Let the oscillating body be in a medium in which all the particles are interconnected. The particles of the medium in contact with it will begin to vibrate, as a result of which periodic deformations (for example, compression and tension) occur in the areas of the medium adjacent to this body. During deformations, elastic forces appear in the medium, which tend to return the particles of the medium to their original state of equilibrium.

Thus, periodic deformations that appear in some place in an elastic medium will propagate at a certain speed, depending on the properties of the medium. In this case, the particles of the medium are not drawn into translational motion by the wave, but perform oscillatory movements around their equilibrium positions; only elastic deformation is transferred from one part of the medium to another.

The process of propagation of oscillatory motion in a medium is called wave process or simply wave. Sometimes this wave is called elastic, because it is caused by the elastic properties of the medium.

Depending on the direction of particle oscillations relative to the direction of wave propagation, longitudinal and transverse waves are distinguished.Interactive demonstration of transverse and longitudinal waves

Longitudinal wave – This is a wave in which particles of the medium oscillate along the direction of propagation of the wave.

A longitudinal wave can be observed on a long soft spring large diameter. By hitting one of the ends of the spring, you can notice how successive condensations and rarefactions of its turns will spread throughout the spring, running one after another. In the figure, the dots show the position of the spring coils at rest, and then the positions of the spring coils at successive time intervals equal to a quarter of the period.

Thus, aboutthe longitudinal wave in the case under consideration represents alternating condensations (Сг) and rarefaction (Once) spring coils.
Demonstration of longitudinal wave propagation

Transverse wave - This is a wave in which the particles of the medium oscillate in directions perpendicular to the direction of propagation of the wave.

Let us consider in more detail the process of formation of transverse waves. Let us take as a model of a real cord a chain of balls (material points) connected to each other by elastic forces. The figure depicts the process of propagation of a transverse wave and shows the positions of the balls at successive time intervals equal to a quarter of the period.

At the initial moment of time (t 0 = 0) all points are in a state of equilibrium. Then we cause a disturbance by deviating point 1 from the equilibrium position by an amount A and the 1st point begins to oscillate, the 2nd point, elastically connected to the 1st, comes into oscillatory motion a little later, the 3rd even later, etc. . After a quarter of the oscillation period ( t 2 = T 4 ) will spread to the 4th point, the 1st point will have time to deviate from its equilibrium position by a maximum distance equal to the oscillation amplitude A. After half a period, the 1st point, moving down, will return to the equilibrium position, the 4th deviated from the equilibrium position by a distance equal to the amplitude of oscillations A, the wave has propagated to the 7th point, etc.

By the time t 5 = T The 1st point, having completed a complete oscillation, passes through the equilibrium position, and the oscillatory movement will spread to the 13th point. All points from the 1st to the 13th are located so that they form a complete wave consisting of depressions And ridge

Demonstration of shear wave propagation

The type of wave depends on the type of deformation of the medium. Longitudinal waves are caused by compression-tension deformation, transverse waves are caused by shear deformation. Therefore, in gases and liquids, in which elastic forces arise only during compression, the propagation of transverse waves is impossible. In solids, elastic forces arise both during compression (tension) and shear, therefore, both longitudinal and transverse waves can propagate in them.

As the figures show, in both transverse and longitudinal waves, each point of the medium oscillates around its equilibrium position and shifts from it by no more than an amplitude, and the state of deformation of the medium is transferred from one point of the medium to another. Important difference elastic waves in a medium from any other ordered movement of its particles is that the propagation of waves is not associated with the transfer of matter in the medium.

Consequently, when waves propagate, the energy of elastic deformation and momentum are transferred without transfer of matter. Wave energy in elastic medium consists of the kinetic energy of oscillating particles and the potential energy of elastic deformation of the medium.

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 vibrations in an elastic medium. You will learn what a wave is, how it appears, and how it is characterized. Let's study the properties and differences between longitudinal and transverse waves.

We move on to studying issues related to waves. Let's talk about what a wave is, how it appears and how it is characterized. It turns out that, in addition to simply an oscillatory process in a narrow region of space, it is also possible for these oscillations to propagate in a medium; it is precisely this propagation that is wave motion.

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

Rice. 1. Thought experiment

Let us place a ball 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. moving away, approaching - 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 come close to this ball vibrate. They will be transmitted to other particles, more distant. Thus, the vibration will spread in all directions. Please note in in this case the oscillation state will propagate. We call this propagation of a state of oscillation 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 interaction between particles. In other words, a wave can only exist when there is an external disturbing force and forces that resist the action of the disturbance force. In this case, these are elastic forces. The process of propagation in this case will be related to the density and strength of interaction between the particles of a given medium.

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

Let's talk about wave types. There are two types - longitudinal and transverse waves. What's happened 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 wave is called longitudinal, when propagating the particles of the medium oscillate along the direction of propagation of the wave.

Rice. 2. Longitudinal wave

As for the transverse wave, then transverse wave can exist only in solids and on the surface of liquids. A transverse wave is a wave whose propagation causes particles of the medium to oscillate perpendicular to the direction of propagation of the wave.

Rice. 3. Transverse wave

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

List of additional literature:

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

Lesson objectives:

educational:

• formation of the concept of “mechanical wave”;
• consideration of the conditions for the occurrence of two types of waves;
• wave characteristics;

developing:

• developing the ability to apply knowledge in specific situations;

educational:

• fostering cognitive interest;
• positive motivation for learning;
• accuracy when performing tasks.

Lesson type: lesson in the formation of new knowledge.

Equipment:

for demonstrations: rubber cord, glass of water, pipette, Wave Machine layout, computer, multimedia projector, Waves presentation.

Lesson progress

1. Organizational moment.

Announcing the topic and objectives of the lesson.

2. Updating basic knowledge

Test

Option #1

. Swing movement.

B. The movement of a ball falling to the Earth,

2. Which of the following vibrations are free?

B. Vibrations of the loudspeaker cone during operation of the loudspeaker.

3. The frequency of body oscillations is 2000 Hz. What is the period of oscillation?

4. The equation x=0.4 cos 5nt is given. Determine the amplitude and period of oscillation.

5. A load suspended on a thread makes small vibrations. Assuming the oscillations are undamped, indicate the correct answers.

. The longer the thread, the higher the oscillation frequency.

B. When the load passes the equilibrium position, the speed of the load is maximum.

B. The load undergoes periodic motion.

Option No. 2

1. Which of the following movements are mechanical vibrations?

. Movement of tree branches.

B. Movement of raindrops to the ground.

B. The movement of the sounding string of a guitar.

2. Which of the following oscillations are forced?

. Oscillations of a load on a spring after a single deviation from its equilibrium position.

B. Movement of the piston in the cylinder of an internal combustion engine.

B. Oscillations of a load on a string, once removed from the equilibrium position and released.

3. The period of body oscillation is 0.01 s. What is the oscillation frequency?

4. The body commits harmonic oscillation according to the law =20 sin nt. Determine the amplitude and period of oscillations.

5. A load suspended on a spring makes small vibrations in the vertical direction. Assuming the oscillations are undamped, indicate the correct answers.

. The greater the spring stiffness, the longer the oscillation period.

B. The period of oscillation depends on the amplitude.

B. The speed of the load changes periodically over time.

3. Formation of new knowledge.

The basic physical model of matter is a set of moving and interacting atoms and molecules. The use of this model makes it possible to explain, using molecular kinetic theory, the properties of various states of matter and the physical mechanism of energy and momentum transfer in these media. In this case, by medium we can understand gas, liquid, solid.

Let us consider a method of energy transfer without matter transfer as a result of sequential transfer of energy and momentum along a chain between neighboring particles of the medium interacting with each other.

Wave process is a process of energy transfer without matter transfer.

Demonstration of experience:

Let's attach a rubber cord to the ceiling and, with a sharp movement of the hand, make its free end vibrate. As a result of external influence on the medium, a disturbance arises in it - a deviation of the particles of the medium from the equilibrium position;

Follow the propagation of waves on the surface of the water in a glass, creating them with drops of water falling from the pipette.

A mechanical wave is a disturbance propagating in an elastic medium from point to point (gas, liquid, solid).

Introducing the mechanism of wave formation using the “Wave Machine” model. In this case, take into account the oscillatory motion of particles and the propagation of oscillatory motion.

There are longitudinal and transverse waves.

Longitudinal – waves in which particles of the medium oscillate along the direction of propagation of the wave. (Gases, liquids, solids). It is observed when a nail is driven in with a hammer, a longitudinal impulse sweeps along the nail, driving it deeper.

Transverse - waves in which particles vibrate perpendicular to the direction of propagation of the wave (solids). Observed in a rope, one end of which begins to oscillate.

A traveling wave, the main property of which is the transfer of energy without the transfer of matter: electromagnetic radiation from the Sun heats the Earth, ocean waves erode the shores.

Characteristics of the wave.

Wavelength is the distance traveled by a wave during one period of oscillation of its particles. At a distance of a wavelength there are adjacent crests or troughs in a transverse wave or thickenings or rarefaction in a longitudinal wave.

λ - wavelength.

Wave speed - the speed of movement of crests and troughs in a transverse wave and condensations and rarefaction in a longitudinal one.

v – wave speed

Introduction to formulas for determining wavelength:

λ = v / v

v – frequency

T – period

Formation of skills and abilities.

Problem solving.

1. A boy carries buckets of water on a rocker, the period of free oscillations of which is 1.6 s. At what speed does the boy move when the water begins to splash out especially strongly if his step length is 65 cm?

2. A wave propagates along the surface of the water in a lake at a speed of 8 m/s. What are the period and frequency of oscillation of the buoy if the wavelength is 3 m?

3. The wavelength in the oceans can reach 400 m, and the period is 14.5 s. Determine the speed of propagation of such a wave.

Lesson summary.

1. What is a wave?

2. What is the process of wave generation?

3. What waves do we perceive while in the classroom?

4. Does the transfer of matter in the medium occur during the formation of waves?

5. List the characteristics of waves.

6. How are speed, wavelength and frequency related?

Homework:

P.31-33 (textbook Physics-9)

No. 439.438 (Rymkevich A.P.)

In waves are any disturbances in the state of matter or a field that propagate in space over time.

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

1) tensile (compressive) deformation;

2) shear deformation.

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

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

If some body oscillates in an elastic medium, then it affects the particles of the medium adjacent to it and causes them to 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 increasingly distant from the body, removing them from the equilibrium position. Over time, an increasing number of particles of the medium become involved in oscillatory motion.

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

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

The geometric location of the points to which the oscillations reach at 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 region in which oscillations have not yet arisen.

The geometric location of points oscillating in the same phase is called wave surface. The wave surface can be drawn through any point in space covered by the wave process. Consequently, there is an infinite number of wave surfaces, while there is only one wave front at each moment of time, it moves all the time. The shape of the front can be different depending on the shape and size of the source of oscillations 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 part of the wave front differs little from part of the plane, therefore waves with such a front are called plane.

Let us assume that during time some part of the wave front has moved by . Magnitude

is called the speed of propagation of the wave front or phase velocity waves in this place.

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

Oscillations from a source can be both harmonic and 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 ones (each of which contains oscillations of the same frequency). A monochromatic (sine) wave is an abstraction: such a wave must be infinitely extended in space and time.