We began our study of vibrations with mechanical vibrations. We were further convinced that the basis of sound phenomena, that is, phenomena perceived by the ear, also lies in mechanical vibrations, which differ from the oscillations of a pendulum only more high frequencies. Then we...

§ 33. Wave phenomena

We now move on to studying the propagation of oscillations. If we're talking about about mechanical vibrations, i.e. about the oscillatory movement of particles of any solid, liquid or gaseous medium, then the propagation of vibrations means the transmission of vibrations from one part...

§ 34. Speed ​​of wave propagation

The simplest observations convince us that the propagation of mechanical waves does not occur instantly. Everyone saw how the circles on the water gradually and evenly expanded or how the sea waves ran. Here we see directly that the spread...

§ 35. Radar, hydroacoustic ranging and sound measurement

If the speed of wave propagation is known, then measuring their delay allows us to solve inverse problem: find the distance they traveled. The insignificant periods of time spent by electromagnetic waves covering ground distances are no longer...

§ 36. Transverse waves in a cord

We'll move on now to more detailed study mechanical waves. Their properties depend on many circumstances: on the type of connection between adjacent sections of the medium, on the size of the medium (for example, in the body limited sizes the distribution pattern will be different than...

§ 37. Longitudinal waves in an air column

We will now get acquainted with another type of waves, and again we will take an elongated body, namely a column of air enclosed in a pipe. A piston can move along the pipe. Let's make this piston perform a harmonic oscillation. What will happen at the table...

§ 38. Waves on the surface of a liquid

We have already mentioned waves, the formation of which is caused not by elastic force, but by gravity. That is why it should not surprise us that the waves propagating along the surface of a liquid are not longitudinal. However, they are not transverse either: two...

§ 39. Energy transfer by waves

The propagation of a mechanical wave, which is a sequential transfer of motion from one part of the medium to another, thereby means the transfer of energy. This energy is delivered by the wave source when it sets in motion the directly adjacent...

§ 40. Wave reflection

Let us place in the path of the waves in a water bath a flat plate, the length of which is large compared to the wavelength. We will see the following. Behind the plate there is an area in which the surface of the water remains almost at rest (Fig. 83). In other words, a record with...

24-25.Wave phenomena. Propagation of mechanical waves. Wavelength. Wave propagation speed. Problem solving.

Physics teacher

Razdolnenskaya secondary school of І - ІІІ levels

Education Department of the Starobeshevsky District Administration

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, in addition to just oscillatory process in a narrow region of space, it is also possible for these vibrations to propagate in the 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.

Mechanical waves can propagate in an elastic medium .

Elastic is a medium that consists of large quantity particles interacting with each other through elastic forces.

The propagation process 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 precisely 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 whose propagation causes particles of the medium to oscillate along the direction of propagation of the wave.

R is. 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.

Figure “Longitudinal and transverse waves”

Wavelength. Wave speed

The lesson is devoted to the topic “Characteristics of wave motion.” To begin with, let us remember that mechanical wave is a vibration that propagates over time in an elastic medium. Since it is an oscillation, the wave will have all the characteristics that correspond to an oscillation: amplitude, oscillation period and frequency. In addition, the wave has its own special characteristics. One of these characteristics is wavelength. Wavelength is indicated Greek letter l (lambda, or they say “lambda”) and is measured in meters.

A – amplitude [m]

T – period [s]

ν – frequency [Hz]

l – wavelength [m]

What is wavelength?

Wavelength is the shortest distance between particles vibrating with the same phase.

Rice. 1. Wavelength, wave amplitude

It is more difficult to talk about wavelength in a longitudinal wave, because there it is much more difficult to observe particles that perform the same vibrations. But there is also a characteristic - wavelength, which determines the distance between two particles performing the same vibration, vibration with the same phase.

Next characteristic is the speed of wave propagation (or simply wave speed). Wave speed denoted, just like any other speed, by the letter V and measured in m/s. How to clearly explain what wave speed is? The easiest way to do this is using a transverse wave as an example. Imagine a seagull flying over the crest of a wave. Its flight speed over the crest will be the speed of the wave itself.

Rice. 2. To determine the wave speed

Wave speed depends on what the density of the medium is, what the forces of interaction between the particles of this medium are. Let's write down the relationship between wave speed, wave length and wave period: . Formula "Wavelength"

Velocity can be defined as the ratio of the wavelength, the distance traveled by the wave in 1 period, to the period of oscillation of the particles of the medium in which the wave propagates. In addition, remember that . Then we have another relationship for the wave speed: V = lν.

It is important to note that

When a wave passes from one medium to another, its characteristics change: the speed of the waves, the wavelength. And here the oscillation frequency remains the same.

Waves in nature and technology

Interactive task

Before we start solving problems, let's answer the questions:

1. What is the main property of all waves, regardless of their nature?
2. Why can’t transverse waves exist in gases and liquids?
3. What kind of body can create in environment sound wave?

Solve problems using the above material:

When solving problems, the speed of sound in air is considered given and equal to 330 m/s.
1. In the oceans, the wavelength reaches 300 m and the period is 13.5 s. Determine the speed of propagation of such a wave.
2. Determine the sound wavelength at a frequency of 200 Hz.
3. The observer heard the sound of an artillery shot 6 s after he saw the flash. How far away was the gun from him?
4. The length of the sound waves emitted by the violin. can vary from 23 mm to 1.3 m. What is the frequency range of the violin?
5. The distance to the obstacle that reflects the sound is 66 m. How long will it take for a person to hear the echo?

You can suggest a number of other problems and solve them using a tablet, for example R No. 439-444.

Homework:Paragraphs 42-44, exercise 6, page 129.

cabbage opposite end of the stretching | knitted cord (Fig. 4.2). | If a disturbance of the environment causes - | Xia periodic external force, changing over time according to harmonic law, then the waves it causes are called harmonic. In this case, at each point of the medium, harmonic vibrations with frequency external influence. We will primarily consider harmonic waves or waves close to harmonic. This is the simplest type of wave motion. Study harmonic waves is of paramount importance in constructing the theory of any wave motion.
The main feature of wave motion

A visual representation of the main features of wave motion can be obtained by considering waves on the surface of water. The waves look like rounded shafts running forward (Fig. 4.3). The distances between the shafts, or ridges, are approximately the same. However, if you throw in water light subject, for example Matchbox, then it will not be carried forward by the wave, but will begin to oscillate up and down, remaining almost exactly in one place.
When a wave propagates, the form moves (moves a certain state of a vibrating medium), but does not transfer the substance in which the wave propagates. Water disturbances that arise in one place, for example from a thrown stone, are transmitted to neighboring areas and gradually spread in all directions. There is no flow of water: only the shape of its surface moves.
Wave speed
The most important characteristic of a wave is the speed of its propagation. Waves of any nature do not propagate through space instantly. Their speed is finite. One can imagine, for example, that a seagull flies over the sea in such a way that it always ends up above the same wave crest. The speed of the wave in this case will be equal to the speed of the seagull. Waves on the surface of water are convenient for observation because the speed of their propagation is low.
Transverse and longitudinal waves
It is not difficult TE.KZh6 to observe waves propagating along a rubber cord. If one end of the cord is secured and, slightly pulling the cord with your hand, bring its other end into oscillatory motion, then a wave will run along the cord (Fig. 4.4). The faster the cord is pulled, the faster the wave speed will be. The wave will reach the anchoring point, be reflected and run back. Here, as the wave propagates, changes in the shape of the cord occur. Each section of the cord oscillates relative to its constant equilibrium position. Please note that when a wave propagates along the cord, its individual sections oscillate in the direction perpendicular to the direction distribution - 161
6 - 5654
Rice. 4.4
Direction of vibration
wave propagation

Direction
Rice. 4.5 waves (Fig. 4.5). Such waves are called transverse.
But not every wave is transverse. Oscillations can also occur along the direction of wave propagation (Fig. 4.6). Then the wave is called longitudinal. It is convenient to observe a longitudinal wave using a long soft spring of large diameter. By hitting one of the ends of the spring with your palm (Fig. 4.7, a), you can see how compression (elastic impulse) runs along the spring. Using a series of successive blows, it is possible to excite a wave in the spring, which represents successive compression and extension of the spring, running one after another (Fig. 4.7,6). Oscillations of any coil of the spring occur in the direction of wave propagation.
From mechanical waves highest value have sound waves. However, the study of sound waves is more difficult task than the study of wills along a cord or spring. We will deal with them in detail later.
Wave energy
When a wave propagates, motion is transferred from one part of the body to another. The transfer of motion by a wave is associated with the transfer of energy without the transfer of matter. The energy comes from a source that excites vibrations at the beginning of a cord, string, etc., and spreads along with the wave. This energy, for example, in a cord is composed of kinetic Direction
Direction of wave propagation oscillations
Rice. 4.7
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b) the energy of movement of sections of the cord and potential energy its elastic deformation.
The energy of the wave from a stone thrown into the water increases the kinetic energy of the float on the surface of the water, and can also increase the potential energy of a chip floating near the shore.
As the wave propagates, a gradual decrease in the amplitude of oscillations occurs due to the transformation of part mechanical energy to the inner one. If these losses can be neglected, then through cross section, for example a cord, the same amount of mechanical energy will pass per unit time.
Electromagnetic waves
Mechanical waves propagate in matter: gas, liquid or solid. There is, however, another type of wave that does not require any substance to propagate. This electromagnetic waves, which in particular include radio waves and light. An electromagnetic field can exist in a vacuum (in emptiness), that is, in a space that does not contain atoms. Despite the unusual nature of these waves, their sharp difference from mechanical waves, electromagnetic waves behave similarly to mechanical waves during their propagation. In particular, electromagnetic waves also propagate with terminal speed and carry energy with them. This the most important properties all types of waves.

A pleasant picture can be observed in childhood: the quiet surface of the water on the river. And all you have to do is throw a small pebble - this picture immediately changes. Around the place where the stone hit the water, waves scatter in circles. Everyone has read stories about sea ​​travel, O monstrous strength sea ​​waves, easily swinging big ships. However, when observing these phenomena, not everyone knows that the sound of a splash of water reaches our ear through waves in the air that we breathe, that the light with which we visually perceive our surroundings is also a wave movement. Waves on the surface of water, light and sound waves can be combined together. These are all examples of wave motion. But the waves have different nature appearance. What is a wave from a physics point of view? A wave is an oscillation that travels through space over time. The main property of waves is that the wave propagates without transferring matter. For example, if a small leaf from a tree lies on the surface of the water. Let's throw a stone into the water. As mentioned earlier, waves will begin to spread from the stone in all directions. At the same time, having reached the leaf, they will not force it to move towards the wave. The leaf will remain in place, but at the same time it will make oscillatory movements up and down. That is, only the shape of the water will change, but no flow will arise. One of the most important characteristics water is the speed of its spread. The speed of propagation of any wave is always finite. The speed of waves on the surface of the water is relatively low, so they are very easy to observe.
It is also easy to observe waves propagating along a rubber cord. If one end of the cord is secured and, slightly pulling the cord with your hand, the other end is set into an oscillatory motion, then a wave will run along the cord. The faster the cord is pulled, the faster the wave speed will be. The wave will reach the point where the cord is attached, be reflected and run back. In this experiment, as the wave propagates, changes in the shape of the cord occur. Each section of the cord oscillates about its constant equilibrium position. Let us pay attention to the fact that when a wave propagates along the cord, oscillations occur in a direction perpendicular to the direction of wave propagation. Such waves are called transverse.
In this case, elastic deformation occurs in such waves, called shear deformation. Individual layers of matter shift relative to each other. During shear deformation, elastic forces arise in a solid body, tending to return the body to its original state. It is the elastic forces that cause vibrations of the particles of the medium. But oscillations of medium particles can also occur along the direction of wave propagation. Such a wave is called longitudinal. It is convenient to observe a longitudinal wave on a long soft spring of large diameter. By hitting one of the ends of the spring with your palm, you can see how compression (elastic impulse) runs along the spring. Using a series of successive blows, it is possible to excite a wave in the spring, which represents successive compression and extension of the spring, running one after another.
Compressive deformation occurs in a longitudinal wave. Elastic forces associated with this deformation occur both in solids and in liquids and gases.
Examples longitudinal waves can serve acoustic waves, i.e. those that are perceived by the human ear. When a mechanical wave propagates, motion is transmitted from one particle of the medium to another. Associated with the transfer of motion is the transfer of energy. The main property of all waves, regardless of their nature, is that they transfer energy without transferring matter. The energy comes from a source that excites vibrations at the beginning of a cord, string, etc., and spreads along with the wave. Energy is transmitted through any cross section, such as a cord. This energy is made up of kinetic energy motion of particles of the medium and the potential energy of their elastic deformation. Gradual decrease The amplitude of particle vibrations during wave propagation is associated with the conversion of part of the mechanical energy into internal energy.
How does mechanical waves propagate? Let's follow the movement individual particles substances in wave motion. First, consider a transverse wave that propagates, for example, along a rubber cord. Each section of the cord has mass and elasticity. When the cord is deformed in any section, elastic forces appear. These forces tend to return the cord to its original position. Due to inertia, the section of the oscillating cord does not stop in the equilibrium position, but passes through it, continuing to move until the elastic forces stop this section at the moment maximum deviation from the equilibrium position. Instead of a cord, let's take a chain of identical metal balls suspended on threads. The balls are connected to each other by springs (Fig.). The mass of the springs is much less than the mass of the balls. In this model, the inertial (mass) and elastic properties are separated: the mass is concentrated mainly in the balls, and the elasticity is concentrated in the springs. This division is not significant when considering wave motion. If you deflect the leftmost ball to horizontal plane perpendicular to the chain of balls, then the spring is deformed and a force will begin to act on the 2nd ball, causing it to deviate in the same direction as the 1st ball. Due to inertia, the movement of the 2nd ball will not occur in coordination with the 1st. Its movement, repeating the movement of the 1st ball, will be delayed in time. If the 1st ball is forced to oscillate with a period T (simply by hand or using some mechanism), then the 2nd ball will also begin to oscillate after the 1st, but with some lag in phase. The third ball, under the influence of the elastic force caused by the movement of the 2nd ball, will also begin to oscillate, falling even further behind in phase, etc. Finally, all the balls will begin to move forced oscillations with the same frequency, but with different phases. In this case, a transverse wave will run along the chain of balls. Figure a, b, c, d, e, f shows the process of wave propagation. The positions of the balls at successive moments of time, spaced from each other by a quarter of the oscillation period, are shown (top view). The arrows on the balls are the vectors of the speeds of their movement at the corresponding moments of time. On the model elastic body in the form of a chain of massive balls connected by springs (Fig. a), one can observe the process of propagation of longitudinal waves. The balls are suspended so that they can only oscillate along the chain. If the 1st ball is put into oscillatory motion with period T, then a longitudinal wave will run along the chain, consisting of alternating compactions and rarefaction of the balls (Fig. b). This figure corresponds to figure e for the case of shear wave propagation.

Municipal budget educational institution– average

Comprehensive school No. 2 named after A.I. Herzen, Klintsy Bryansk region

Lesson on the topic

Prepared and conducted:

Physics teacher

Prokhorenko Anna

Alexandrovna

Klintsy, 2013

Content:

Lesson on the topic “Wave phenomenon. Propagation of mechanical waves. Wavelength. Wave speed. »

The purpose of the lesson: introduce the concepts of wave, wave length and speed, wave propagation conditions, types of waves, teach students to apply formulas to find wave length and speed; study the reasons for the propagation of transverse and longitudinal waves;

Methodological tasks:

Educational : familiarizing students with the origin of the term “wave, wavelength, wave speed”; show students the phenomenon of wave propagation, and also prove through experiments the propagation of two types of waves: transverse and longitudinal.

Developmental : promote the development of speech, thinking, cognitive and general labor skills; promote mastery of techniques scientific research: analysis and synthesis.

Educational :

Lesson type: learning new material.

Methods: verbal, visual, practical.

Equipment: computer, presentation.

Demos:

Transverse and longitudinal waves.

Propagation of transverse and longitudinal waves.

Lesson plan:

Organization of the beginning of the lesson.

Motivational stage. Setting goals and objectives for the lesson.

Learning new material

Consolidation of new knowledge.

Summing up the lesson.

DURING THE CLASSES

1. Organizational stage

2. Motivational stage. Setting goals and objectives for the lesson.

What did you observe in these video clips? (Waves)

What types of waves did you see?

Based on your answers, we will try to set goals for today’s lesson, for this let’s remember what is the plan for studying the concept, in this case the concept of a wave? (What is a wave, i.e. definition, types of waves, characteristics of waves)

In today's lesson I will help you with the concepts of wave, wave length and speed, the condition of wave propagation, types of waves, teach students to use formulas for finding wave length and speed; study the reasons for the propagation of transverse and longitudinal waves;With develop a conscientious attitude towards educational work, positive motivation for learning, communication skills; promote the development of humanity, discipline, aesthetic perception peace.

1. Learning new material

Now you need to use the plan that is presented on the screen and on pieces of paper on your desks and, after reading paragraphs 42 and 43, find necessary information and write it out.

Plan:

Wave concept

Conditions for wave occurrence

Wave source

What is needed for a wave to occur?

Types of waves (definitions)

Wave – vibrations that propagate in space over time. Waves arise mainly due to elastic forces.

Wave Features:

Mechanical waves can propagate only in some medium (substance): in a gas, in a liquid, in a solid.

In a vacuum, a mechanical wave cannot arise.

The source of the waves are oscillating bodies that create environmental deformation in the surrounding space. (rice)

For a mechanical wave to occur it is necessary:

1. Presence of an elastic medium

2 . Presence of a source of oscillations - deformation of the medium

Types of waves:

Transverse - in which vibrations occur perpendicular to the direction of wave movement. Occurs only in solids.

Longitudinal- in which oscillations occur along the direction of wave propagation.They occur in any environment (liquids, gases, solids).

Consider a table summarizing previous knowledge. (Look at the presentation)

We conclude: mechanical wave:

the process of propagation of vibrations in an elastic medium;

in this case, energy transfer occurs from particle to particle;

there is no transfer of substance;

to create a mechanical wave it is necessary elastic medium: liquid, solid or gas.

Now let’s consider and write down the main characteristics of waves.

What quantities characterize the wave

Each wave travels at a certain speed. Under speedvwaves understand the speed of propagation of a disturbance. The speed of a wave is determined by the properties of the medium in which the wave propagates. When a wave passes from one medium to another, its speed changes.

The wavelength λ is the distance over which the wave propagates in the time equal to the period fluctuations in it.

Main characteristics: λ=v* T, λ - wavelength m,v– propagation speed m/s, T – wave period s.

4. Consolidation of new knowledge.

What is a wave?

Conditions for the formation of waves?

What types of waves do you know?

Can a transverse wave propagate in water?

What is wavelength?

What is the speed of wave propagation?

How to relate speed and wavelength?

We consider 2 types and determine which waves are which?

Solve problems:

Determine the wavelength at a frequency of 200 Hz if the wave speed is 340 m/s. (68000 m=68 km)

A wave propagates along the surface of the water in a lake at a speed of 6 m/s. A tree leaf floats on the surface of the water. Determine the frequency and period of vibration of the leaf if the wavelength is 3 m. (0.5 m, 2 s -1 )

The wavelength is 2 m, and its propagation speed is 400 m/s. Determine how many complete oscillations this wave makes in 0.1 s (20)

Let's consider it interesting : Waves on the surface of a liquid are neither longitudinal nor transverse. If you throw a small ball onto the surface of the water, you will see that it moves, swaying on the waves, along a circular path. Thus, a wave on the surface of a liquid is the result of the addition of longitudinal and lateral movement water particles.

5. Summing up the lesson.

So let's summarize.

What words would you use to describe the state after the lesson?:

Knowledge is only knowledge when it is acquired through the efforts of one’s thoughts, and not through memory;

Oh, how tired I am of this fuss.....

You understood the bliss of study, good luck, the law and the secret

Studying the topic “Mechanical Waves” is not so easy!!!

6 . Information about homework.

Prepare answers to questions according to plan using §§42-44

It’s good to know formulas and definitions on the topic “Waves”

Optional: create a crossword puzzle on the topic “Mechanical waves”

Tasks:

The fisherman noticed that in 10 seconds the float made 20 oscillations on the waves, and the distance between adjacent wave humps was 1.2 m. What is the speed of wave propagation?(T=n/t; T=10/5=2s; λ=υ*ν; ν=1/T; λ=υ/T; υ=λ*T*υ=1*2=2(m/s ))

The length of the wave is 5 m, and its frequency is 3 Hz. Determine the speed of the wave.(1.6 m/s)

Introspection

The lesson was held in 11th grade on the topic “Wave phenomenon. Propagation of mechanical waves. Wavelength. Wave speed."Is the thirteenth lesson in the physics section " Mechanical vibrations and waves." Lesson type: learning new material.

The lesson took into account the triune didactic purpose: educational, developmental, educational. Educational purpose I introduced students to the origin of the term “wave, wavelength, wave speed”; show students the phenomenon of wave propagation, and also prove through experiments the existence of two types of waves: transverse and longitudinal. As a developmental goal, I set students to develop clear ideas about the conditions for wave propagation; development of logical and theoretical thinking, imagination, memory when solving problems and consolidating learning skills. I set the educational goal: to form a conscientious attitude towards educational work, positive motivation for learning, and communication skills; contribute to the education of humanity, discipline, and aesthetic perception of the world.

During the lesson we went through the following steps:

Organizational stage

Motivational and setting goals and objectives for the lesson. At this stage, based on the watched video fragment, we determined the goals and objectives for the lesson and carried out motivation. Using: verbal method in the form of a conversation, a visual method in the form of watching a video fragment.

Learning new material

At this stage, I provided for a logical connection when explaining new material: consistency, accessibility, understandability. The main methods of the lesson were: verbal (conversation), visual (demonstrations, computer modelling). Form of work: individual.

Consolidating new material

When consolidating students' learning skills, I used interactive tasks from the multimedia manual in the section “Mechanical Waves”, solving problems at the board with an explanation. The main methods of the lesson were: practical (problem solving), verbal (discussion on issues)

Summarizing.

At this stage, I used the verbal method in the form of a conversation, the guys answered the questions posed.

Reflection was carried out. We found out whether the goals set at the beginning of the lesson were achieved, what was difficult for them this lesson. Two students were given marks for the problems and several students were given marks for the answers.

Information about homework.

At this stage, students were asked to write down homework in the form of an answer to a question according to the plan and a couple of problems on a piece of paper. And optionally create a crossword puzzle.

I believe that the triune didactic goal of the lesson has been achieved.