstable resonances with Saturn's inner moons create gaps in Saturn's rings. A special case of 1:1 resonance (between bodies with similar orbital radii) causes large Solar System bodies to clear out the neighborhoods around their orbits, pushing out almost everything else around them.
Atomic, partial and molecular
Nuclear magnetic resonance (NMR) is a name given to a physical resonance phenomenon associated with the observation of specific quantum mechanical magnetic properties of an atomic nucleus if an external magnetic field is present. Many scientific methods use NMR phenomena to study molecular physics, crystals, and non-crystalline materials. NMR is also commonly used in modern medical imaging techniques such as magnetic resonance imaging (MRI).
The benefits and harms of resonance
In order to draw some conclusion about the pros and cons of resonance, it is necessary to consider in which cases it can manifest itself most actively and noticeably for human activity.
Positive effect
The response phenomenon is widely used in science and technology. For example, the operation of many radio circuits and devices is based on this phenomenon.
Negative impact
However, the phenomenon is not always useful. You can often find references to cases where suspension bridges broke when soldiers walked across them “in step.” At the same time, they refer to the manifestation of the resonant effect of resonance, and the fight against it becomes large-scale.
Fighting resonance
But despite the sometimes disastrous consequences of the response effect, it is quite possible and necessary to fight it. To avoid the unwanted occurrence of this phenomenon, it is usually used two ways to simultaneously apply resonance and combat it:
- “Dissociation” of frequencies is carried out, which, if they coincide, will lead to undesirable consequences. To do this, they increase the friction of various mechanisms or change the natural frequency of vibration of the system.
- They increase the damping of vibrations, for example, by placing the engine on a rubber lining or springs.
It reaches its greatest value when the frequency of the driving force is equal to the natural frequency of the oscillatory system.
A distinctive feature of forced oscillations is the dependence of their amplitude on the frequency of changes in the external force. To study this dependence, you can use the setup shown in the figure:
A spring pendulum is mounted on a crank with a handle. When the handle rotates uniformly, a periodically changing force is transmitted to the load through a spring. Changing with a frequency equal to the frequency of rotation of the handle, this force will cause the load to perform forced vibrations. If you rotate the crank handle very slowly, the weight along with the spring will move up and down in the same way as the suspension point ABOUT. The amplitude of forced oscillations will be small. With faster rotation, the load will begin to oscillate more strongly, and at a rotation frequency equal to the natural frequency of the spring pendulum ( ω = ω sob), the amplitude of its oscillations will reach a maximum. With a further increase in the frequency of rotation of the handle, the amplitude of the forced oscillations of the load will again become smaller. A very fast rotation of the handle will leave the load almost motionless: due to its inertia, the spring pendulum, not having time to follow changes in the external force, will simply tremble in place.
The phenomenon of resonance can also be demonstrated with string pendulums. We hang a massive ball 1 and several pendulums with threads of different lengths on a rail. Each of these pendulums has its own frequency of oscillation, which can be determined by knowing the length of the string and the acceleration of gravity.
Now, without touching the light pendulums, we take ball 1 out of its equilibrium position and release it. The swinging of the massive ball will cause periodic oscillations of the rack, as a result of which a periodically changing elastic force will begin to act on each of the light pendulums. The frequency of its changes will be equal to the frequency of oscillations of the ball. Under the influence of this force, the pendulums will begin to perform forced oscillations. In this case, pendulums 2 and 3 will remain almost motionless. Pendulums 4 and 5 will oscillate with a slightly larger amplitude. And at the pendulum b, having the same thread length and, therefore, natural frequency of oscillations as ball 1, the amplitude will be maximum. This is resonance.
Resonance occurs due to the fact that an external force, acting in time with the free vibrations of the body, does positive work all the time. Due to this work, the energy of the oscillating body increases, and the amplitude of the oscillations increases.
A sharp increase in the amplitude of forced oscillations at ω = ω sob called resonance.
The change in the amplitude of oscillations depending on the frequency with the same amplitude of the external force, but with different friction coefficients and, is shown in the figure below, where curve 1 corresponds to the minimum value and curve 3 corresponds to the maximum.
It can be seen from the figure that it makes sense to talk about resonance if the damping of free oscillations in the system is small. Otherwise, the amplitude of forced oscillations at ω = ω 0 differs little from the amplitude of oscillations at other frequencies.
The phenomenon of resonance in life and technology.
Resonance phenomenon can play both a positive and negative role.
It is known, for example, that even a child can swing the heavy “tongue” of a large bell, but only if he pulls the rope in time with the free vibrations of the “tongue.”
The action of a reed frequency meter is based on the use of resonance. This device is a set of elastic plates of various lengths reinforced on a common base. The natural frequency of each plate is known. When the frequency meter comes into contact with an oscillatory system, the frequency of which needs to be determined, the plate whose frequency coincides with the measured frequency begins to oscillate with the greatest amplitude. By noticing which plate has entered resonance, we will determine the oscillation frequency of the system.
The phenomenon of resonance can also be encountered when it is completely undesirable. So, for example, in 1750, near the city of Angers in France, a detachment of soldiers walked in step across a 102 m long chain bridge. The frequency of their steps coincided with the frequency of free vibrations of the bridge. Because of this, the vibration range of the bridge increased sharply (resonance occurred), and the circuits broke. The bridge collapsed into the river.
In 1830, a suspension bridge near Manchester in England collapsed for the same reason while a military detachment was marching across it.
In 1906, the Egyptian Bridge in St. Petersburg, across which a cavalry squadron was passing, collapsed due to resonance.
Now, to prevent such cases, military units, when crossing the bridge, are ordered to “knock their feet”, to walk not in formation, but at a free pace.
If a train passes through a bridge, then, in order to avoid resonance, it passes it either at a slow speed, or, conversely, at maximum speed (so that the frequency of the wheels hitting the rail joints does not turn out to be equal to the natural frequency of the bridge).
The car itself (oscillating on its springs) also has its own frequency. When the frequency of impacts of its wheels at the rail joints turns out to be equal to it, the car begins to sway violently.
The phenomenon of resonance occurs not only on land, but also in the sea, and even in the air. For example, at certain propeller shaft frequencies, entire ships came into resonance. And at the dawn of the development of aviation, some aircraft engines caused such strong resonant vibrations of parts of the aircraft that it fell apart in the air.
Many surprising and sometimes incomprehensible phenomena happen in our lives. However, the explanation for many of them may be quite simple, but not immediately obvious. For example, one of the favorite children's pastimes is swinging. It would seem that there is nothing complicated here - everything is clear and understandable. But have you ever wondered why, if you act correctly on a swing, the swing will become larger and larger? The whole point is that you need to act strictly at certain times and in a certain direction, otherwise the result of the action may not be a swing, but a complete stop of the swing. To prevent this from happening, it is necessary that the frequency of the external influence coincides with the oscillation frequency of the swing itself, in which case the swing range will increase. This phenomenon is called resonance. Let's try to figure out what resonance is, where it occurs in our lives, and what you need to know about this phenomenon.
From the point of view of physics, “resonance” is a sharp increase in the amplitude of forced oscillations when the natural frequency of the oscillatory system coincides with the frequency of the external driving force. This is only an external manifestation of resonance. The internal reason is that an increase in the oscillation amplitude indicates an increase in the energy of the oscillatory system. This can only happen if energy is supplied to the physical system from the outside according to the law of conservation and change of energy. Therefore, the external force must do positive work, increasing the energy of the system. This is only possible when the external force is periodically changing with a frequency equal to the natural frequency of the oscillatory system. The simplest option is the swing option, which we have already described, and which occurs in all pendulum systems and devices. But this is far from the only case of a person using the resonance effect.
Resonance, like any other physical phenomenon, has both positive and negative consequences. Among the positive ones we can highlight the use of resonance in musical instruments. The special shape of the violin, cello, double bass, and guitar promotes the resonance of standing sound waves inside the body of the instrument that make up the harmonica, and the musical instrument gives music lovers an extraordinary sound. The most famous musical instrument makers, such as Nicolo Amati, Antonio Stradivari and Andrea Guarneri, perfected the form, selected rare woods and produced special varnish to enhance the resonating effect, while maintaining the softness and delicacy of the timbre. That is why each such instrument has its own special, unique sound.
In addition, there is a known method of resonant destruction during crushing and grinding of rocks and materials. It goes like this. When the crushed material moves with acceleration, inertial forces will cause stresses and deformations that periodically change their sign - the so-called forced vibrations. The coincidence of the corresponding frequencies will cause resonance, and the forces of friction and air resistance will restrain the growth of the oscillation amplitude, but it can still reach a value significantly exceeding the deformation under accelerations that do not change sign. Resonance will make the crushing and grinding of rocks and materials much more efficient. Resonance plays the same role when drilling holes in concrete walls using an electric drill with a hammer drill.
We also use the phenomenon of resonance in various devices that use radio waves, such as televisions, radios, mobile phones, and so on. The radio or television signal broadcast by a transmitting station has a very small amplitude. Therefore, in order to see an image or hear a sound, it is necessary to amplify them and, at the same time, reduce the noise level. This is achieved using the phenomenon of resonance. To do this, you need to adjust the natural frequency of the receiver, which is basically an electromagnetic oscillatory circuit, to the frequency of the transmitting station. If the frequencies coincide, resonance will occur, and the amplitude of the radio or television signal will increase significantly, while the accompanying noise will remain virtually unchanged. This will ensure a fairly high-quality broadcast.
One type of magnetic resonance, electron paramagnetic resonance, discovered in 1944 by Russian physicist E.K. Zavoisky, is used in the study of the crystal structure of elements, the chemistry of living cells, chemical bonds in substances, etc. Electrons in substances behave like microscopic magnets. In different substances, they reorient in different ways if the substance is placed in a constant external magnetic field and exposed to a radio frequency field. The return of electrons to their original orientation is accompanied by a radio frequency signal, which carries information about the properties of the electrons and their environment. This method is a type of spectroscopy.
Despite all the benefits that can be obtained using resonance, we should not forget about the dangers that it can bring. Earthquakes or seismic waves, as well as the operation of highly vibrating technical devices, can cause destruction of parts of buildings or even entire buildings. In addition, earthquakes can lead to the formation of huge resonant waves - tsunamis with very great destructive force.
Resonance can also cause bridge destruction. There is a version that one of the wooden bridges in St. Petersburg (now it is stone) was actually destroyed by a military unit. As newspapers of the time reported, the unit rode horses, which had to be subsequently pulled out of the water. Naturally, the horses of the guards moved in formation, and not at random. Another bridge, the Tacoma Bridge, was a suspension bridge across the Tacoma Narrows in the United States and was destroyed on November 7, 1940. The cause of the collapse of the central span was wind at a speed of about 65 km/h.
In our time, resonant vibrations caused by the wind almost caused the collapse of the Volgograd bridge, now unofficially called the “Dancing Bridge”. On May 20, 2010, wind and waves rocked it to such an extent that it had to be closed. At the same time, a deafening grinding sound of multi-ton metal structures was heard. For an hour, the road surface of the bridge across the Volga looked like a sheet of paper blowing in the wind. The concrete waves, according to eyewitnesses, were about a meter high. When the bridge “danced,” several dozen cars were driving across it. Fortunately, the bridge stood and no one was hurt.
Thus, resonance is a very effective tool for solving many practical problems, but at the same time it can cause serious destruction, harm to health and other negative consequences.
Matveeva E.V., physics teacher
GBOU School No. 2095 “Pokrovsky Quarter”
With every little effort you make on the path to get closer to the Divine, the Deity makes a much greater effort to get closer to you.
HA. Livraga
Resonance is like an iceberg. In general, it represents a universal law (for example, Tesla considered the law of resonance to be the most general natural law). But only a small part of it is open to our eyes. This includes almost the entire range of associations associated with the word “resonance”. These are pendulums on a common thread, and dishes rattling in the closet in response to a tram passing along the street, and swinging swings, and the St. Petersburg bridge, which collapsed from the march of a company of soldiers passing across it, and laser generation, etc.
What does the depths conceal and how can we find out about it? Firstly, you can wait until, through the efforts of science, a piece of the underwater part appears above the surface. This method works because, despite the efforts of tireless researchers, the iceberg resonance actually floats to the surface. And every day it opens up more and more new facets for us. This includes magnetic resonance imaging - “Nobel laureate” in 2003, and bioresonance with numerous areas of its practical application (homeopathy, acupuncture, Voll and Kirlian diagnostics, etc.), and much more. Secondly, you can catch a glimpse of the underwater part of the iceberg yourself by diving into the depths of some phenomenon outside or inside yourself. But when we surface, we are faced with the inevitable difficulty of describing what we have experienced adequately and understandably to others. And then we either keep our experience to ourselves, or try to translate it into a universal language - a figurative, symbolic language of legends, myths and parables, or the language of science. In both cases, we draw a parallel with what is already known, accepted and understood, calling for help an effective tool of thought - the principle of analogies. For example, in a situation when we understand each other without words, when we feel the thoughts and feelings of a friend, regardless of the distance and time separating us, we can say: we are on the same wavelength, we are in resonance. And the principle of analogies is also resonance - agreement, consonance, correspondence of principles and laws applicable to many planes of manifestation of life: “As above, so below, as below, so above.”
Richard Gerber calls resonance “the key to understanding and controlling any system, which will open the door to the invisible world of life processes.” What is a key? This is what reveals the meaning of what is happening outside and inside us. This is what helps to approach the study of the unknown not only with questions of what and how is happening, but also why and why. Perhaps there is a reason to look at the physics of resonance in the hope of finding such a key in it (is it by chance that the word “reason” means “reasonable argument”, “meaning”)? The key to understanding and managing not just any system. The key to understanding and managing yourself. So, on a good journey to explore the underwater part of the iceberg-resonance, and at the same time ourselves. After all, a person is like an iceberg. And everything we know about ourselves is only a tiny part of our true nature (scientists, for example, believe that in our daily life we use only 4% of our brain's capabilities).
“Know yourself, and you will know the Universe and the Gods.”
Resonance: what, how and why
All connections between phenomena are established exclusively through various types of simple and complex resonances - coordinated vibrations of physical systems.
N. Tesla
Resonance (from the Latin resono - “I sound in response, I respond”) is:
1) sharp increase:
amplitudes of mechanical (sound) vibrations under the influence of external influences, when the frequency of natural vibrations of the system coincides with the frequency of vibrations of the external influence - mechanical (acoustic) resonance;
current strength in the circuit when the frequency of the external influence approaches the natural frequency of the circuit’s oscillations - electrical resonance;
the number of photons absorbed by the system, causing quantum transitions to a higher energy level, when the photon energy coincides with the difference in the energies of two energy levels - quantum resonance;
Resonance conditions
Condition one: “we are not alone.” A person, whether he wants it or not, never exists on his own, never lives in isolation. A person continuously interacts with a wide range of all kinds of creatures and phenomena that affect him. When does such interaction become resonance?
Condition two: the meaning of the word “resonance” tells us this. Resonance is observed only when something in us corresponds, harmonizes, agrees with the influence from the outside and responds to it, when this influence has something to cling to. This means that our inner nature is similar to the nature that surrounds us - “man is a microcosm of the Macrocosm.” What is this similarity based on, what interacts within us and outside of us?
Condition three: “there is no rest, everything moves, rotating.” Everything inside and outside of us is permeated with various vibrations - mechanical, acoustic, electromagnetic, etc. Even in the simplest single-celled organism, vibrations occur at the subatomic, atomic, molecular, subcellular and cellular levels. And our bodies are truly multi-level ensembles of vibrating particles, from atoms to organs and tissues. For example, DNA molecules and cell membranes can vibrate in the radio wave frequency range. Organs also vibrate at a frequency characteristic of most people (heart and muscles of internal organs - 7 Hz; alpha mode of brain function - 4-6 Hz, beta mode - 20-30 Hz). And what we perceive from the outside with the help of our senses (hearing - air vibrations, vision - electromagnetic vibrations in the visible range, touch - mechanical and thermal vibrations, etc.), and what we emit outside (thoughts, emotions, words , actions) - all are vibrations, varying in character and intensity. We perceive the vibrational nature of a swinging swing or a sounding string directly; light and heat - using special devices; and we do not perceive thoughts and emotions at all, since the speed of their vibrations goes beyond the perceptual ability of our senses.
From the third condition it is easy to approach the meaning of resonance as the law of harmonious unification, the birth of the Whole. A person is a complex system, consisting of an astronomical number of parts, large and small, vibrating with a period from fractions of a second (molecular oscillations, ion flows, etc.) to several years (hormonal). But despite such an abundance of component parts, thanks to their resonant synchronization, our body is a single whole. Man as a whole is part of a more global Whole - nature, society, humanity. And it interacts both with the Whole itself and with its other full parts. This interaction is the more successful, the more human activity is in harmony, in accordance with the laws of existence of the whole. We cannot help but be part of the whole. We can become an inharmonious part of it, opposing ourselves to the rest, like a cancer cell, but this opposition will ultimately affect us, our health on all planes (even a cancer cell, by killing the body, deprives itself of the future). After all, health is harmony, agreement, correspondence between the external and the internal, the whole and its part. In modern Russian, the word “whole” means “one from which nothing is subtracted or separated,” but originally this word meant “healthy.”
E/m wave frequencies:
102-108 Hz - radio waves (20-2x104 Hz - audible sound)
109-1011 Hz - microwave radio waves
1013-1014 Hz - infrared light (heat)
1015 Hz - visible light
1015-1016 Hz - ultraviolet light
1017-1020 Hz - X-ray radiation
1020-1022 Hz - gamma radiation
The resonant unification of parts into a single whole occurs according to the principle of “minimum energy”: each of the participants in a common cause who are in resonance (be it pendulums on a common thread, organs in the body or people united by good will and a noble goal) requires less energy than if operated separately. This does not mean that every part is working at half capacity. This means that a group of people, working with full dedication, is able to do something that each individual would never dare to do. This means that the properties of the whole are qualitatively superior to the simple sum of the properties of its constituent parts.
Resonance serves as an indicator of the properties inherent in the object, and allows you to identify even very weak vibrations. For example, if two musical instruments are tuned in the same way and you start playing one of them, the other will also sound. Resonance methods for studying substances and processes occurring in a living organism are based on this property. An important conclusion follows from this: using resonance, it is possible to identify and enhance only those properties of an object that already exist in it. At the same time, the effects should not be intense or energetically powerful. Especially at the stage when the object is especially susceptible to them. Thus, the right word spoken at the right time can create a miracle. And many fateful, turning points in our lives are consequences of this kind of resonance.
Resonance is the key to understanding and managing yourself
Like attracts like.Or: whoever you get along with, that’s what you want.
A person is simultaneously influenced by the “external environment” and influences it himself. A person, on the one hand, is a system in which resonance can be excited; on the other hand, he is capable of acting as an external force that causes resonance in others. Does all this happen by itself, without conscious control on the part of the person? Partly yes. This is especially true for a wide range electromagnetic interactions person and the surrounding space. But with thoughts, emotions and their verbal expression, the situation is different. It is not difficult to admit that a person is responsible for his actions. But, according to karma, which does not sleep, “actions” should include not only physical actions, but also words, emotions and thoughts. Of course, we cannot be responsible for the actions of all those who influence us! But these influences give rise to a response in us (the literal translation of the word “resonance”), our own reaction, which, manifesting itself outside, becomes an “action” for the consequences of which we are already responsible. It turns out to be a “chain reaction”: impact - response = impact - response = impact... Otherwise, this can be called a chain of actions and reactions, causes and consequences. Sometimes such a chain becomes a vivid illustration of the principle “what goes around comes around.” For example: the boss neighbor scolded dad; dad “shared” his irritation with mom; Mom rashly spanked her son; the son kicked the dog. And the dog, going out for a walk, bit... a neighbor! Fortunately, “relay races” of joy, kindness, and gratitude also exist... Which response we will give the green light, and which we will keep to ourselves (or not generate at all), depends only on us. And ideally, “hatred is not conquered by hatred, but by love” (Buddha).
Responsibility is not an easy thing. It is much more pleasant to look for the cause of your troubles outside and consider yourself an innocent victim of someone’s bad influence. But the law of resonance is inexorable: any impact only reveals what is hidden in us. “Problems” are not external, they are within ourselves. For example, a person gets sick. Why? Because he was attacked by “enemies” - viruses, microbes, allergens, carcinogens, etc.? The tactics for preventing and treating the disease with this approach are obvious: one must defend against the enemy with all one’s might, and if he has penetrated, then destroy it immediately. But is this approach always justified? Is there an alternative? There is, and it goes back to ancient times. Its essence is that all external “enemies” are capable of hitting only those who are already ready to get sick. Which means main reason illnesses are in the person himself. “If the vibrations of an evil spirit, the causative agent of a disease, and a person coincide, the person gets sick” (Ayurveda). And in order to recover, a person’s efforts in understanding this cause and in changing himself and medical help from the outside must meet each other halfway.
The resonance of internal and external underlies the perception of information, exploration of the unknown, discoveries and insights. The mystery of knowledge does not happen in a vacuum. Ideas are in the air, but only those who are tuned in to perceive them can catch them. The discovery of a secret is the Response of knowledge to the Call of the efforts of the researcher. Great discoveries are made by a few, small discoveries accompany each of us. And they are always preceded by a search, new knowledge always comes to fertile soil, fertilized with knowledge already accepted and applied by us. It is not without reason that they say that any new information should contain a share (30-50%) of what is known. Only then will she be understood. After all, resonance with the known enhances the ability to perceive the new.
The law of “like attracts like” is also true in the sphere of relationships. For example, if something irritates us in someone, this is a sure sign that we carry this quality within ourselves. And we can direct all that energy of indignation that we are used to pouring out on the offender to searching for the appropriate quality and overcoming it. Therefore, one of the criteria for a person’s moral purity is his kindness and tolerance towards others.
There are periods in life when a person does not find a common language with anyone and cannot fit into any group. At the same time, he either passively waits for others to take steps towards him, or aggressively invades someone else's territory. Let's imagine an established orchestra and a musician whose instrument is out of tune. And the musician either waits for the instrument to tune itself, or does not want to change anything at all, believing that his instrument is the only one that is tuned correctly. It is clear that this musician’s part will be in clear dissonance with the overall sound of the orchestra and the conductor will be forced to take action. What will the musician do? Will he confirm his opposition to the hostile world or... will he tune his instrument in unison with the orchestra?
A person's thoughts and feelings are like an instrument. How to set it up? To find such an “instrument”, the harmony of whose sound we have no doubt, whose music of life awakens in us the desire to follow it. This could be a real person or a hero from movies, novels, legends and myths. And if his example resonates in us, it means that in our soul there is at least one string tuned in unison with the soul of the hero. “The ability to admire means the ability to achieve, and love and respect for the great means that a person is able to grow up to them” (A. Besant). And it doesn’t matter if this inspiring quality has not yet fully manifested itself in us, if the sound of our instrument is still far from ideal. The main thing is that we want to achieve it, that we have found and heard in ourselves the string along which gradually, effort by effort, we will tune our instrument. And its more and more harmonious sound will touch the corresponding strings in the souls of other people.
A person, step by step, step by step cognizing himself, goes towards his own destiny, learns to respond to its Call and becomes a Call for others. Every effort, every victory over oneself, every right step on this path brings the Meeting-Resonance of a person and his Destination closer. Resonance, which provides a chance to see the next step, as well as joy and strength to achieve it. “Every step you take along the way makes the horizon you are going to move one step further. When one sacrament opens before you, it can be compared to the power of a springboard, throwing you up to another sacrament, even higher and more hidden... and so on constantly” (H.A. Livraga).
The nature of the standard tuning fork
(according to B.V. Gladkov)
The amazing commitment of musicians to a sound signal whose frequency of vibration of the fundamental tone is equal to 440 Hz (or close to it) has long been traced. This signal has been elevated to the rank of a standard international tuning fork, intended for tuning all musical instruments. The standard tuning fork is assigned the value of the note “A” in the first octave of the musical scale. So why this sound and not any other?
“There is a legend that in ancient times, near the ancient Egyptian city of Thebes, every morning at dawn this sound was made by a huge statue, known as the colossus of Memnon, and Theban musicians came to it to tune their instruments. The Colossus of Memnon stopped sounding at the beginning of our era, and it is now impossible to verify the truth of the legend” (G.E. Shilov).
On the other hand, relatively recently it was found that the first cry of a newborn, announcing a change in “place of residence,” turned out to be almost the same in pitch (or frequency of the sound signal) in all individuals, regardless of gender and race. With a spread of about -3%, the signal value on the frequency scale corresponds to 440 Hz (note A). In particular, Bulgarian phoniatrist Ivan Maksimov writes about this. Probably, this sound began to play the role of a reference sound, since it corresponds to the first cry of a newborn. But then the question remains: why does a newborn make this particular sound? And does the legend of the Colossus of Memnon have any basis?
There is a well-known fact in Indian classical music: if you place a sitar in an empty room in the corner, and a skilled sitar player plays opposite, the other sitar will begin to vibrate at the same frequency as the first, repeating the melody. But this only happens if the musician is a high-class one. A singer with the power of his voice can smash a glass into pieces, provided that the note taken exactly matches the frequency characteristics of this glass.
IN AND. Cherepanov. Resonance methods for studying matter
A person is in resonance with the Earth: the heart rate averages 70 beats per minute - 7 Hz (1 Hz - 1 vibration per second). The frequency of the Earth's "pulse" is about 7.5 Hz (according to N. Tesla).
Resonance methods for studying substances are the most sensitive and accurate. They have found wide application in physics, chemistry, biology and medicine. Each substance has its own frequency or energy spectrum characteristic only of it. This set of frequencies serves as the calling card of a substance, by studying which one can recognize chemical composition, structure, symmetry, the nature of internal interactions (electrical, magnetic, etc.) between the structural units of a substance and its other characteristics.
The theory of resonance in chemistry, proposed in the 30s. XX century L. Pauling, allows us to judge the equivalence of certain bonds and structural elements in molecules, their symmetry, stability and reactivity. Within the framework of the resonance theory, such widely used concepts as one- and three-electron bonds, hybridization of bond orbitals, superconjugation, as well as the concept of the partially ionic nature of covalent bonds between different atoms were introduced.
Everything that happens on the plane of matter is only a reflection in dense matter of what is happening on the higher planes, and we can always find support for our limping imagination by studying development on the physical plane.
A. Besant
25. Forced vibrations. The phenomenon of resonance. Resonance curves.
Forced vibrations- vibrations that occur under the influence of external forces that change over time.
Self-oscillations differ from forced oscillations in that the latter are caused by periodic external influence and occur with the frequency of this influence, while the occurrence of self-oscillations and their frequency are determined by the internal properties of the self-oscillating system itself.
Newton's second law for such an oscillator will be written in the form: . If we introduce the notation: and replace the acceleration with the second derivative of the coordinate with respect to time, we obtain the following differential equation:
The solution to this equation will be the sum of the general solution of the homogeneous equation and the particular solution of the inhomogeneous one. The general solution of the homogeneous equation has already been obtained here and it has the form:
Where A,φ are arbitrary constants that are determined from the initial conditions.
Let's find a particular solution. To do this, we substitute a solution of the form: into the equation and obtain the value for the constant:
Then the final solution will be written as:
Reasonì ns(fr. resonance, from lat. resono- I respond) is the phenomenon of a sharp increase in the amplitude of forced oscillations, which occurs when the frequency of the external influence approaches certain values (resonant frequencies) determined by the properties of the system.
An increase in amplitude is only a consequence of resonance, and the reason is the coincidence of the external (exciting) frequency with the internal (natural) frequency of the oscillatory system. Using the phenomenon of resonance, even very weak periodic oscillations can be isolated and/or amplified. Resonance is the phenomenon that at a certain frequency of the driving force the oscillatory system is especially responsive to the action of this force.
The mechanical resonance system most familiar to most people is a regular swing. If you push the swing according to its resonant frequency, the range of motion will increase, otherwise the motion will fade. The resonant frequency of such a pendulum can be found with sufficient accuracy in the range of small displacements from the equilibrium state using the formula:
Where g is the acceleration due to gravity (9.8 m/s² for the Earth’s surface), and L- length from the point of suspension of the pendulum to its center of mass
Resonance phenomena can cause irreversible damage in various mechanical systems, such as improperly designed bridges. Thus, in 1905, the Egyptian Bridge in St. Petersburg collapsed while a horse squadron was passing across it, and in 1940, the Tacoma Bridge in the USA collapsed. To prevent such damage, there is a rule that forces the formation of soldiers to break stride when passing bridges.
R 
resonant curve of an oscillating circuit Resonance curve of the oscillatory circuit: w0 - frequency of natural oscillations; W is the frequency of forced oscillations; DW is a frequency band near w0, at the boundaries of which the oscillation amplitude is V = 0.7 Vmakc. The dotted line is the resonance curve of two connected circuits.
26. Basic concepts and starting points of thermodynamics. Reversible and irreversible processes. Circular processes (cycles).
Thermodynamics- a branch of physics that studies the relationships and transformations of heat and other forms of energy
List of principles of thermodynamics
The first law of thermodynamics is the law of conservation of energy as applied to thermodynamic systems. (The amount of heat received by the system goes to change its internal energy and do work against external forces)
Δ U = Q − A
The second law of thermodynamics imposes restrictions on the direction of thermodynamic processes, prohibiting the spontaneous transfer of heat from less heated bodies to more heated ones. Also formulated as the law of increasing entropy. dS≥0 ( Clausius inequality)
The third law of thermodynamics tells how entropy behaves near absolute zero temperatures. 
Reversible process(i.e. equilibrium) - a thermodynamic process that can occur both in the forward and in the reverse direction, passing through the same intermediate states, and the system returns to its original state without energy consumption, and in environment no macroscopic changes remain.
A reversible process can be made to flow in the opposite direction at any time by changing any independent variable by an infinitesimal amount.
Reversible processes produce the most work. It is generally impossible to obtain more work from the system. This gives reversible processes theoretical importance. In practice, a reversible process cannot be realized. It flows infinitely slowly, and you can only get closer to it.
Irreversible is a process that cannot be carried out in the opposite direction through all the same intermediate states. All real processes are irreversible. Examples of irreversible processes: diffusion, thermal conductivity, etc.
Thermodynesì logical qiì kly- circular processes in thermodynamics, that is, processes in which the initial and final parameters that determine the state of the working fluid (pressure, volume, temperature, entropy) coincide.
Thermodynamic cycles are models of processes occurring in real heat engines to convert heat into mechanical work. The only reversible cycle for a machine in which heat transfer occurs only between the working fluid, the heater and the refrigerator is the Carnot Cycle. There are also other cycles (for example, Stirling and Ericsson cycles), in which reversibility is achieved by introducing an additional heat reservoir - a regenerator