Propagation of vibrations in an elastic medium. Longitudinal and transverse waves. A. Propagation of vibrations

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 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. A transverse Waves are waves propagating perpendicular to the direction of vibration.

What do you think the waves were on the rope or sea ​​waves? 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.

§ 1 Propagation of oscillations in a medium. Longitudinal and transverse waves

Let us consider how oscillations propagate in various media. Often you could observe how circles diverge from a float or a stone thrown into the water. Oscillations that create a deformation of the medium in space can become a source, for example, of earthquake waves, sea waves or sound. If we consider sound, then vibrations produce both a sound source (string or tuning fork) and a sound receiver, for example, a microphone membrane. The medium through which the wave passes also oscillates.

The process of propagation of oscillations in space over time is called a wave. Waves are disturbances that propagate in space, moving away from their place of origin.

It should be noted that the propagation of mechanical waves is possible only in gas, liquid and solid media. A mechanical wave cannot arise in a vacuum.

Solid, liquid, gaseous media consist of individual particles interacting with each other by bond forces. Excitation of oscillations of particles of a given medium in one place causes forced oscillations of neighboring particles, which, in turn, excite oscillations of the next, and so on.

There are longitudinal and transverse waves.

A wave is called longitudinal if the particles of the medium oscillate in the direction of wave propagation.

A longitudinal wave can be seen in the example of a soft long spring: by compressing and releasing one of its ends (the other end is fixed), we will cause a successive movement of condensation and rarefaction of its coils.

In other words, we observe how a perturbation goes from one end of it to the other, caused by a change in the elastic force, speed of movement or acceleration of the coils of the spring, displacement of the coils from the equilibrium line. In this example, we see a traveling wave.

A traveling wave is a wave that, when moving in space, transfers energy without transferring matter.

a) initial state; b) spring compression; c) transmission of vibrations from one coil to another (condensation and rarefaction of the coils).

In mechanics, the so-called elastic waves are studied.

A medium whose particles are interconnected in such a way that a change in the position of one of them leads to a change in the position of other particles is called elastic.

A wave is called transverse if the particles of the medium oscillate in a direction perpendicular to the direction of wave propagation.

If a rubber cord is stretched horizontally, one end is rigidly fixed, and the other is brought into vertical oscillatory motion, then we can observe a transverse wave.

For the experiment, we will model chains of springs and balls, and on this model we will analyze the movement of longitudinal and transverse waves.

In the case of a longitudinal wave (a), the balls are displaced along, and the springs are either stretched or compressed, that is, compression or tension deformation occurs. It must be remembered that in a liquid and gaseous medium, such deformation is accompanied by compaction of the medium or its rarefaction.

If the ball is displaced perpendicular to the chain (b), then the so-called shear deformation will occur. In this case, we will see the movement of a transverse wave. It should be remembered that in a liquid and gaseous medium, shear deformation is impossible.

Therefore, the following definition holds.

Longitudinal mechanical waves can propagate in any media: liquid, gaseous and solid. Transverse waves can only exist in solid media.

§ 2 Brief summary of the topic of the lesson

The propagation of mechanical waves is possible only in gas, liquid and solid media. A mechanical wave cannot in any way arise in a vacuum.

There are longitudinal and transverse waves. Longitudinal mechanical waves can propagate in any media: liquid, gaseous and solid. Transverse waves can only exist in solid media.

List of used literature:

1. Physics. Big encyclopedic Dictionary/ Ch. ed. A. M. Prokhorov. - 4th ed. - M.: Great Russian Encyclopedia, 1999. - S. 293-295.
2. Irodov I. E. Mechanics. Basic laws / I.E. Irodov. - 5th ed., Rev.-M .: Basic Knowledge Laboratory, 2000, pp. 205-223.
3. Irodov I.E. Mechanics of oscillatory systems / I.E. Irodov. - 3rd ed., Rev. - M .: Basic Knowledge Laboratory, 2000, pp. 311-320.
4. Peryshkin A.V. Physics. Grade 9: textbook / A.V. Peryshkin, E.M. Gutnik. – M.: Bustard, 2014. – 319p. Collection of test tasks in physics, Grade 9. / E.A. Maron, A.E. Maron. Publishing house "Enlightenment", Moscow, 2007.

Used images:

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 spread in solid, liquid and gaseous bodies, tk. 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 particles of the medium that are more and more distant from the body, taking them out of equilibrium. 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, due to sound waves due to elasticity 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.

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Lecture No. 9

mechanical waves

6.1. Propagation of vibrations in an elastic medium.

6.2. Plane wave equation.

6.3. wave equation.

6.4. Wave propagation speed in various media.

Mechanical oscillations propagating in an elastic medium (solid, liquid or gaseous) are called mechanical or elastic waves.

The process of propagation of oscillations in a continuous medium is commonly called a wave process or a wave. The particles of the medium in which the wave propagates are not involved by the wave in translational motion. they only oscillate around their equilibrium positions. Together with the wave, only the state of oscillatory motion and its energy are transmitted from particle to particle of the medium. For this reason the main property of all waves, regardless of their nature, is the transfer of energy without the transfer of matter.

Considering the dependence on the direction of particle oscillations with respect to the direction in which the wave propagates, we distinguish longitudinal and transverse waves.

longitudinal, if the oscillations of the particles of the medium occur in the direction of wave propagation. Longitudinal waves are associated with volumetric tensile-compression deformation of the medium; therefore, they can propagate both in solids and in liquids and gaseous media.

An elastic wave is called transverse, if the oscillations of the particles of the medium occur in planes perpendicular to the direction of propagation of the wave. Transverse waves can occur only in a medium that has the elasticity of the form, i.e., is able to resist shear deformation. Only solid bodies have this property.

On fig. 6.1.1 shows a harmonic shear wave propagating along the 0 axis X. The wave graph gives the dependence of the displacement of all particles of the medium on the distance to the source of vibrations at a given time. The distance between the nearest particles oscillating in the same phase is called wavelength. The wavelength is also equal to that distance, a certain phase of the oscillation spreads over the ĸᴏᴛᴏᴩᴏᴇ during the oscillation period

Not only particles located along the 0 axis oscillate X, but a set of particles enclosed in a certain volume. The locus of points to which oscillations reach by the moment of time t, commonly called wave front. 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. Wave surfaces come in all shapes. In the simplest cases, they have the shape of a plane or sphere. Accordingly, the wave in these cases is called flat or spherical. In a plane wave, the wave surfaces are a set of planes parallel to each other, and in a spherical wave, they are a set of concentric spheres.