A medium is called elastic if there are interaction forces between its particles that prevent any deformation of this medium. When a body oscillates in an elastic medium, it acts on 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 more and more distant from the body, taking them out of their equilibrium position. Gradually, all particles of the medium are involved in oscillatory motion.
The bodies that cause elastic waves propagating in the medium are wave sources(oscillating tuning forks, strings of musical instruments).
elastic waves called mechanical perturbations (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 to be continuous and continuous, and its particles are infinitesimal volume elements (sufficiently small compared to the wavelength) in which the a large number of molecules. When the wave propagates in continuum the particles of the medium participating in the oscillations at each moment of time have certain phases of the oscillation.
The locus of points of 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, waves are plane, spherical, etc.
A line drawn perpendicular to the wave front in the direction of wave propagation is called a beam. The beam indicates the direction of wave propagation.;;
AT plane wave wave surfaces are planes perpendicular to the direction of wave propagation (Fig. 15.1). Plane waves can be obtained on the surface of water in a flat bath by means of vibrations of 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. This wave propagates from the same speed in all directions. The rays are the radii of the spheres (Fig. 15.2).
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 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 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.
Finished works
THESE WORKS
Much is already behind and now you are a graduate, if, of course, you write your thesis on time. But life is such a thing that only now it becomes clear to you that, having ceased to be a student, you will lose all student joys, many of which you have not tried, putting everything off and putting it off for later. And now, instead of catching up, you're tinkering with your thesis? There is a great way out: download the thesis you need from our website - and you will instantly have a lot of free time!
Diploma works have been successfully defended in the leading Universities of the Republic of Kazakhstan.
Cost of work from 20 000 tenge
COURSE WORKS
The course project is the first serious practical work. It is with writing a term paper that preparation for the development of graduation projects begins. If a student learns to correctly state the content of the topic in a course project and correctly draw it up, then in the future he will not have problems either with writing reports or with compiling theses, nor with the performance of other practical tasks. In order to assist students in writing this type of student work and to clarify the questions that arise in the course of its preparation, in fact, this information section was created.
Cost of work from 2 500 tenge
MASTER'S THESES
Currently in higher educational institutions Kazakhstan and the CIS countries, the degree of higher education is very common. vocational education, which follows after the bachelor's degree - master's degree. In the magistracy, students study with the aim of obtaining a master's degree, which is recognized in most countries of the world more than a bachelor's degree, and is also recognized by foreign employers. The result of training in the magistracy is the defense of a master's thesis.
We will provide you with up-to-date analytical and textual material, the price includes 2 science articles and abstract.
Cost of work from 35 000 tenge
PRACTICE REPORTS
After completing any type of student practice (educational, industrial, undergraduate) a report is required. This document will be proof practical work student and the basis for the formation of assessments for practice. Usually, in order to compile an internship report, it is required to collect and analyze information about the enterprise, consider the structure and work schedule of the organization in which the internship takes place, draw up calendar plan and describe your practice.
We will help you write a report on the internship, taking into account the specifics of the activities of a particular enterprise.
Let's start with the definition of an elastic medium. As the name implies, an elastic medium is a medium in which elastic forces act. In relation to our goals, we 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 doing so, we will consider extended media. We will specify how long this is in the future, but for now we will consider that this is enough. For example, imagine a long spring fixed at both ends. If several coils are compressed in some place of the spring, then the compressed coils will tend to expand, and the neighboring coils, which turned out to be stretched, will tend to compress. Thus, our elastic medium - the spring will try to return to its original calm (unperturbed) state.
Gases, liquids, solids are elastic media. Important in the previous example is the fact that the compressed section of the spring acts on neighboring sections, or, scientifically speaking, transmits a disturbance. Similarly, in a gas, creating in some place, for example, an area reduced pressure, neighboring regions, trying to equalize the pressure, will transmit the disturbance to their neighbors, who, in turn, to theirs, and so on.
A few words about physical quantities. In thermodynamics, as a rule, the state of a body is determined by the parameters common to the whole body, the 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 the particles of the medium in contact with it into oscillatory motion. As a result, periodic deformations (for example, compression and rarefaction) occur in the elements of the medium adjacent to the body. Under 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 transferred from some parts 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 make oscillatory motions around the equilibrium positions; only the state of deformation is transmitted from one section of the medium to another.
When the fish “pecks” (pulls the hook), circles scatter from the float on the surface of the water. Together with the float, water particles in contact with it are displaced, which involve other particles closest to them, and so on.
The same phenomenon occurs with the particles of a stretched rubber cord, if one of its ends is brought into oscillation (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 oscillations of its first point, then we get the picture shown in Fig. 1.2, bd. 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.
After 1/4 T after the start of the oscillation, point 1 occupies the highest position, and point 2 is just beginning to move. 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 will move down, and point 2 will take the upper position (position c). Point 3 at this moment is just beginning to move.
Over a whole period, the oscillations propagate to point 5 of the cord (position e). At the end of the period T, point 1, moving up, will begin its second oscillation. At the same time, point 5 will also begin to move up, making its first oscillation. In the future, these points will have the same oscillation phases. The set of cord points in the interval 1-5 forms a wave. When point 1 completes the second oscillation, points 5-10 will be involved in the movement on the cord, i.e., a second wave is formed.
If we follow the position of points that have the same phase, it will be seen that the phase, as it were, passes from point to point and moves to the right. Indeed, if point 1 has phase 1/4 in position b, then point 2 has phase 1/4 in position b, and so on.
Waves in which the phase moves at a certain speed are called traveling waves. When observing waves, it is precisely the propagation of the phase that is visible, for example, 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 along 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 resulting elastic deformations, waves are distinguished longitudinal and transverse. In longitudinal waves, the 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 wave propagation. On fig. 1.3 shows the location of the particles of the medium (conditionally 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 compressions and rarefaction of the medium. The waves excited on the surface of the hearth are transverse: they owe their existence to the earth's gravity. In solids, both longitudinal and transverse waves can be generated; a particular type of transverse will are torsional, excited in elastic rods, to which torsional vibrations are applied.
Let us assume that the point source of the wave began to excite oscillations in the medium at the moment of time t= 0; after time t this oscillation will propagate in different directions over a distance r i =c i t, where with i is the speed of the wave in that 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. Wednesday is called isotropic if the speed is the same in all directions. The wave front from a point source of oscillations in a homogeneous and isotropic medium has the form of a sphere; such waves are called spherical.
In an inhomogeneous and non-isotropic ( anisotropic) medium, 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 the oscillations 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 only we consider the small distances traveled by this wave).
When describing wave processes, surfaces are singled out in which all particles oscillate in the same phase; these "surfaces of the same phase" are called wave, or phase.
It is clear that the wave front is the front wave surface, i.e. the most remote from the source that creates the waves, and the wave surfaces can also be spherical, flat or have a complex shape, depending on the configuration of the source of vibrations and the properties of the medium. On fig. 1.4 conditionally shown: I - spherical wave from a point source, II - wave from an oscillating plate, III - elliptical wave from a point source in an anisotropic medium, in which the wave propagation velocity With varies smoothly as the angle α increases, reaching a maximum along the AA direction and a minimum along the BB.
Oscillations excited at any point in the medium (solid, liquid or gaseous) propagate in it at a finite speed, depending on the properties of the medium, being transmitted from one point of the medium to another. The farther the particle of the medium is located from the source of oscillations, the later it will begin to oscillate. In other words, the entrained particles will lag behind in phase those particles that entrain them.
When studying the propagation of oscillations, the discrete (molecular) structure of the medium is not taken into account. The medium is considered as continuous, i.e. continuously distributed in space and possessing elastic properties.
So, An oscillating body placed in an elastic medium is a source of oscillations that propagate from it in all directions. The process of propagation of oscillations in a medium is called wave.
When a wave propagates, the particles of the medium do not move along with the wave, but oscillate around their equilibrium positions. Together with the wave, only the state of oscillatory motion and energy are transferred from particle to particle. That's why basic property of all waves,regardless of their nature,is the transfer of energy without the transfer of matter.
Waves happen transverse (vibrations occur in a plane perpendicular to the direction of propagation) and longitudinal (concentration and rarefaction of particles of the medium occurs in the direction of propagation).
where υ is the wave propagation velocity, is the period, ν is the frequency. From here, the speed of wave propagation can be found by the formula:
| . | (5.1.2) |
The locus 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, i.e. there are an infinite number of wave surfaces. The wave surfaces remain stationary (they pass through the equilibrium position of particles oscillating in the same phase). There is only one wavefront, and it moves all the time.
Wave surfaces can be of any shape. In the simplest cases, wave surfaces have the form plane or spheres, respectively, the waves are called flat or spherical . In a plane wave, the wave surfaces are a system of planes parallel to each other; in a spherical wave, they are a system of concentric spheres.
