Propagation of vibrations in a medium. Waves. Longitudinal and transverse waves. Formation and propagation of waves in an elastic medium

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The process of propagation of vibrations in an elastic medium is called sound.

The process of propagation of oscillations in space is called a wave. The boundary separating oscillating particles from particles that have not yet begun to oscillate is called the water front. The propagation of a wave in a medium is characterized by a speed called the speed of an ultrasonic wave. The distance between the nearest particles oscillating in the same way (in the same phase) is called the wavelength. The number of waves passing through a given point in 1 second is called the frequency of the ultrasound.

The process of propagation of oscillations in an elastic medium is called wave motion, or an elastic wave.

The process of propagation of oscillations in space over time is called a wave. Waves propagating due to the elastic properties of the medium are called elastic. Elastic waves are transverse and longitudinal.

The process of vibration propagation in an elastic medium is called a wave. If the direction of oscillation coincides with the direction of wave propagation, then such a wave is called a longitudinal wave, for example, a sound wave in air. If the direction of oscillation is perpendicular to the direction of wave propagation, then such a wave is called transverse.

The process of propagation of oscillations in space is called the wave process.

The process of propagation of oscillations in space is called a wave.

The process of propagation of particle oscillations in an elastic medium is called a wave process or simply a wave.

The processes of propagation of fluctuations of liquid or gas particles in a pipe are complicated by the influence of its walls. Oblique reflections along the pipe walls create conditions for the formation of radial oscillations. Having set the task of studying axial vibrations of liquid or gas particles in narrow pipes, we must take into account a number of conditions under which radial vibrations can be neglected.

A wave is the process of propagation of oscillations in a medium. Each particle of the medium oscillates around the equilibrium position.

A wave is the process of propagation of vibrations.

The process of propagation of oscillations in an elastic medium considered by us is an example of wave motions, or, as they usually say, waves. So, for example, it turns out that electromagnetic waves (see § 3.1) can propagate not only in matter, but also in vacuum. The so-called gravitational waves (gravity waves) have the same property, with the help of which perturbations of the gravitational fields of bodies are transmitted, due to a change in the masses of these bodies or their positions in space. Therefore, in physics, waves are any perturbations of the state of matter or field propagating in space. So, for example, sound waves in gases or liquids are pressure fluctuations propagating in these media, and electromagnetic waves are fluctuations in the strengths E and H of the electromagnetic field propagating in space.

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.

In this way, 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

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

Let the oscillating body be in a medium, all particles of which are interconnected. The particles of the medium in contact with it will begin to oscillate, 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 have appeared in some place of the 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 involved by the wave in translational motion, but perform oscillatory motions around their equilibrium positions, only elastic deformation is transmitted from one part of the medium to another.

The process of propagation of oscillatory motion in a medium is called wave process or just 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 in relation to the direction of wave propagation, longitudinal and transverse waves are distinguished.Interactive demonstration of transverse and longitudinal waves

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

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

Thus, aboutLongitudinal wave in the case under consideration is an alternating cluster (Sg) and rarefaction (Once) spring coils.
Longitudinal Wave Propagation Demonstration

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

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 shows 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 (t0 = 0) all points are in equilibrium. Then we cause a perturbation by deviating point 1 from the equilibrium position by the value 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 period of oscillation ( t 2 = T 4 ) spread to the 4th point, the 1st point will have time to deviate from its equilibrium position by a maximum distance equal to the amplitude of oscillations 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 propagated to the 7th point, etc.

By the time t5 = T The 1st point, having made 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 hollows And comb.

Demonstration of shear wave propagation

The type of wave depends on the type of deformation of the medium. Longitudinal waves are due to compressive - tensile deformation, transverse waves - to 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, the propagation of both longitudinal and transverse waves is possible 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. An important difference between elastic waves in a medium and any other ordered motion of its particles is that the propagation of waves is not associated with the transfer of matter in the medium.

Consequently, during the propagation of waves, the energy of elastic deformation and momentum are transferred without the transfer of matter. The energy of a wave in an elastic medium consists of the kinetic energy of the oscillating particles and the potential energy of the elastic deformation of the medium.

Topic: Propagation of oscillations in a medium. Waves.
Physics. Grade 9
Purpose: To acquaint students with wave motion, consider its features, mechanism
wave propagation.
Tasks:

educational: deepening knowledge about the types of oscillatory motion, using the connection of physics
with literature, history, mathematics; formation of concepts wave motion,
mechanical wave, type of waves, their propagation in an elastic medium;
developing: development of skills to compare, systematize, analyze, draw conclusions;
educational: education of communication.

Didactic type of lesson: Learning new material.
Equipment: Laptop, multimedia projector, video clip - waves on a spring, presentation
PowerPoint

To the lesson.
During the classes:
I. Testing knowledge and skills.
1. Answer questions.
 Read the sentences carefully. Determine if free vibrations are possible:
float on the surface of the water; bodies on a channel dug through the globe; birds on a branch;
ball on a flat surface; a ball in a spherical hole; human hands and feet; athlete on
trampoline; needles in a sewing machine.
 Which car, loaded or unloaded, will make more frequent
fluctuations?
 There are two types of clocks. Some are based on fluctuations of the load on the rod, others are based on the load on
spring. How can the frequency of each watch be adjusted?
 The Tacoma Narrous Bridge in America swayed and collapsed with occasional gusts of wind.
Explain why?
2. Problem solving.
The teacher offers to perform a competence-oriented task, structure and content
which is presented below.
Stimulus: Assess existing knowledge on the topic "Mechanical vibrations".
Task formulation: Within 5 minutes, using the given text, determine the frequency and
period of contraction of the human heart. Write down the data that you will not be able to use in the decision
tasks.
The total length of blood capillaries in the human body is about 100 thousand km, which is 2.5 times
exceeds the length of the equator, and the total internal area is 2400 m2. The blood capillaries have
10 times thinner than hair. Within a minute, the heart ejects about 4 liters into the aorta.
blood, which then moves to all points of the body. The heart beats 100,000 beats on average.
once a day. For 70 years of human life, the heart contracts 2 billion 600 million times and
pumps 250 million times.
Form for the task:
1. Data necessary to determine the period and frequency of heart contraction:
but) ___________; b) _________
Formula for calculation: ______________
Calculations _______________
=________; T=_____________
ν
2. Extra data
but) ___________
b) ___________

in) ___________
G) ___________
Model response:
Data necessary to determine the period and frequency of heart contraction:
a) Number of contractions N=100000; b) Contraction time t=1 day.
ν
c1; T=1/1.16=0.864 s
Formula for calculation: =ν N/t; T=1/ν
Calculations =100000/(24*3600)=1.16
=1,16
c1; T=0.864 s.
ν
Or a) Number of contractions N=2600000000; b) Time of contractions t=70 years. But this data
lead to more complex calculations, and therefore are irrational.
redundant data
a) The total length of blood vessels is 100 thousand km
b) total internal area - 2400 m2
c) Within a minute, the heart ejects about 4 liters of blood into the blood.
d) The thickness of the blood vessels is 10 times less than the thickness of the hair.
Model response field
Selected data to determine the frequency and period of contraction of the heart.
Formulas for calculation are given.
The calculations are done and the correct answer is given.
Redundant information has been removed from the text.
Tool
estimates
response
1
1
1
1
II.
Explanation of new material.
All particles of the medium are interconnected by the forces of mutual attraction and repulsion, i.e.
interact with each other. Therefore, if at least one particle is removed from the equilibrium position
(make it oscillate), then it will pull a nearby particle along with it (thanks to
interaction between particles, this movement begins to spread in all directions). So
Thus, vibrations will be transmitted from one particle to another. Such movement is called wave.
A mechanical wave (wave motion) is the propagation of oscillations in an elastic
environment.
Oscillations propagating in space with time are called waves.
or
In this definition, we are talking about the so-called traveling waves.
The main general property of traveling waves of any nature is that, propagating in
space, transfer energy, but without the transfer of matter.
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 the 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 of elastic forces in it,
caused by deformation.

In addition to elastic waves, there are other types of waves, for example, waves on the surface of a liquid,
electromagnetic waves.
Wave processes are found in almost all areas of physical phenomena, so their study
is of great importance.
There are two types of wave motion: transverse and longitudinal.
Transverse wave - particles oscillate (move) perpendicular to (across) the velocity
wave propagation.
Examples: a wave from a thrown stone ...
Longitudinal wave - particles oscillate (move) parallel to the propagation velocity
waves.
Examples: sound waves, tsunamis…
mechanical waves
Cord Spring
transverse
longitudinal
transverse waves.
longitudinal waves.
Elastic shear deformation occurs.
body volume
does not change.
Elastic forces tend to return the body to
initial position. These forces cause
environmental fluctuations.
The shift of the layers relative to each other in
liquid and gas does not lead to the appearance
elastic forces, therefore
only in solids.
Occur during compressive deformation.
Elastic forces arise in solid
bodies, liquids and gases. These forces
cause fluctuations in individual sections
environment, therefore, are distributed in all
environments.
In solids, the propagation velocity
more.
III.
Fixing:
1. Interesting tasks.
a) In 1883. During the infamous eruption of the Indonesian volcano Krakatoa, aerial
waves generated by underground explosions circumnavigated the globe three times.
What type of wave is a shock wave? (To longitudinal waves).
b) Tsunami is a formidable companion of earthquakes. This name was born in Japan and means
giant wave. When it rolls ashore, it seems that this is not a wave at all, but
the sea, furious, indomitable, rushes ashore. It is not surprising that the tsunami
produce havoc on it. During the earthquake of 1960, they rushed to the coast of Chile

waves up to six meters high. The sea receded and advanced several times during the second
half a day.
What type of waves are tsunamis? What is the amplitude of the 1960 tsunami that hit the
Chile? (Tsunamis refer to
wave is 3 m).
(tsunami illustration:
longitudinal waves. Amplitude
http://ru.wikipedia.org/wiki/Image:2004_Indian_Ocean_earthquake_Maldives_tsunami_wave.jpg
c) Rifts are signs of small wave ripples. They have existed on earth since the advent of free-flowing
environments - snow and sand. Their imprints are found in ancient geological strata (sometimes together with
dinosaur tracks). The first scientific observations on riffles were made by Leonardo da Vinci. IN
in deserts, the distance between adjacent crests of wave ripples is measured from 112 cm (usually 38 cm)
with an average depth of depressions between the ridges of 0.31 cm.
Assuming that the corrugations are a wave, determine the amplitude of the wave (0.150.5 cm).
Rifle illustration:
http://rusnauka.narod.ru/lib/phisic/destroy/gl7/image246.gif
2. Physical experience. Individual work.
The teacher invites students to complete a competence-oriented task, structure and
the content of which is presented below
Stimulus: evaluate the acquired knowledge on the topic "Wave motion".
Task formulation: using the given devices and the knowledge gained in the lesson,
define:
what waves are formed on the surface of the wave;
what is the shape of the wave front from a point source;
Do the particles of the wave move in the direction of the wave propagation?
draw a conclusion about the features of the wave motion.

Equipment: a beaker from a calorimeter, a pipette or burette, a glass tube, a match.
The waves that form on the surface of the water are __________
Waves on the surface of the water have the shape of _________
A match placed on the surface of the water during the propagation of a wave, ___________
Form for completing the task
Feature of wave motion _________________
Model response field
Assessment Tool
response
The waves that form on the surface of the water are transverse.
Waves on the surface of the water have the shape of a circle.
A match placed on the surface of the water during the propagation of a wave does not
moves.
A feature of wave motion - during wave motion does not occur
displacement of matter along the direction of wave propagation.
Total
III.
Homework: §31, 32
1
1
1
2
5
http://schoolcollection.edu.ru/catalog/rubr/8f5d721086a611daa72b0800200c9a66/21674/

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, 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 exist only 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'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 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.