Resonance is a physical phenomenon. Theory and real examples. Resonance - sometimes harmful, sometimes useful. What is resonance?

RESONANCE(French resonance, from Latin resono - I respond) - frequency-selective response of oscillations. systems for periodic ext. impact, with which there is a sharp increase in the amplitude of stationary ones. Observed as the external frequency approaches. influence to certain values ​​characteristic of a given system. In linear oscillations. systems, the number of such resonant frequencies corresponds to the number of degrees of freedom and they coincide with the frequencies natural vibrations. In nonlinear oscillations. systems, the reactive and dissipative parameters of which depend on the magnitude of the external influence, R. can also manifest itself as a response to external influences. force impact, and as a reaction to periodic. change settings. In the strict sense, the term "R." applies only to the case of force.

Resonance in linear systems with one degree of freedom. An example of the simplest case of R. is represented by forced oscillations, excited by an external source - harmonic emf ~ E 0 cos pt with amplitude E 0 and frequency p- V oscillatory circuit(Fig. 1, a).

Rice. 1. Oscillatory systems with one degree of freedom: sequential ( A) and parallel ( b) oscillatory circuits, mathematical pendulum ( V) and elastic oscillator ( G),

Amplitude x and phase f of forced oscillations [ q(t) = x cos( pt+f)] are determined by the amplitude and frequency of the external. strength:

Where F = E 0 /L, d = ( R + R i)/2L.

Amplitude dependence X stationary forced oscillations depending on frequency p the driving force with its constant amplitude is called. resonance curve (Fig. 2). In linear oscillation. circuit resonance curves corresponding to different F, are similar, and the phase-frequency characteristic f( p) does not depend on the force amplitude.

Investment of energy into oscillations. contour proportional first degree, and energy dissipation is proportional. the square of the vibration amplitude. This ensures a limitation of the amplitudes of stationary forced oscillations at R. Approximation of frequency p to own frequency w 0 is accompanied by an increase in the amplitude of forced oscillations, the more sharp the lower the coefficient. attenuation d. When R. the current flowing through the circuit is I == = px cos( pt + f - p/2), is in phase with the emf of the side source (f = p/2). A decrease in the amplitude of forced oscillations during inaccurate tuning is due to a violation of the in-phase behavior of the current and voltage in the circuit.

An important characteristic of the resonant properties of oscillations. system (oscillator) is quality factor Q, by definition, is equal to the ratio of the energy stored in the system to the energy dissipated during the oscillation period, multiplied by 2p. When exposed to a resonant frequency, the amplitude of forced oscillations x V Q times more than in quasi-static. case, when the number of periods of oscillation, during which a stationary amplitude is established, is also proportional. Q. Finally, it determines the frequency selectivity of resonant systems. Bandwidth P. Dw, within which the amplitude of forced oscillations decreases by a factor of X, inverse proportion. quality factor: Dw = w 0 / Q= 2d.

When R. in electric. circuits, the reactive part of the complex impedance becomes zero. At the same time, in the subsequent The voltage drop circuits on the coil and on the capacitor have an amplitude QE 0 . However, they add up in antiphase and cancel each other out. In a parallel circuit (Fig. 1, b) when R., mutual compensation of currents occurs in the capacitive and inductive branches. Unlike serial R., with Krom ext. the force effect is carried out by a voltage source; in a parallel circuit, resonant phenomena are realized only when external. the influence is set by the current source. Accordingly, R. in sequence. the circuit is called voltage relay, and in a parallel circuit - current recirculation. If a voltage generator is included in a parallel circuit instead of a current generator, then at the resonant frequency the conditions of not a maximum, but a minimum current will be met, since due to the compensation of currents in the branches containing reactive elements, the conductivity of the circuit turns out to be minimal (anti-resonance phenomenon).

The phenomenon of R. in mechanical engineering has similar features. and other oscillations. systems. In linear systems, according to the principle of superposition, the system's response to periodic the non-sinusoidal effect can be found as the sum of the responses to each of the harmonics. impact component. If the period of the non-sinusoidal force is T, then the resonant increase in oscillations can occur not only under the condition w 0! 2 p /T, but depending on the shape E(t) and under the conditions w 0 ! 2p n/T, Where n= 1, 2,... (R. on harmonics).

Resonance curves are determined by observing a change in the amplitude of forced oscillations or by slowly tuning the frequency p forcing force, or with a slow change in property. frequency w 0 . With a high quality factor of the oscillator ( Q 1) both methods give almost identical results. Frequency characteristics obtained at a finite rate of frequency change differ from static ones. resonance curves corresponding to infinitely slow tuning: to dynamic. frequency characteristics there is a shift of the maximum in the direction of frequency tuning, proportional. m, where is the relaxation time of oscillations in the circuit,

Rice. 3. Static and dynamic amplitude-frequency characteristics resonance at different frequency rise rates: p(t)= w 0 + t/m, m = 0(1) , 0.0625 (g), 0.25(3), 0.695 ( 4) .

t*- time during which the frequency p is within the resonance band Dw. With rapid frequency tuning, as m increases, the height decreases and the resonance curves expand, and their shape becomes more asymmetrical (Fig. 3).

Resonance in linear oscillatory systems with several degrees of freedom. Oscillation systems with several degrees of freedom represent a set of interacting oscillators. An example is a pair of oscillations. circuits connected due to mutual induction (Fig. 4). Forced oscillations in such a system are described by the equations

Inductive coupling leads to the fact that oscillations in the department. circuits cannot occur independently of each other. However, for any fluctuations. systems with several degrees of freedom can be used to find normal coordinates, which are linear combinations of independent variables. For normal coordinates, a system of equations similar to (2) is transformed into a chain of equations for forced oscillations of the same type as for single oscillations. contours, with the difference that each of the normal coordinates is affected by forces applied, generally speaking, in different parts of the total oscillations. systems. When considering the laws of motion in normal coordinates, all the laws of motion in systems with one degree of freedom are valid.

Rice. 4. An oscillatory system with two degrees of freedom - a pair of circuits with coupling due to mutual induction.

A resonant increase in oscillations occurs in all parts of the oscillations. systems at the same frequencies (Fig. 5), equal to the natural frequencies. system vibrations. Normal frequencies do not coincide with partial ones, i.e. with their own. frequencies of the oscillators included in the overall system. If the frequency of the external force is equal to one of the partial frequencies, then R. does not occur in the aggregate system. On the contrary, in this case the amplitudes of forced oscillations reach a minimum, similar to the case of antiresonance in a system with one degree of freedom. The ability to suppress oscillations, the frequency of which is equal to one of the partial ones, is used in electrical applications. filters and mechanical dampers. hesitation.

In a system consisting of weakly coupled oscillators with identical partial frequencies, resonant maxima corresponding to close normal frequencies can merge, so that the frequency response has one maximum (Fig. 6). Increasing the coupling between oscillators leads to an increase in the interval between the normal frequencies of the system. Changing the shape of the resonance curves with increasing coefficient. connections are illustrated in Fig. 6. A system of oscillators with coupling close to critical has a frequency response that is flattened near R, and the steepness of its slopes is higher than that of a single oscillator with the same level of losses. This property is usually used to create strip electric. filters.

Rice. 6. Resonance curves of a double-circuit oscillatory system at g Q = 1(1 ), and 2(3); g = M/L, L 1 = L 2 .

Resonance in distributed oscillatory systems. In distributed systems (see System with distributed parameters)The amplitude and phase of oscillations depend on spatial coordinates. Linear distributed oscillations. systems are characterized by a set of normal frequencies and natural frequencies. functions, which describe the spatial distribution of the amplitudes of their own. hesitation. The resonant properties (quality factor) of distributed systems are determined not only by their own. by attenuation, but also by connection with the environment, in which part of the oscillation energy (electrical, elastic, etc.) is emitted. In distributed systems with high quality factor ( Q 1) , forced oscillations represent, the spatial distribution of amplitudes of which is a superposition of their own. function (mod), and the phase of oscillation is the same at all points. The action of external forces with frequencies close to their own leads to a resonant increase in the amplitude of forced oscillations at all points in the volume of a distributed resonant system (resonator).

In distributed systems, all general properties of radios remain in force. A special feature of radio in distributed systems (as well as in systems with several degrees of freedom) is the dependence of the amplitudes of forced oscillations not only on frequency, but also on the spatial distribution of the driving force. R. occurs if the spatial distribution of external force repeats the shape of its own. functions, and the frequency is equal to the corresponding normal frequency. If the spatial distribution of the external force is unfavorable, forced oscillations are not excited. This occurs, in particular, when a concentrated force is applied at points for which the amplitude of the corresponding normal vibration becomes zero. Thus, by applying a concentrated force at a point that is a nodal point for the movement of the string, it is impossible to excite its oscillations, since the work done by the force will be zero. If the distribution of forces is such that the work done by them is different. parts of the system, has opposite signs and generally does not lead to a change in energy; forced oscillations are also not excited.

Resonance in nonlinear oscillatory systems. In elastic systems, the nonlinear element is a spring, for which the relationship between deformation and elastic force is nonlinear, i.e., it is broken. In electric systems, an example of a nonlinear dissipative element is a diode, the current-voltage characteristic of which does not obey Ohm’s law. Nonlinear reactive (energy-intensive) elements are capacitors with or inductors with ferrite cores. The parameters of these elements are capacitance, inductance, resistance, as well as their own. frequency and coefficient attenuation in nonlinear systems can be considered functions of current or voltage. At the same time, in nonlinear systems it does not hold superposition principle.

In nonlinear systems, harmonic. force excites inharmonious. oscillations, in the spectrum of which there are multiple frequencies, therefore R. at harmonics occurs p with a sinusoidal external. strength. In oscillation systems with a sufficiently high quality factor and frequency selectivity, max. The amplitude is that spectral component whose frequency is close to the frequency P. Considering only oscillations with a frequency close to the resonant one, it is also possible in this case to obtain a family of resonance curves. For a system with nonlinear reactive (energy-intensive) elements at r! w 0 these curves are shown in Fig. 7. The shape of the resonance curve depends on the amplitude of the driving force and, as it increases, it becomes more and more asymmetrical. Since the natural frequency Since the oscillations of a nonlinear oscillator depend on their amplitude, the maxima on the resonance curves shift towards higher or lower frequencies. Starting from a certain value of the force amplitude, the resonance curves acquire an ambiguous beak-shaped shape. In a certain frequency range, the stationary amplitude of forced oscillations turns out to depend on the history of the establishment of oscillations (the phenomenon of oscillation hysteresis). In this case, parts of the resonance curves corresponding to unstable states form on the plane ( x, p)region of physically unrealizable modes (shaded in Fig. 7).

Rice. 7. A family of amplitude-frequency curves in the case of nonlinear resonance at various amplitudes of the external force ( F 1 < F 2 < < F 3 < F 4 ) . The dotted line is an unstable section of the resonance curve. The region of unstable states is shaded. The arrows mark the points of abrupt changes in the amplitudes of oscillations when the frequency is tuned upward ( AB) and down (CD).

On the phenomenon of nonlinear radiation in widespread oscillations. systems can render creatures. influence of the effects of self-focusing and the formation of shock waves, especially in cases where a large number of waves fit along the length.

Phenomena related to resonance. In nonlinear oscillations. external systems periodic the impact causes not only the excitation of forced oscillations, but also the modulation of energy-intensive and dissipative parameters. The phenomenon of excitation of oscillations during periodic modulation of energy-intensive parameters is called. parametric resonance.

If the modulation depth of an energy-intensive parameter is insufficient to excite parametric R., in oscillation. the system partially compensates for losses. Resonant response to the action of a weak signal with frequency p! w 0 is the same as that of a linear oscillator with a higher quality factor. In addition, combination fluctuations are formed. frequencies mр + n w M, where w M is the modulation frequency of the parameter, If the frequency matches R and (w M - R) forced oscillations in a parametrically regenerated system depend on the relationships between the phases of the parametric. influence and weak strength (signal). In this case, both an increase and a decrease in the amplitude of forced oscillations can occur compared to the absence of parametric parameters. regeneration (the phenomena of “strong” and “weak” R.).

The effect of loss regeneration and increasing the equivalent quality factor occurs in resonant systems with nonlinear losses, which contain elements C negative differential resistance or positive circuit feedback. Such systems are called potentially self-oscillating. If on potentially self-oscillation. the system is affected by per-podich. strength means. amplitudes with frequency R, it can influence the damping of oscillations in the system so that during a certain fraction of the period of action of the damping force it becomes negative. The result is potentially self-oscillation. the system is excited by oscillations at a frequency w close to its own, if the additional condition w = R/n. Happening n= 1 corresponds to external frequency synchronization. by force. At n 2 this phenomenon is called. autoparametric excitation, by analogy with parametric resonance, in contrast to which with autoparametric. During excitation, modulation occurs not of the energy-intensive, but of the dissipative parameters of the system.

The term "R." is also used in relation to processes in quantum systems, when the frequency is external. influence (radiation) is equal to the frequency of the quantum transition, so the condition is satisfied

where is the energy, respectively n -, m-th levels of the quantum system. When (3) is fulfilled, the probabilities of quantum transitions increase sharply, which manifests itself as an increase in the intensity of energy exchange - absorption and emission (see. Quantum electronics, Laser).

R. can be the cause of instability and mechanical destruction. engineering structures and electrical networks. In vibration transducers, R. makes it possible to achieve amplitudes of elastic vibrations due to periodic action of a relatively weak force. In radiophysics and radio engineering, the phenomenon of radiation underlies many. methods for filtering signals of different frequencies, detecting and receiving weak signals.

Lit.: Gorelik G.S., Oscillations and waves, 2nd ed., M., 1959; Strelkov S.P., Introduction to the theory of oscillations, 2nd ed., M., 1964; Kharkevich A.A., Fav. works, vol. 2, M., 1973; Fundamentals of the theory of oscillations, ed. V.V. Migulina, 2nd ed., M., 1988. G. V. Belokopytov.

The essence of the phenomenon of resonance (translated from Latin as “I sound in response” or “I respond”) is a sharp increase in the amplitude of natural oscillations observed in structures exposed to external factors. The main condition for its occurrence is the coincidence of the frequency of these oscillations external to the system with its own frequency parameters, as a result of which they begin to work “in unison.”

Types of resonance phenomena

Most often, resonance in physics is observed when studying so-called “linear” formations, the parameters of which do not depend on the current state. Their typical representatives are structures with one degree of freedom (these include a load suspended on a spring, or a circuit with an inductance and a capacitive element connected in series).

Note! In both of these cases, the presence of an influence external to the given system (mechanical or electrical) is assumed.

Let us consider what resonance is and what its essence is in more detail.

The phenomenon of resonance can be observed in structures with the following mechanical device. Let us assume that there is a load of mass M freely suspended on an elastic spring. It is acted upon by an external force, the amplitude of which varies according to a sinusoid:

To assess the nature of oscillations of such a system, it is necessary to use Hooke’s law, according to which the force caused by the spring is equal to kx, where x is the magnitude of the deviation of the mass M from the average position. The coefficient k describes the internal properties associated with its elasticity.

Based on these assumptions and after applying simple mathematical calculations, it is possible to obtain a result that allows us to draw the following conclusions:

• Forced mechanical vibrations belong to the category of harmonic phenomena that have a frequency that coincides with the same parameter for the external stimulus;
• The amplitude (span), as well as the phase characteristics of mechanical structures depend on how its own parameters correlate with the characteristics of the harmonic effect;
• When a signal or mechanical effect that did not vary according to a sinusoidal law was applied to a linear system, resonance phenomena were observed only in special situations;
• For their appearance, it is necessary that the external pump (signal) contain harmonic components comparable to the natural frequency of the system.

Each of these components, even if several of them are found, will cause its own resonant response. Moreover, the complex response (according to the superposition principle) is equal to the sum of the same responses observed from the action of each of the external harmonic components.

Important! In the case when such an effect does not contain components with similar frequencies at all, resonance cannot occur at all.

To analyze all components of mixtures that resonate with system frequencies, the Fourier method is used, which makes it possible to decompose a complex oscillation of an arbitrary shape into the simplest harmonic components.

Electrical oscillatory circuit

In electrical circuits consisting of a capacitive component C and an inductor L, when observing resonant phenomena, it is necessary to distinguish between the following two situations with different characteristics:

• Serial connection of elements in a circuit;
• Their parallel inclusion.

In the first case, when the natural oscillations coincide with the frequency of the external influence (EMF), changing according to a sinusoidal law, sharp bursts of amplitude are observed, coinciding in phase with the external signal source.

When the same elements are connected in parallel under the influence of an external harmonic EMF, the phenomenon of “anti-resonance” appears, consisting of a sharp decrease in the amplitude of the EMF.

Additional Information. This effect, called parallel (or resonance of currents), is explained by the mismatch in the phases of the natural and external oscillations of the EMF.

At resonant frequencies, the reactances of each of the parallel branches are equalized in value, so that currents of approximately the same amplitude flow in them (but they are always out of phase).

As a result, the current signal common to the entire circuit is an order of magnitude smaller. These properties perfectly describe the behavior of filter circuits and chains, in which the use of resonance for electrical needs is expressed very clearly.

Complex vibrational structures

In systems with linear characteristics, characterized by the use of several (two in a particular case) circuits, resonance phenomena are possible only if there is a connection between them.

The following rules apply to connected contours:

• They retain all the basic properties of single-circuit linear structures;
• In such circuits, oscillations are possible at two resonant frequencies, called normal;
• If the forced influence does not coincide in frequency with any of them, when it changes smoothly, the “response” in the system will occur sequentially on each;
• In this case, its graph will have the form of a merged or double resonance with a blunt peak and two small bursts (“humps”);
• When the normal frequencies are not very different from one another and are close to the same parameter for the external EMF, the response of the system will have the same form, but the two “humps” will practically merge into one;
• The shape of the resonance curve in the latter case will have almost the same appearance as in the single-circuit linear version.

In circuits with many degrees of freedom, basically the same reactions are preserved as in systems with two parameters.

Nonlinear systems

The response of systems whose characteristics are determined by the current state (they are called nonlinear) has a more complex form and is characterized by asymmetric manifestations. The latter depend on the ratio of the characteristics of external influences and the frequencies of the natural forced oscillations of the system.

Note! In this case, they can appear as fractional parts of frequencies affecting the system of oscillations, or in the form of multiples of them.

An example of responses observed in nonlinear systems are the so-called ferroresonance phenomena. They are possible in electrical circuits that include inductance with a ferromagnetic core, and belong to the category of structural.

The latter is explained by the peculiarities of the composition of matter at the atomic level, when studying it it is discovered that ferromagnetic structures are a set of a huge number of elementary magnets (spins). Each of these states in response to external “pumping” is determined by many different factors, that is, it manifests itself in technology as nonlinear.

In conclusion, it should be summarized that, regardless of the type of system under study, the essence of resonance phenomena lies in observing the responses of oscillatory structures to external influences applied to them. A thorough study of these physical phenomena allows us to obtain practical results that facilitate the introduction of completely new technologies into production.

Video

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 oscillation frequency, 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, in order 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.

We often hear the word resonance: “public resonance”, “event that caused resonance”, “resonant frequency”. Quite familiar and ordinary phrases. But can you say exactly what resonance is?

If the answer jumped out at you, we are truly proud of you! Well, if the topic “resonance in physics” raises questions, then we advise you to read our article, where we will talk in detail, clearly and briefly about such a phenomenon as resonance.

Before talking about resonance, you need to understand what oscillations are and their frequency.

Oscillations and Frequency

Oscillations are a process of changing the states of a system, repeated over time and occurring around an equilibrium point.

The simplest example of oscillation is riding on a swing. We present it for a reason; this example will be useful to us in understanding the essence of the phenomenon of resonance in the future.

Resonance can only occur where there is vibration. And it doesn’t matter what kind of vibrations they are - electrical voltage fluctuations, sound vibrations, or simply mechanical vibrations.

In the figure below we describe what fluctuations can be.

By the way! For our readers there is now a 10% discount on any type of work

Oscillations are characterized by amplitude and frequency. For the swings already mentioned above, the oscillation amplitude is the maximum height to which the swing flies. We can also swing the swing slowly or quickly. Depending on this, the oscillation frequency will change.

Oscillation frequency (measured in Hertz) is the number of oscillations per unit time. 1 Hertz is one oscillation per second.

When we swing a swing, periodically rocking the system with a certain force (in this case, the swing is an oscillatory system), it performs forced oscillations. An increase in the amplitude of oscillations can be achieved if this system is influenced in a certain way.

By pushing the swing at a certain moment and with a certain periodicity, you can swing it quite strongly, using very little effort. This will be a resonance: the frequency of our influences coincides with the frequency of oscillations of the swing and the amplitude of the oscillations increases.

The essence of the phenomenon of resonance

Resonance in physics is a frequency-selective response of an oscillatory system to a periodic external influence, which manifests itself in a sharp increase in the amplitude of stationary oscillations when the frequency of the external influence coincides with certain values ​​characteristic of a given system.

The essence of the phenomenon of resonance in physics is that the amplitude of oscillations increases sharply when the frequency of influence on the system coincides with the natural frequency of the system.

There are known cases when the bridge along which soldiers were marching resonated with the marching step, swayed and collapsed. By the way, this is why now, when crossing the bridge, soldiers are supposed to walk at a free pace, and not in step.

Examples of resonance

The phenomenon of resonance is observed in a variety of physical processes. For example, sound resonance. Let's take a guitar. The sound of the guitar strings itself will be quiet and almost inaudible. However, there is a reason that the strings are installed above the body - the resonator. Once inside the body, the sound from the vibrations of the string intensifies, and the one who holds the guitar can feel how it begins to slightly “shake” and vibrate from the blows on the strings. In other words, resonate.

Another example of observing resonance that we encounter is circles on water. If you throw two stones into the water, the passing waves from them will meet and increase.

The action of a microwave oven is also based on resonance. In this case, resonance occurs in water molecules that absorb microwave radiation (2.450 GHz). As a result, the molecules resonate, vibrate more strongly, and the temperature of the food rises.

Resonance can be both beneficial and harmful. And reading the article, as well as the help of our student service in difficult educational situations, will only bring you benefit. If, while completing your coursework, you need to understand the physics of magnetic resonance, you can safely contact our company for quick and qualified help.

Finally, we suggest watching a video on the topic “resonance” and making sure that science can be exciting and interesting. Our service will help with any work: from an essay on “The Internet and Cybercrime” to a coursework on the physics of oscillations or an essay on literature.

The word "resonance" is used by people every day in a variety of different ways. It is pronounced by politicians and TV presenters, written by scientists in their works, and studied by schoolchildren in lessons. This word has several meanings relating to different areas of human activity.

Where does the word resonance come from?

We all learn what resonance is for the first time from a school physics course. In scientific dictionaries, this term is given a detailed explanation from the point of view of mechanics, electromagnetic radiation, optics, acoustics and astrophysics.

From a technical point of view, resonance is a phenomenon of the response of an oscillatory system and not an external influence. When the periods of influence and response of the system coincide, resonance occurs - a sharp increase in the amplitude of the oscillations in question.

The simplest example of mechanical resonance is given in his works by the medieval scientist Toricelli. A precise definition of the phenomenon of resonance was given by Galileo Galilei in his work on pendulums and the sound of musical strings. What is electromagnetic resonance, explained in 1808 by James Maxwell, founder of modern electrodynamics.

You can find out what “resonance” is not only in Wikipedia, but in the following reference publications:

• physics textbooks for grades 7-11;
• physical encyclopedia;
• scientific and technical encyclopedic dictionary;
• dictionary of foreign words of the Russian language;
• philosophical encyclopedia.

Resonance in polemics and rhetoric

The word “resonance” acquired another meaning in the field of social sciences. This word refers to the public’s response to a certain phenomenon in people’s lives, a certain statement, or incident. Typically, the word “resonance” is used when something causes many people to have a similar and very strong reaction at the same time. There is even a commonly used expression “wide public resonance”, which is a speech cliche. It is best to avoid it in your own speech, written or oral.

In the philosophical dictionary, resonance is interpreted as a concept that has a figurative meaning and is understood as agreement or like-mindedness of two people, two souls in compassion, sympathy or antipathy, sympathy or indignation.

In the meaning of “strong response”, “unanimous assessment”, the word resonance is very popular with politicians, speakers, and announcers. It helps to convey an emotional upsurge, a unanimous impulse, and emphasize the significance of what is happening.

Where do we meet resonance?

In the literal sense, the word resonance should be used in relation to many natural processes occurring around us. All children who ride on a regular swing or carousel on a playground exploit mechanical resonance.

Housewives, heating food in the microwave, use electromagnetic resonance. The television and radio broadcasting network, the operation of mobile phones and wifi for the Internet are built on the principles of resonance.

Sound resonance allows us to enjoy music or indulge in echoes in mountains and indoor spaces where the walls do not have sufficient sound insulation. The operation of echo sounders and many other measuring instruments is based on the principle of acoustic resonance.

Why is resonance dangerous?

In the natural scientific sense, resonance as a phenomenon can not only be useful to humans, but also dangerous. The most striking example is construction.

When designing buildings and structures, structural calculations for resonance are strictly necessary. This is how all high-rise buildings, towers, power line supports, transmitting and receiving antennas, as well as high-rise buildings that resonate with winds at high altitudes are calculated.

All bridges and extended objects must be checked for resonance. In 2010, a video of a bridge across the Volga, which spread like a silk ribbon, spread all over the Internet. The results of the investigation showed that the bridge structures resonated with the wind.

A similar incident occurred in the USA. On November 7, 1940, one of the spans of the Tacoma Suspension Bridge, located in Washington state, collapsed. Even during construction, experts noted vibrations of the bridge deck associated with the wind and the low height of the supports. As a result of the collapse, numerous studies and calculations were carried out, which became the basis for modern bridge construction technologies. Among specialists, even the term “Tacoma Bridge” arose, meaning the poor quality of construction calculations.

Each of us encounters resonance every day. You need to remember this phenomenon in everyday life, whether you decide to swing on a pedestrian bridge or put metal utensils in the microwave (this is prohibited by the rules). And the word “resonance” itself can be used in your speech to decorate it and enhance the impression of what you said.