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 a body vibrates in elastic medium, then it affects the particles of the medium adjacent to it and causes them to perform forced vibrations. 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 also include: 1) waves on the surface of water, where the connection of adjacent sections of the water surface is caused not by elasticity, but by gravity and surface tension forces; 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.

Let's start with the definition of an elastic medium. As one can conclude from the name, an elastic medium is a medium in which elastic forces act. With regard to our goals, we will add that with any disturbance of this environment (not an emotional violent reaction, but a deviation of the parameters of the environment in some place from equilibrium), forces arise in it, striving to return our environment to its original equilibrium state. In this case, we will consider extended media. We will clarify how extensive this is in the future, but for now we will assume that this is enough. For example, imagine a long spring attached at both ends. If several turns of the spring are compressed in some place, the compressed turns will tend to expand, and the adjacent turns that are stretched will tend to compress. Thus, our elastic medium - the spring - will try to return to its original calm (undisturbed) state.

Gases, liquids, and solids are elastic media. An important thing in the previous example is the fact that the compressed section of the spring acts on neighboring sections, or, in scientific terms, transmits a disturbance. In a similar way, in gas, creating in some place, for example, an area of ​​​​low pressure, neighboring areas, trying to equalize the pressure, will transmit the disturbance to their neighbors, who in turn, to their own, and so on.

A few words about physical quantities. In thermodynamics, as a rule, the state of a body is determined by parameters common to the entire body, gas pressure, its temperature and density. Now we will be interested in the local distribution of these quantities.

If an oscillating body (string, membrane, etc.) is in an elastic medium (gas, as we already know, is an elastic medium), then it sets into oscillatory motion the particles of the medium in contact with it. As a result, periodic deformations (for example, compression and discharge) occur in the elements of the environment adjacent to the body. With these deformations, elastic forces appear in the medium, tending to return the elements of the medium to their original states of equilibrium; Due to the interaction of neighboring elements of the medium, elastic deformations will be transmitted from one part of the medium to others, more distant from the oscillating body.

Thus, periodic deformations caused in some place of an elastic medium will propagate in the medium at a certain speed, depending on its physical properties. In this case, the particles of the medium perform oscillatory movements around equilibrium positions; Only the state of deformation is transmitted from one part of the medium to another.

When a fish “bites” (pulls the hook), circles scatter across the surface of the water from the float. Together with the float, the water particles in contact with it move, which involve other particles closest to them in movement, and so on.

The same phenomenon occurs with particles of a stretched rubber cord if one end of it is vibrated (Fig. 1.1).

The propagation of oscillations in a medium is called wave motion. Let us consider in more detail how a wave arises on a cord. If we fix the position of the cord every 1/4 T (T is the period with which the hand oscillates in Fig. 1.1) after the start of oscillation of its first point, you will get the picture shown in Fig. 1.2, b-d. Position a corresponds to the beginning of oscillations of the first point of the cord. Its ten points are marked with numbers, and the dotted lines show where the same points of the cord are located at different points in time.

1/4 T after the start of oscillation, point 1 occupies the highest position, and point 2 is just beginning its movement. Since each subsequent point of the cord begins its movement later than the previous one, then in the interval 1-2 points are located, as shown in Fig. 1.2, b. After another 1/4 T, point 1 will take the equilibrium position and move downward, and point 2 will take the upper position (position c). Point 3 at this moment is just beginning to move.

Over the entire period, the oscillations propagate to point 5 of the cord (position d). At the end of period T, point 1, moving upward, will begin its second oscillation. At the same time, point 5 will begin to move upward, making its first oscillation. In the future, these points will have the same oscillation phases. The combination of cord points in the interval 1-5 forms a wave. When point 1 completes the second oscillation, another 5-10 points on the cord will be involved in the movement, i.e. a second wave will form.

If you trace the position of points that have the same phase, you will see that the phase seems to move from point to point and moves to the right. Indeed, if in position b point 1 has phase 1/4, then in position c point 2 has the same phase, etc.

Waves in which the phase moves at a certain speed are called traveling. When observing waves, it is the phase propagation that is visible, such as the movement of the wave crest. Note that all points of the medium in the wave oscillate around their equilibrium position and do not move with the phase.

The process of propagation of oscillatory motion in a medium is called a wave process or simply a wave.

Depending on the nature of the elastic deformations that arise, waves are distinguished longitudinal And transverse. In longitudinal waves, particles of the medium oscillate along a line coinciding with the direction of propagation of the oscillations. In transverse waves, particles of the medium oscillate perpendicular to the direction of propagation of the wave. In Fig. Figure 1.3 shows the location of particles of the medium (conventionally depicted as dashes) in longitudinal (a) and transverse (b) waves.

Liquid and gaseous media do not have shear elasticity and therefore only longitudinal waves are excited in them, propagating in the form of alternating compression and rarefaction of the medium. The waves excited on the surface of the hearth are transverse: they owe their existence to gravity. In solids, both longitudinal and transverse waves can be generated; A particular type of transverse will is torsional, excited in elastic rods to which torsional vibrations are applied.

Let us assume that a point source of a wave began to excite oscillations in the medium at the moment of time t= 0; after time has passed t this vibration will spread in different directions at a distance r i =c i t, Where with i- wave speed in a given direction.

The surface to which the oscillation reaches at some point in time is called the wave front.

It is clear that the wave front (wave front) moves with time in space.

The shape of the wave front is determined by the configuration of the oscillation source and the properties of the medium. In homogeneous media, the speed of wave propagation is the same everywhere. The environment is called isotropic, if this speed is the same in all directions. The wave front from a point source of oscillations in a homogeneous and isotropic medium has the shape of a sphere; such waves are called spherical.

In a non-uniform and non-isotropic ( anisotropic) environment, as well as from non-point sources of oscillations, the wave front has complex shape. If the wave front is a plane and this shape is maintained as vibrations propagate in the medium, then the wave is called flat. Small sections of the wave front of a complex shape can be considered a plane wave (if we only consider the short distances traveled by this wave).

When describing wave processes, surfaces are identified in which all particles vibrate in the same phase; these “surfaces of the same phase” are called wave or phase.

It is clear that the wave front represents the front wave surface, i.e. the most distant from the source creating the waves, and the wave surfaces can also be spherical, flat, or have a complex shape, depending on the configuration of the source of oscillations and the properties of the medium. In Fig. 1.4 conventionally shows: I - a spherical wave from a point source, II - a wave from a vibrating plate, III - an elliptical wave from a point source in an anisotropic medium in which the wave propagation speed With changes smoothly as the angle α increases, reaching a maximum along the AA direction and a minimum along BB.

Topic: Propagation of oscillations in a medium. Waves.
Physics. 9th grade.
Purpose: To introduce students to wave motion, to consider its features and mechanism
wave propagation.
Tasks:
­
educational: deepening knowledge about the types of oscillatory motion, using the connections of physics
with literature, history, mathematics; formation of the concepts of 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 skills.
­
­
Didactic type of lesson: Learning new material.
Equipment: Laptop, multimedia projector, video – waves on a spring, presentation
PowerPoint

To the lesson.
Lesson progress:
I. Testing knowledge and skills.
1. Answer questions.
 Read the phrases carefully. Determine whether free vibrations are possible:
float on the surface of the water; bodies on a canal dug through the globe; birds on a branch;
ball on a flat surface; ball in a spherical hole; human hands and feet; athlete on
trampoline; needles in sewing machine.
 Which car, loaded or unloaded, will make more frequent trips on springs?
hesitation?
 There are two types of clocks. Some are based on vibrations of the load on the rod, others - on the
spring. How can you regulate the frequency of each watch?
 During periodic gusts of wind, the Tacoma Narrous Bridge in America swayed and collapsed.
Explain why?
2. Problem solving.
The teacher offers to complete a competency-oriented task, structure and content
which is presented below.
Stimulus: Evaluate existing knowledge on the topic “Mechanical vibrations.”
Problem formulation: Within 5 minutes, using the text provided, determine the frequency and
period of contraction of the human heart. Write down data that you cannot use in your decision.
tasks.
Total length There are approximately 100 thousand km of blood capillaries in the human body, which is 2.5 times
exceeds the length of the equator, and the total internal area is 2400 m2. Blood capillaries have
10 times thinner than hair. Within a minute, the heart pumps about 4 liters into the aorta.
blood, which then moves to all points of the body. The heart beats on average 100 thousand times.
once a day. Over 70 years of human life, the heart contracts 2 billion 600 million times and
pumps 250 million times.
Form for completing the task:
1. Data necessary to determine the period and frequency of heart contraction:
A) ___________; b) _________
Formula for calculation: ______________
Calculations _______________
=________; T=____________
ν
2. Redundant data
A) ___________
b)___________

V) ___________
G) ___________
Model answer:
Data necessary to determine the period and frequency of heart contraction:
a) Number of reductions 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 abbreviations N=2600000000; b) Time of reduction t=70 years. - But this data
lead to more complex calculations and are therefore 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 releases 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
Data are highlighted to determine the frequency and period of heart contraction.
Formulas for calculation are given.
The calculations have been completed and the correct answer is given.
Unnecessary data has been extracted from the text.
Tool
assessments
answer
1
1
1
1
II.
Explanation of new material.
All particles of the medium are interconnected by 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. This movement is called wave motion.
A mechanical wave (wave motion) is the propagation of vibrations in an elastic
environment.
Oscillations that propagate through space over time are called waves.
or
IN this definition We are talking about so-called traveling waves.
Basics general property traveling waves of any nature is that, spreading in
space, transfer energy, but without transferring matter.
In a traveling wave, energy transfer occurs without matter transfer.
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 emergence 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 occur in almost all areas physical phenomena, so studying them
is of great importance.
Wave motion is of two types: transverse and longitudinal.
Transverse wave - particles oscillate (move) perpendicular (across) the speed
wave propagation.
Examples: a wave from a thrown stone...
Longitudinal wave - particles oscillate (move) parallel to the speed of propagation
waves.
Examples: sound waves, tsunamis...
Mechanical waves
Cord Spring
transverse
longitudinal
Transverse waves.
Longitudinal waves.
Elastic shear deformation occurs.
Body volume
doesn't change.
Elastic forces tend to return the body to
starting position. These forces cause
environmental fluctuations.
Shift of layers relative to each other in
liquids and gases does not lead to the appearance
elastic forces, therefore arise
only in solids.
Occurs during compressive deformation.
Elastic forces arise in solids
bodies, liquids and gases. These forces
cause vibrations in individual areas
environment, therefore they spread in all
environments
In solids, the speed of propagation
more.
III.
Fastening:
1. Interesting tasks.
a) In 1883 During the infamous eruption of the Indonesian volcano Krakatoa, air strikes
waves generated by underground explosions circled the globe three times.
What type of waves is a shock wave? (Towards longitudinal waves).
b) Tsunami is a formidable companion to earthquakes. This name was born in Japan and means
giant wave. When it rolls onto the shore, it seems that it is not a wave at all, but
the sea, furious, indomitable, rushes to the shore. It is not surprising that the tsunami
wreak havoc on it. During the 1960 earthquake, people rushed to the coast of Chile

waves up to six meters high. The sea retreated 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
Chile? (Tsunamis refer to
waves is 3 m).
(tsunami illustration:
longitudinal waves. Amplitude
http://ru.wikipedia.org/wiki/Image:2004_Indian_Ocean_earthquake_Maldives_tsunami_wave.jpg
c) Riffles are signs of small wave ripples. They have existed on earth since the appearance of bulk
medium - snow and sand. Their imprints are found in ancient geological strata (sometimes together with
dinosaur tracks). The first scientific observations of 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 the depth of the depressions between the ridges on average 0.31 cm.
Assuming that the riffles are a wave, determine the amplitude of the wave (0.150.5 cm).
Reef illustration:
http://rusnauka.narod.ru/lib/physic/destroy/gl7/image246.gif
2. Physical experience. Individual work.
The teacher invites students to complete a competency-oriented task, structure and
the contents of which are presented below
Stimulus: evaluate acquired knowledge on the topic “Wave motion”.
Problem formulation: using the equipment provided and the knowledge gained in the lesson,
define:
what waves are formed on the surface of the wave;
what shape does the wave front from a point source have;
Do wave particles move in the direction of wave propagation?
draw a conclusion about the features of wave motion.

Equipment: calorimeter glass, pipette or burette, glass tube, match.
Waves formed on the surface of water are __________
Waves on the surface of the water have the shape _________
A match placed on the surface of water as a wave propagates ___________
Form for completing the task
Features of wave motion _________________
Model response field
Assessment Tool
answer
Waves formed on the surface of water are transverse.
Waves on the surface of the water have the shape of a circle.
A match placed on the surface of water while a wave is propagating does not
moves.
The peculiarity of wave motion is that during wave motion there is no
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/

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

Let us consider how vibrations propagate in various media. Often you could observe how circles spread across the water from a float or from a thrown stone. Oscillations that create environmental deformation in space can become a source, for example, of earthquake waves, sea ​​waves or sound. If we consider sound, vibrations are produced by both the sound source (a string or a tuning fork) and the sound receiver, for example, a microphone membrane. The medium itself through which the wave travels also vibrates.

The process of vibrations propagating in space over time is called a wave. Waves are disturbances propagating in space, moving away from the place of their origin.

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

Solid, liquid, and gaseous media consist of individual particles interacting with each other through bonding 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 ones, etc.

There are longitudinal and transverse waves.

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

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 sequential movement of condensations and rarefaction of its turns.

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

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

a) initial state; b) spring compression; c) transmission of vibrations from one turn to another (condensation and discharge of turns).

In mechanics, 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 propagation of the wave.

If we stretch a rubber cord horizontally, one end is rigidly fixed, and the other is set in a vertical oscillatory motion, we will be able to observe a transverse wave.

For the experiment, we will simulate chains of springs and balls and use this model to 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, a compressive or tensile deformation occurs. It must be remembered that in liquid and gaseous media such deformation is accompanied by compaction of the medium or its rarefaction.

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

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 on the topic of the lesson

Propagation of mechanical waves is possible only in gaseous, 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. - P. 293-295.
2. Irodov I. E. Mechanics. Basic laws / I.E. Irodov. – 5th ed., revised – M.: Laboratory basic knowledge, 2000, pp. 205–223.
3. Irodov I.E. Mechanics of oscillatory systems / I.E. Irodov. – 3rd ed., revised – M.: Laboratory of Basic Knowledge, 2000, pp. 311–320.
4. Peryshkin A.V. Physics. 9th grade: textbook / A.V. Peryshkin, E.M. Gutnik. – M.: Bustard, 2014. – 319 p. Collection test tasks in physics, 9th grade. /E.A.Maron, A.E.Maron. Publishing house "Prosveshchenie", Moscow, 2007.

Images used:

A medium is called elastic if there are interaction forces between its particles that prevent any deformation of this medium. When any body oscillates in an elastic medium, it affects the particles of the medium adjacent to the body 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 that are increasingly distant from the body, removing them from their equilibrium position. Gradually all particles of the medium are involved in oscillatory motion.

Bodies that cause elastic waves propagating in a medium are wave sources(oscillating tuning forks, strings of musical instruments).

Elastic waves are called mechanical disturbances (deformations) produced by sources that propagate in an elastic medium. Elastic waves cannot propagate in a vacuum.

When describing the wave process, the medium is considered solid and continuous, and its particles are infinitesimal volume elements (quite small compared to the wavelength) in which there is large number molecules. When a wave propagates in a continuous medium, the particles of the medium participating in the oscillations have certain oscillation phases at each moment of time.

The geometric locus of points in the medium oscillating in the same phases forms wave surface.

The wave surface separating the oscillating particles of the medium from particles that have not yet begun to oscillate is called the wave front. Depending on the shape of the wave front, plane waves, spherical waves, etc. are distinguished.

A line drawn perpendicular to the wave front in the direction of wave propagation is called a ray. The beam indicates the direction of wave propagation.;;

IN plane wave wave surfaces are planes perpendicular to the direction of wave propagation (Fig. 15.1). Plane waves can be produced on the surface of water in a flat bath by oscillating a flat rod.

In a spherical wave, the wave surfaces are concentric spheres. A spherical wave can be created by a ball pulsating in a homogeneous elastic medium. Such a wave propagates at the same speed in all directions. The rays are the radii of the spheres (Fig. 15.2).