How to explain vibrations in an elastic medium. Formation and propagation of waves in an elastic medium

Waves

The main types of waves are elastic (for example, sound and seismic waves), waves on the surface of a liquid, and electromagnetic waves(including light and radio waves). Feature waves is that when they propagate, there is a transfer of energy without transfer of matter. Consider first the propagation of waves in elastic medium.

Wave propagation in an elastic medium

An oscillating body placed in an elastic medium will drag along and lead to oscillating motion surrounding particles of the environment. The latter, in turn, will affect neighboring particles. It is clear that the entrained particles will lag behind in phase those particles that entrain them, since the transfer of oscillations from point to point is always carried out at a finite speed.

So, an oscillating body placed in an elastic medium is a source of vibrations that propagate from it in all directions.

The process of propagation of oscillations in a medium is called a wave. Or elastic wave is the process of propagation of a perturbation in an elastic medium .

Waves happen transverse (oscillations occur in a plane perpendicular to the direction of wave propagation). These include electromagnetic waves. Waves happen longitudinal when the direction of oscillation coincides with the direction of wave propagation. For example, sound propagation in air. Compression and rarefaction of particles of the medium occur in the direction of wave propagation.

Waves can be different shape, can be regular or irregular. Special meaning in wave theory has a harmonic wave, i.e. an infinite wave in which the change in the state of the medium occurs according to the sine or cosine law.

Consider elastic harmonic waves . A number of parameters are used to describe the wave process. Let us write down the definitions of some of them. The perturbation that occurred at some point in the medium at some point in time propagates in the elastic medium at a certain speed. Spreading from the source of vibrations, the wave process covers more and more new parts of space.

geometric place points to which oscillations reach a certain point in time is called the wave front or wave front.

The wave front separates the part of space already involved in the wave process from the area in which oscillations have not yet arisen.

The locus of points oscillating in the same phase is called the wave surface.

There can be many wave surfaces, and there is only one wave front at any time.

Wave surfaces can be of any shape. In the simplest cases, they have the shape of a plane or sphere. Accordingly, the wave in this case is called flat or spherical . In a plane wave, wave surfaces are a set of planes parallel to each other, in spherical wave- many concentric spheres.

Let a plane harmonic wave propagate with a velocity along the axis . Graphically, such a wave is depicted as a function (zeta) for a fixed point in time and represents the dependence of the displacement of points with different meanings from the equilibrium position. is the distance from the source of vibrations , at which, for example, the particle is located. The figure gives an instantaneous picture of the distribution of perturbations along the direction of wave propagation. The distance over which the wave propagates in a time equal to the period of oscillation of the particles of the medium is called wavelength .

,

where is the wave propagation velocity.

group speed

A strictly monochromatic wave is an endless sequence of "humps" and "troughs" in time and space.

The phase velocity of this wave, or (2)

With the help of such a wave it is impossible to transmit a signal, because. at any point of the wave, all "humps" are the same. The signal must be different. Be a sign (label) on the wave. But then the wave will no longer be harmonic, and will not be described by equation (1). The signal (impulse) can be represented according to the Fourier theorem as a superposition of harmonic waves with frequencies contained in a certain interval Dw . A superposition of waves that differ little from each other in frequency

called wave packet or wave group .

The expression for a group of waves can be written as follows.

(3)

Icon w emphasizes that these quantities depend on frequency.

This wave packet can be a sum of waves with slightly different frequencies. Where the phases of the waves coincide, there is an increase in amplitude, and where the phases are opposite, there is a damping of the amplitude (the result of interference). Such a picture is shown in the figure. In order for the superposition of waves to be considered as a group of waves, it is necessary to fulfill next condition Dw<< w 0 .

In a non-dispersive medium, all plane waves forming a wave packet propagate with the same phase velocity v . Dispersion is the dependence of the phase velocity of a sinusoidal wave in a medium on frequency. We will consider the phenomenon of dispersion later in the Wave Optics section. In the absence of dispersion, the velocity of the wave packet travel coincides with the phase velocity v . In a dispersive medium, each wave disperses at its own speed. Therefore, the wave packet spreads over time, its width increases.

If the dispersion is small, then the spreading of the wave packet does not occur too quickly. Therefore, the movement of the entire packet can be assigned a certain speed U .

The speed at which the center of the wave packet (the point with the maximum amplitude value) moves is called the group velocity.

In a dispersive medium v¹ U . Along with the movement of the wave packet itself, there is a movement of "humps" inside the packet itself. "Humps" move in space at a speed v , and the package as a whole with the speed U .

Let us consider in more detail the motion of a wave packet using the example of a superposition of two waves with the same amplitude and different frequencies w (different wavelengths l ).

Let us write down the equations of two waves. Let us take for simplicity the initial phases j0 = 0.

Here

Let be Dw<< w , respectively Dk<< k .

We add the fluctuations and carry out transformations using the trigonometric formula for the sum of cosines:

In the first cosine, we neglect Dwt and Dkx , which are much smaller than other quantities. We learn that cos(–a) = cosa . Let's write it down finally.

(4)

The factor in square brackets changes with time and coordinates much more slowly than the second factor. Therefore, expression (4) can be considered as a plane wave equation with an amplitude described by the first factor. Graphically, the wave described by expression (4) is shown in the figure shown above.

The resulting amplitude is obtained as a result of the addition of waves, therefore, maxima and minima of the amplitude will be observed.

The maximum amplitude will be determined by the following condition.

(5)

m = 0, 1, 2…

xmax is the coordinate of the maximum amplitude.

The cosine takes the maximum value modulo through p .

Each of these maxima can be considered as the center of the corresponding group of waves.

Resolving (5) with respect to xmax get.

Since the phase velocity called the group speed. The maximum amplitude of the wave packet moves with this speed. In the limit, the expression for the group velocity will have the following form.

(6)

This expression is valid for the center of a group of an arbitrary number of waves.

It should be noted that when all terms of the expansion are accurately taken into account (for an arbitrary number of waves), the expression for the amplitude is obtained in such a way that it follows from it that the wave packet spreads over time.
The expression for the group velocity can be given a different form.

Therefore, the expression for the group velocity can be written as follows.

(7)

is an implicit expression, since v , and k depends on the wavelength l .

Then (8)

Substitute in (7) and get.

(9)

This is the so-called Rayleigh formula. J. W. Rayleigh (1842 - 1919) English physicist, Nobel laureate in 1904, for the discovery of argon.

It follows from this formula that, depending on the sign of the derivative, the group velocity can be greater or less than the phase velocity.

In the absence of dispersion

The intensity maximum falls on the center of the wave group. Therefore, the energy transfer rate is equal to the group velocity.

The concept of group velocity is applicable only under the condition that the wave absorption in the medium is small. With a significant attenuation of the waves, the concept of group velocity loses its meaning. This case is observed in the region of anomalous dispersion. We will consider this in the Wave Optics section.

string vibrations

When transverse vibrations are excited, standing waves are established in a stretched string fixed at both ends, and knots are located at the places where the string is fixed. Therefore, only such vibrations are excited in a string with noticeable intensity, half of the wavelength of which fits an integer number of times over the length of the string.

This implies the following condition.

Or

(n = 1, 2, 3, …),

l- string length. The wavelengths correspond to the following frequencies.

(n = 1, 2, 3, …).

The phase velocity of the wave is determined by the string tension and the mass per unit length, i.e. the linear density of the string.

F - string tension force, ρ" is the linear density of the string material. Frequencies vn called natural frequencies strings. Natural frequencies are multiples of the fundamental frequency.

This frequency is called fundamental frequency .

Harmonic vibrations with such frequencies are called natural or normal vibrations. They are also called harmonics . In general, the vibration of a string is a superposition of different harmonics.

String vibrations are noteworthy in the sense that, according to classical concepts, discrete values ​​of one of the quantities characterizing vibrations (frequency) are obtained for them. For classical physics, such discreteness is an exception. For quantum processes, discreteness is the rule rather than the exception.

Elastic wave energy

Let at some point of the medium in the direction x a plane wave propagates.

(1)

We single out an elementary volume in the medium ΔV so that within this volume the displacement velocity of the particles of the medium and the deformation of the medium are constant.

Volume ΔV has kinetic energy.

(2)

(ρ ΔV is the mass of this volume).

This volume also has potential energy.

Let's remember to understand.

Relative displacement, α - coefficient of proportionality.

Young's modulus E = 1/α . normal voltage T=F/S . From here.

In our case .

In our case, we have

(3)

Let's also remember.

Then . We substitute into (3).

(4)

For the total energy we get.

Divide by elementary volume ΔV and obtain the volumetric energy density of the wave.

(5)

We obtain from (1) and .

(6)

We substitute (6) into (5) and take into account that . We will receive.

From (7) it follows that the volume energy density at each moment of time at different points in space is different. At one point in space, W 0 changes according to the square sine law. And the average value of this quantity from the periodic function . Consequently, the average value of the volumetric energy density is determined by the expression.

(8)

Expression (8) is very similar to the expression for the total energy of an oscillating body . Consequently, the medium in which the wave propagates has a reserve of energy. This energy is transferred from the source of oscillations to different points of the medium.

The amount of energy carried by a wave through a certain surface per unit time is called the energy flux.

If through a given surface in time dt energy is transferred dW , then the energy flow F will be equal.

(9)

- Measured in watts.

To characterize the flow of energy at different points in space, a vector quantity is introduced, which is called energy flux density . It is numerically equal to the energy flow through a unit area located at a given point in space perpendicular to the direction of energy transfer. The direction of the energy flux density vector coincides with the direction of energy transfer.

(10)

This characteristic of the energy carried by a wave was introduced by the Russian physicist N.A. Umov (1846 - 1915) in 1874.

Consider the flow of wave energy.

Wave energy flow

wave energy

W0 is the volumetric energy density.

Then we get.

(11)

Since the wave propagates in a certain direction, it can be written.

(12)

This is energy flux density vector or the energy flow through a unit area perpendicular to the direction of wave propagation per unit time. This vector is called the Umov vector.

~ sin 2 ωt.

Then the average value of the Umov vector will be equal to.

(13)

Wave intensity – time average value of the energy flux density carried by the wave .

Obviously.

(14)

Respectively.

(15)

Sound

Sound is the vibration of an elastic medium perceived by the human ear.

The study of sound is called acoustics .

The physiological perception of sound: loud, quiet, high, low, pleasant, nasty - is a reflection of its physical characteristics. A harmonic oscillation of a certain frequency is perceived as a musical tone.

The frequency of the sound corresponds to the pitch.

The ear perceives the frequency range from 16 Hz to 20,000 Hz. At frequencies less than 16 Hz - infrasound, and at frequencies above 20 kHz - ultrasound.

Several simultaneous sound vibrations is consonance. Pleasant is consonance, unpleasant is dissonance. A large number of simultaneously sounding oscillations with different frequencies is noise.

As we already know, sound intensity is understood as the time-averaged value of the energy flux density that a sound wave carries with it. In order to cause a sound sensation, a wave must have a certain minimum intensity, which is called hearing threshold (curve 1 in the figure). The threshold of hearing is somewhat different for different people and is highly dependent on the frequency of the sound. The human ear is most sensitive to frequencies from 1 kHz to 4 kHz. In this area, the hearing threshold is on average 10 -12 W/m 2 . At other frequencies, the hearing threshold is higher.

At intensities of the order of 1 ÷ 10 W/m2, the wave ceases to be perceived as sound, causing only a sensation of pain and pressure in the ear. The intensity value at which this happens is called pain threshold (curve 2 in the figure). The threshold of pain, like the threshold of hearing, depends on the frequency.

Thus, lies almost 13 orders. Therefore, the human ear is not sensitive to small changes in sound intensity. To feel the change in volume, the intensity of the sound wave must change by at least 10 ÷ 20%. Therefore, not the sound power itself is chosen as the intensity characteristic, but the next value, which is called the sound power level (or loudness level) and is measured in bels. In honor of the American electrical engineer A.G. Bell (1847-1922), one of the inventors of the telephone.

I 0 \u003d 10 -12 W / m 2 - zero level (threshold of hearing).

Those. 1 B = 10 I 0 .

They also use a 10 times smaller unit - the decibel (dB).

Using this formula, the decrease in intensity (attenuation) of a wave over a certain path can be expressed in decibels. For example, an attenuation of 20 dB means that the intensity of the wave is reduced by a factor of 100.

The entire range of intensities at which the wave causes a sound sensation in the human ear (from 10 -12 to 10 W / m 2) corresponds to loudness values ​​from 0 to 130 dB.

The energy that sound waves carry with them is extremely small. For example, to heat a glass of water from room temperature to boiling with a sound wave with a volume level of 70 dB (in this case, about 2 10 -7 W will be absorbed per second by water), it will take about ten thousand years.

Ultrasonic waves can be received in the form of directed beams, similar to beams of light. Directed ultrasonic beams have found wide application in sonar. The idea was put forward by the French physicist P. Langevin (1872 - 1946) during the First World War (in 1916). By the way, the method of ultrasonic location allows the bat to navigate well when flying in the dark.

wave equation

In the field of wave processes, there are equations called wave , which describe all possible waves, regardless of their specific form. In terms of meaning, the wave equation is similar to the basic equation of dynamics, which describes all possible movements of a material point. The equation of any particular wave is a solution to the wave equation. Let's get it. To do this, we differentiate twice with respect to t and in all coordinates the plane wave equation .

(1)

From here we get.

(*)

Let us add equations (2).

Let's replace x in (3) from equation (*). We will receive.

We learn that and get.

, or . (4)

This is the wave equation. In this equation, the phase velocity, is the nabla operator or the Laplace operator.

Any function that satisfies equation (4) describes a certain wave, and the square root of the reciprocal of the coefficient at the second derivative of the displacement from time gives the phase velocity of the wave.

It is easy to verify that the wave equation is satisfied by the equations of plane and spherical waves, as well as by any equation of the form

For a plane wave propagating in the direction , the wave equation has the form:

.

This is a one-dimensional second-order wave equation in partial derivatives, valid for homogeneous isotropic media with negligible damping.

Electromagnetic waves

Considering Maxwell's equations, we wrote down an important conclusion that an alternating electric field generates a magnetic one, which also turns out to be variable. In turn, the alternating magnetic field generates an alternating electric field, and so on. The electromagnetic field is able to exist independently - without electric charges and currents. The change in the state of this field has a wave character. Fields of this kind are called electromagnetic waves . The existence of electromagnetic waves follows from Maxwell's equations.

Consider a homogeneous neutral () non-conductive () medium, for example, for simplicity, vacuum. For this environment, you can write:

, .

If any other homogeneous neutral non-conducting medium is considered, then it is necessary to add and to the equations written above.

Let us write Maxwell's differential equations in general form.

, , , .

For the medium under consideration, these equations have the form:

, , ,

We write these equations as follows:

, , , .

Any wave processes must be described by a wave equation that connects the second derivatives with respect to time and coordinates. From the equations written above, by simple transformations, we can obtain the following pair of equations:

,

These relations are identical wave equations for the fields and .

Recall that in the wave equation ( ) the factor in front of the second derivative on the right side is the reciprocal of the square of the phase velocity of the wave. Hence, . It turned out that in vacuum this speed for an electromagnetic wave is equal to the speed of light.

Then the wave equations for the fields and can be written as

and .

These equations indicate that electromagnetic fields can exist in the form of electromagnetic waves whose phase velocity in vacuum is equal to the speed of light.

Mathematical analysis of Maxwell's equations allows us to draw a conclusion about the structure of an electromagnetic wave propagating in a homogeneous neutral non-conductive medium in the absence of currents and free charges. In particular, we can draw a conclusion about the vector structure of the wave. The electromagnetic wave is strictly transverse wave in the sense that the vectors characterizing it and perpendicular to the wave velocity vector , i.e. to the direction of its propagation. The vectors , and , in the order in which they are written, form right-handed orthogonal triple of vectors . In nature, there are only right-handed electromagnetic waves, and there are no left-handed waves. This is one of the manifestations of the laws of mutual creation of alternating magnetic and electric fields.

waves are any perturbations of the state of matter or field, propagating in space over time.

Mechanical called waves that arise in elastic media, i.e. in media in which forces arise that prevent:

1) tensile (compression) deformations;

2) shear deformations.

In the first case, there longitudinal wave, in which the oscillations of the particles of the medium occur in the direction of propagation of the oscillations. Longitudinal waves can propagate in solid, liquid and gaseous bodies, because they are associated with the appearance of elastic forces when changing volume.

In the second case, there exists in space transverse wave, in which the particles of the medium oscillate in directions perpendicular to the direction of propagation of vibrations. Transverse waves can only propagate in solids, because associated with the emergence of elastic forces when changing forms body.

If a body oscillates in an elastic medium, then it acts on the particles of the medium adjacent to it, and makes them perform forced oscillations. The medium near the oscillating body is deformed, and elastic forces arise in it. These forces act on the particles of the medium that are more and more distant from the body, removing them from the equilibrium position. Over time, an increasing number of particles of the medium is involved in oscillatory motion.

Mechanical wave phenomena are of great importance for everyday life. For example, thanks to the sound waves caused by the elasticity of the environment, we can hear. These waves in gases or liquids are pressure fluctuations propagating in a given medium. As examples of mechanical waves, one can also cite: 1) waves on the water surface, where the connection of adjacent sections of the water surface is due not to elasticity, but to gravity and surface tension forces; 2) blast waves from shell explosions; 3) seismic waves - fluctuations in the earth's crust, propagating from the place of an earthquake.

The difference between elastic waves and any other ordered motion of the particles of the medium is that the propagation of oscillations is not associated with the transfer of the substance of the medium from one place to another over long distances.

The locus of points to which oscillations reach a certain point in time is called front waves. The wave front is the surface that separates the part of space already involved in the wave process from the area in which oscillations have not yet arisen.

The locus of points oscillating in the same phase is called wave surface. The wave surface can be drawn through any point in the space covered by the wave process. Consequently, there are an infinite number of wave surfaces, while there is only one wave front at any moment of time, it moves all the time. The shape of the front can be different depending on the shape and dimensions of the oscillation source and the properties of the medium.

In the case of a homogeneous and isotropic medium, spherical waves propagate from a point source, i.e. the wave front in this case is a sphere. If the source of oscillations is a plane, then near it any section of the wave front differs little from a part of the plane, therefore waves with such a front are called plane waves.

Let us assume that during the time some section of the wave front has moved to . Value

is called the propagation speed of the wave front or phase speed waves at this location.

A line whose tangent at each point coincides with the direction of the wave at that point, i.e. with the direction of energy transfer is called beam. In a homogeneous isotropic medium, the beam is a straight line perpendicular to the wave front.

Oscillations from the source can be either harmonic or non-harmonic. Accordingly, waves run from the source monochromatic and non-monochromatic. A non-monochromatic wave (containing oscillations of different frequencies) can be decomposed into monochromatic waves (each of which contains oscillations of the same frequency). A monochromatic (sinusoidal) wave is an abstraction: such a wave must be infinitely extended in space and time.

Consider the experiment shown in Figure 69. A long spring is suspended on threads. They strike with a hand on its left end (Fig. 69, a). From the impact, several coils of the spring come together, an elastic force arises, under the influence of which these coils begin to diverge. As the pendulum passes the equilibrium position in its movement, so the coils, bypassing the equilibrium position, will continue to diverge. As a result, some rarefaction is already formed in the same place of the spring (Fig. 69, b). With a rhythmic impact, the coils at the end of the spring will periodically either approach or move away from each other, oscillating near their equilibrium position. These vibrations will gradually be transmitted from coil to coil along the entire spring. Condensations and rarefaction of the coils will spread along the spring, as shown in Figure 69, f.

Rice. 69. The appearance of a wave in a spring

In other words, a perturbation propagates along the spring from its left end to the right end, i.e., a change in some physical quantities characterizing the state of the medium. In this case, this perturbation is a change over time in the elastic force in the spring, acceleration and speed of the oscillating coils, their displacement from the equilibrium position.

• Perturbations propagating in space, moving away from their place of origin, are called waves.

In this definition, we are talking about the so-called traveling waves. The main property of traveling waves of any nature is that they, propagating in space, carry energy.

For example, the oscillating coils of a spring have energy. Interacting with neighboring coils, they transfer part of their energy to them and a mechanical disturbance (deformation) propagates along the spring, i.e., a traveling wave is formed.

But at the same time, each coil of the spring oscillates around its equilibrium position, and the entire spring remains in its original place.

Thus, in a traveling wave, energy is transferred without transfer of matter.

In this topic, we will consider only elastic traveling waves, a special case of which is sound.

• Elastic waves are mechanical disturbances propagating in an elastic medium

In other words, the formation of elastic waves in a medium is due to the appearance in it of elastic forces caused by deformation. For example, if you hit a metal body with a hammer, then an elastic wave will appear in it.

In addition to elastic, there are other types of waves, such as electromagnetic waves (see § 44). Wave processes occur in almost all areas of physical phenomena, so their study is of great importance.

When waves appeared in the spring, its coils oscillated along the direction of wave propagation in it (see Fig. 69).

• Waves in which vibrations occur along the direction of their propagation are called longitudinal waves.

In addition to longitudinal waves, there are also transverse waves. Let's consider this experience. Figure 70, a shows a long rubber cord, one end of which is fixed. The other end is brought into oscillatory motion in a vertical plane (perpendicular to a horizontal cord). Due to the elastic forces arising in the cord, the vibrations will propagate along the cord. Waves arise in it (Fig. 70, b), and the fluctuations of the cord particles occur perpendicular to the direction of wave propagation.

Rice. 70. The emergence of waves in the cord

• Waves in which oscillations occur perpendicular to the direction of their propagation are called transverse waves.

The movement of particles of a medium in which both transverse and longitudinal waves are formed can be clearly demonstrated using a wave machine (Fig. 71). Figure 71, a shows a transverse wave, and Figure 71, b shows a longitudinal wave. Both waves propagate in the horizontal direction.

Rice. 71. Transverse (a) and longitudinal (b) waves

The wave machine has only one row of balls. But, by observing their movement, one can understand how waves propagate in continuous media extended in all three directions (for example, in a certain volume of solid, liquid or gaseous matter).

To do this, imagine that each ball is part of a vertical layer of matter located perpendicular to the plane of the picture. Figure 71, a shows that when a transverse wave propagates, these layers, like balls, will move relative to each other, oscillating in the vertical direction. Therefore, transverse mechanical waves are shear waves.

And longitudinal waves, as can be seen from Figure 71, b, are compression and rarefaction waves. In this case, the deformation of the layers of the medium consists in changing their density, so that the longitudinal waves are alternating compressions and rarefaction.

It is known that elastic forces during the shear of layers arise only in solids. In liquids and gases, adjacent layers freely slide over each other without the appearance of opposing elastic forces. Since there are no elastic forces, then the formation of elastic waves in liquids and gases is impossible. Therefore, transverse waves can propagate only in solids.

During compression and rarefaction (i.e., when the volume of parts of the body changes), elastic forces arise both in solids and in liquids and gases. Therefore, longitudinal waves can propagate in any medium - solid, liquid and gaseous.

Questions

1. What is called waves?
2. What is the main property of traveling waves of any nature? Does the transfer of matter take place in a traveling wave?
3. What are elastic waves?
4. Give an example of waves that are not elastic.
5. What waves are called longitudinal; transverse? Give examples.
6. Which waves - transverse or longitudinal - are shear waves; waves of compression and rarefaction?
7. Why do transverse waves not propagate in liquid and gaseous media?

To understand how vibrations propagate in a medium, let's start from afar. Have you ever rested on the seashore, watching the waves methodically running on the sand? A wonderful sight, isn't it? But in this spectacle, in addition to pleasure, you can find some benefit, if you think and reason a little. We also reason in order to benefit our mind.

What are waves?

It is generally accepted that waves are the movement of water. They arise due to the wind blowing over the sea. But it turns out that if the waves are the movement of water, then the wind blowing in one direction should, in some time, simply overtake most of the sea water from one end of the sea to the other. And then somewhere, say, off the coast of Turkey, the water would have gone several kilometers from the coast, and there would have been a flood in the Crimea.

And if two different winds blow over the same sea, then somewhere they could organize a huge hole right in the water. However, this does not happen. There are, of course, flooding of coastal areas during hurricanes, but the sea simply brings its waves to the shore, the farther they are, the higher they are, but it does not move itself.

Otherwise, the seas could travel all over the planet along with the winds. Therefore, it turns out that the water does not move with the waves, but remains in place. What then are waves? What is their nature?

Is the propagation of vibrations what waves are?

Oscillations and waves are held in the 9th grade in the course of physics in one topic. It is logical to assume then that these are two phenomena of the same nature, that they are connected. And this is absolutely true. The propagation of vibrations in a medium is what waves are.

It is very easy to see this clearly. Tie one end of the rope to something immovable, and pull the other end and then shake it slightly.

You will see how waves run from the rope by hand. At the same time, the rope itself does not move away from you, it oscillates. Vibrations from the source propagate along it, and the energy of these vibrations is transmitted.

That is why the waves throw objects ashore and fall with force; they themselves transfer energy. However, the substance itself does not move. The sea remains in its rightful place.

Longitudinal and transverse waves

There are longitudinal and transverse waves. Waves in which oscillations occur along the direction of their propagation are called longitudinal. BUT transverse Waves are waves propagating perpendicular to the direction of vibration.

What do you think, what kind of waves did the rope or sea waves have? Shear waves were in our rope example. Our oscillations were directed up and down, and the wave propagated along the rope, that is, perpendicularly.

To get longitudinal waves in our example, we need to replace the rope with a rubber cord. Pulling the cord motionless, you need to stretch it with your fingers in a certain place and release it. The stretched segment of the cord will contract, but the energy of this stretching-contraction will be transmitted further along the cord in the form of oscillations for some time.

We present to your attention a video lesson on the topic “Propagation of vibrations in an elastic medium. Longitudinal and transverse waves. In this lesson, we will study issues related to the propagation of oscillations in an elastic medium. You will learn what a wave is, how it appears, how it is characterized. Let us study the properties and differences between longitudinal and transverse waves.

We turn to the study of issues related to waves. Let's talk about what a wave is, how it appears and what it is characterized by. It turns out that in addition to just an oscillatory process in a narrow region of space, it is also possible to propagate these oscillations in a medium, and it is precisely such propagation that is wave motion.

Let's move on to a discussion of this distribution. To discuss the possibility of the existence of oscillations in a medium, we must define what a dense medium is. A dense medium is a medium that consists of a large number of particles whose interaction is very close to elastic. Imagine the following thought experiment.

Rice. 1. Thought experiment

Let us place a sphere in an elastic medium. The ball will shrink, decrease in size, and then expand like a heartbeat. What will be observed in this case? In this case, the particles that are adjacent to this ball will repeat its movement, i.e. move away, approach - thereby they will oscillate. Since these particles interact with other particles more distant from the ball, they will also oscillate, but with some delay. Particles that are close to this ball, oscillate. They will be transmitted to other particles, more distant. Thus, the oscillation will propagate in all directions. Note that in this case, the oscillation state will propagate. This propagation of the state of oscillations is what we call a wave. It can be said that the process of propagation of vibrations in an elastic medium over time is called a mechanical wave.

Please note: when we talk about the process of occurrence of such oscillations, we must say that they are possible only if there is an interaction between particles. In other words, a wave can only exist when there is an external perturbing force and forces that oppose the action of the perturbing force. In this case, these are elastic forces. The propagation process in this case will be related to the density and strength of interaction between the particles of this medium.

Let's note one more thing. The wave does not carry matter. After all, particles oscillate near the equilibrium position. But at the same time, the wave carries energy. This fact can be illustrated by tsunami waves. Matter is not carried by the wave, but the wave carries such energy that brings great disasters.

Let's talk about the types of waves. There are two types - longitudinal and transverse waves. What longitudinal waves? These waves can exist in all media. And the example with a pulsating ball inside a dense medium is just an example of the formation of a longitudinal wave. Such a wave is a propagation in space over time. This alternation of compaction and rarefaction is a longitudinal wave. I repeat once again that such a wave can exist in all media - liquid, solid, gaseous. A longitudinal wave is a wave, during the propagation of which the particles of the medium oscillate along the direction of wave propagation.

Rice. 2. Longitudinal wave

As for the transverse wave, transverse wave can exist only in solids and on the surface of a liquid. A wave is called a transverse wave, during the propagation of which the particles of the medium oscillate perpendicular to the direction of wave propagation.

Rice. 3. Shear wave

The propagation speed of longitudinal and transverse waves is different, but this is the topic of the next lessons.

List of additional literature:

Are you familiar with the concept of a wave? // Quantum. - 1985. - No. 6. - S. 32-33. Physics: Mechanics. Grade 10: Proc. for in-depth study of physics / M.M. Balashov, A.I. Gomonova, A.B. Dolitsky and others; Ed. G.Ya. Myakishev. - M.: Bustard, 2002. Elementary textbook of physics. Ed. G.S. Landsberg. T. 3. - M., 1974.