"Who dares to say
that we all know
what can be known?
G. Galileo.
Lesson topic: "Mechanical waves".
North Ossetia-Alania, Mozdok district, MBOU secondary school with. Grape
general information
Academic subject: Physics
Lesson topic:“Propagation of an oscillation in a medium. Waves»
The place of the lesson in the structure of the lesson:“Mechanical vibrations. Waves. Sound"
Content Goals:
Educational : withform ideas on the concept of mechanical vibrations wave. Reveal the nature, study the cause of the wave Educational : develop logical thinking; application of technical methods of mental activity of clarification, deepening, awareness and strengthening of knowledge interest in learning and research processes, develop the ability to highlight the main thing, argue your answer, give examples.
educators : bring up attentiveness, concentration, perseverance in achieving the goal. Willpower, curiosity, help students see the practical benefits of knowledge.
Planned educational results:
subject – to know and understand the meaning of the meaning of a mechanical wave.
metasubject:
Regulatory - set a goal, evaluate your work; correct and explain your mistakes.
Communicative - engage in dialogue. Be able to listen and hear, express your thoughts, build statements, participate in a collective discussion of problems, take into account the positions of others.
cognitive - analyze the learning situation; develop operations of thinking; set a task based on the correlation of what is known, semantic reading; the ability to adequately, consciously and arbitrarily speech statements in oral and written speech, conveying the content of the text in accordance with the purpose and compliance with the norms of constructing the text; highlighting is significant.
Personal : to form interest and practical skills, independence in acquiring knowledge about a mechanical wave, a value relationship to each other, to the teacher, to the learning outcome, to develop initiative.
Technologies used Key words: critical thinking technology, collaborative learning technology, information and communication technology.
Information Technology Resources :
List of used sources and literature :
Textbook "Physics Grade 9" A, V. Peryshkin EAT. Gutnik Textbook for educational institutions 2nd edition - M: Bustard, 2014
Lukashnikov.I. collection of tasks in physics for grades 7-9 of educational institutions - M: education
COR in physics Grade 9
Equipment : for experiment: spring, wave machine, geographic map
Lesson type Learning new
Teaching methods Conversation. Demonstration of experiences. Notes on the board and in a notebook. Deductive application of theoretical knowledge.
During the classes
1. Organizational moment
Greetings.
A brief mood for productive work.
2.Front survey
Formation of the topic of the lesson and the purpose of the lesson. Understanding and accepted by the children the objectives of the lesson
Creating a problem situation
a) Analysis of formulas and units of measurement.
E-frequency
T - number of oscillations
N - energy
l - oscillation time
v - amplitude
b) Poll on questions
1. Give an example of oscillatory movement?
2.What fluctuations do you know?
3. Studying a new topic.
Inclusion of students in purposeful activities.
Let's find a connection between oscillations and a wave. Let's turn to a simple experiment. We fix the spring with one ring, and hit the other end with our hand. 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 in its equilibrium movement, so the coils, bypassing the equilibrium position, will continue to diverge. As a result, some vacuum is formed in this place of the spring. If the end of the spring is rhythmically struck with a hand, then with each blow the coils will approach each other, forming a thickening and moving away from each other, forming a vacuum.
Perturbations propagating in space moving away from their place of origin is called a wave. The simplest type of oscillation is waves that arise on the surface of a liquid and radiate from the place of disturbance in the form of concentric circles.
Such waves can arise not only in liquids and gases, but also in solids.
A wave arises only when, together with an external perturbation, forces appear in the medium that counteract it. Usually these are elastic forces.
Mechanical waves arise and mix only in elastic media. This is what allows the particles in the wave to transfer excess energy to neighboring particles. In this case, the particles, having transferred part of the energy, return to their original position. This process continues. Thus, the matter in the wave does not move. The particles of the medium oscillate around their equilibrium positions. Therefore, in a traveling wave, energy is transferred without transfer of matter.
Depending on the direction in which the particles oscillate relative to the direction of movement of the wave, longitudinal and transverse waves are distinguished.
In a longitudinal wave, the particles oscillate in directions that coincide with the movement. Such waves arise as a result of compression and tension.
Therefore, they can occur in gases, liquids and solids.
In a transverse wave, particles oscillate in planes perpendicular to the direction of wave travel. Such waves are the result of shear deformation. Therefore, waves can only arise in solids. For in gases and liquids this type of deformation is impossible.
Demonstration of a wave using a wave machine.
Film screening 5 minutes.
The wave phenomenon in elastic media is characterized by certain values, these include:
E-wave energy
A - wave amplitude
v-wave frequency
T - wave period
Wave speed
Wavelength
The speed of mechanical waves, depending on the type of wave, can vary from hundreds of m/s to 10 km/s
The length of a mechanical wave is understood as the distance that the wave travels in a time equal to the period of oscillation.
Formulas: Invite students to write their own formulas
Oscillations that form in the solid part of the Earth during various tectonic processes or during underground nuclear explosions are called seismic waves.
In the solid part of the Earth, both longitudinal and transverse waves can form.
Longitudinal waves compress and stretch the rocks through which they pass. Longitudinal waves are the fastest. Their speed reaches about 8 km / s, and the speed of transverse waves is 4.5 km / s. The difference in the velocities of the two types of waves makes it possible to determine the epicenter of earthquakes and is recorded by a seismograph instrument. Seismologists try to predict where and when an earthquake might occur so that people can prepare for it. Every 5 minutes, one earthquake occurs on Earth. Hundreds of thousands of earthquakes are recorded every year on the globe. From time to time there are those that violate the integrity of the soil, destroy buildings and lead to human casualties. There are two scales for recording an earthquake, the Richter scale and the Mercalle scale.
The Richter scale measures the strength of seismic waves. Presentation - (Table)
The Merkell scale measures the consequences of earthquakes associated with human casualties and the destruction of buildings. A weak earthquake can have more serious consequences than even very powerful ones if they occur in a city where there are many buildings and where many people live.
Here are some earthquakes of the last century that had catastrophic consequences. (Presentation)
1960 Morocco Agadar
1966 24.04. Tashkent plant 8 points
1969 May 28, Turkey 7.5 points
1969 In 22 states of America 5-7 points
1976 Thai plant 7-8 points 20 thousand people
In recent years in Turkey, in Japan.
Predicting an earthquake is a very difficult task.
There are large areas where there is no earthquake at all and there are areas of frequent earthquakes.
Two areas: Work on the map (the student shows the areas on the map)
The Pacific ring - covers the coast of Kamchatka, Alaska, the coast of North America turns to Australia, through Indonesia, the coast of China, captures Japan and ends in Kamchatka.
The second region is the Mediterranean-Asian. They pass in a wide strip from Portugal and Spain - through Italy, the Balkan Peninsula, Greece, Turkey, the Caucasus, the countries of Asia Minor enter the Baikal region and then merge onto the Pacific coast.
People have always tried to reduce the effects of earthquakes and built special buildings in earthquake-prone areas that could withstand significant tremors. Science cannot but warn, predict these phenomena generated by the force of nature. But work in this area is underway.
Here are some of them.
Before an earthquake, the concentration of radon in water increases, and a few days before the disaster, it normalizes.
The animal world is good at predicting earthquakes. Mass migration of ants, snakes and lizards leave their homes.
Deep-sea fish are thrown ashore, whiskered cod, eel. Dogs, elephants, hippos. (Presentation)
Ultrasound can be a warning signal.
4. Rest and mood for subsequent work.
Physical education minute.
5. Verification work .
Consolidation of the material through group and individual work (mutual verification). Grading.
6. Ensuring children understand the purpose, content and methods of doing homework
2. Composition and solve the problem according to the schedule
3. Prepare a message on the topic "tsunami".
The teacher gives differentiated homework, taking into account the individual abilities of the children.
7. The results of the lesson, reflection.
Can you name the topic of the lesson?
What new did you learn at the lesson today?
Municipal Autonomous General Educational Institution
"Secondary school No. 1 in Svobodny"
mechanical waves
Grade 9
Teacher: Malikova
Tatyana Viktorovna
The purpose of the lesson :
give students the concept of wave motion as a process of propagation of vibrations in space over time; introduce different types of waves; form an idea of the length and speed of wave propagation; show the importance of waves in human life.
Educational objectives of the lesson:
1. Repeat with students the basic concepts that characterize waves.
2. Repeat and introduce students to new facts and examples of the use of sound waves. To teach how to fill in the table with examples from the speeches during the lesson.
3. To teach students to use interdisciplinary connections to understand the phenomena being studied.
Educational tasks of the lesson:
1. Education of worldview concepts (cause-and-effect relationships in the world, the cognizability of the world).
2. Education of moral positions (love for nature, mutual respect).
Developing tasks of the lesson:
1. Development of independent thinking and intelligence of students.
2. Development of communication skills: competent oral speech.
During the classes:
Organizing time
Learning new material
Wave phenomena observed in everyday life. The prevalence of wave processes in nature. The different nature of the causes that cause wave processes. Wave definition. Reasons for the formation of waves in solids, liquids. The main property of waves is the transfer of energy without the transfer of matter. Characteristic features of two types of waves - longitudinal and transverse. Mechanism of propagation of mechanical waves. Wavelength. Wave propagation speed. Circular and linear waves.
Anchoring : demonstration of a presentation on the topic: “Mechanical
waves"; test
Homework : §42,43,44
Demos: transverse waves in the cord, longitudinal and transverse waves on the model
Frontal experiment: acquisition and observation of circular and linear waves
Video clip: circular and linear waves.
We turn to the study of the propagation of oscillations. If we are talking about mechanical vibrations, that is, about the oscillatory motion of any solid, liquid or gaseous medium, then the propagation of vibrations means the transmission of vibrations from one particle of the medium to another. The transmission of oscillations is due to the fact that adjacent sections of the medium are interconnected. This connection can be carried out in various ways. It can be caused, in particular, by the elastic forces arising from the deformation of the medium during its vibrations. As a result, a vibration caused in any way in one place entails the successive occurrence of vibrations in other places, more and more remote from the original, and a so-called wave is obtained.
Why do we study wave motion at all? The fact is that wave phenomena are of great importance for everyday life. These phenomena include the propagation of sound vibrations, due to the elasticity of the air around us. Thanks to elastic waves, we can hear at a distance. Circles running up on the surface of the water from a thrown stone, small ripples on the surface of lakes and huge ocean waves are also mechanical waves, although of a different type. Here, the connection of adjacent sections of the water surface is not due to elasticity, but to the force of gravity or the forces of surface tension.
Tsunamis are huge ocean waves. Everyone has heard of them, but do you know why they form?
They occur mainly during underwater earthquakes, when there are rapid displacements of sections of the seabed. They can also occur as a result of explosions of underwater volcanoes and strong landslides.
In the open sea, tsunamis are not only not destructive, but, moreover, they are invisible. The height of the tsunami waves does not exceed 1-3 m. If such a wave, which has a huge supply of energy, rapidly sweeps under the ship, then it will only gently rise, and then just as smoothly descend. And the tsunami wave sweeps through the ocean spaces truly rapidly, at a speed of 700-1000 km / h. For comparison, a modern jet liner flies at the same speed.
Having arisen, a tsunami wave is able to travel thousands and tens of thousands of kilometers across the ocean, almost without weakening.
Being completely safe in the open ocean, such a wave becomes extremely dangerous in the coastal zone. She puts all her unspent huge energy into a crushing blow to the shore. At the same time, the wave speed decreases to 100-200 km / h, while the height increases to tens of meters.
The last time a tsunami hit Indonesia in December 2004 killed over 120,000 people and made over a million people homeless.
That is why it is so important to study these phenomena and, if possible, prevent such tragedies.
In the air, not only sound waves can propagate, but also destructive blast waves. Seismic stations record ground vibrations caused by earthquakes occurring thousands of kilometers away. This is possible only because seismic waves propagate from the place of the earthquake - vibrations in the earth's crust.
A huge role is also played by wave phenomena of a completely different nature, namely electromagnetic waves. The phenomena caused by electromagnetic waves include, for example, light, the importance of which for human life can hardly be overestimated.
In subsequent lessons, we will consider the use of electromagnetic waves in more detail. In the meantime, let's return to the study of mechanical waves.
The process of propagation of oscillations in space over time is called wave . The particles of the medium in which the wave propagates are not transferred, they only oscillate around their equilibrium positions.
Depending on the direction of particle oscillations with respect to the direction of wave propagation, there are longitudinal and transverse waves.
Experience. Hang a long cord at one end. If the lower end of the cord is quickly taken to the side and returned back, then the “bend” will run up the cord. Each point of the cord oscillates perpendicular to the direction of wave propagation, that is, across the direction of propagation. Therefore, waves of this type are called transverse.
What results in the transmission of oscillatory motion from one point of the medium to another, and why does it occur with a delay? To answer this question, we need to understand the dynamics of the wave.
Displacement towards the lower end of the cord causes deformation of the cord at this point. Elastic forces appear, tending to destroy the deformation, that is, tensions appear that pull the immediately adjacent section of the cord following the section displaced by our hand. The displacement of this second section causes deformation and tension of the next one, and so on. The sections of the cord have mass, and therefore, due to inertia, they do not gain or lose speed under the action of elastic forces instantly. When we brought the end of the cord to the greatest deviation to the right and began to lead it to the left, the adjacent section will still continue to move to the right, and only with some delay will stop and also go to the left. Thus, the delayed transition of the vibration from one point of the cord to another is explained by the presence of elasticity and mass in the material of the cord.
direction propagation direction
wave oscillations
The propagation of transverse waves can also be shown using a wave machine. White balls simulate the particles of the medium, they can slide along the vertical rods. The balls are connected by threads to the disk. When the disc rotates, the balls move in concert along the rods, their movement resembles a wave pattern on the surface of water. Each ball moves up and down without shifting to the sides.
Now let's pay attention to how the two extreme balls move, they oscillate with the same period and amplitude, and at the same time they are either in the upper or lower position. They are said to oscillate in the same phase.
The distance between the nearest points of a wave oscillating in the same phase is called wavelength. The wavelength is denoted by the Greek letter λ.
Now let's try to simulate longitudinal waves. As the disc rotates, the balls oscillate from side to side. Each ball periodically deviates either to the left or to the right from the equilibrium position. As a result of oscillations, the particles either approach each other, forming a clot, or diverge, creating a rarefaction. The direction of the ball oscillations coincides with the direction of wave propagation. Such waves are called longitudinal.
Of course, the definition of wavelength remains in full force for longitudinal waves.
Direction
wave propagation
oscillation direction
Both longitudinal and transverse waves can only occur in an elastic medium. But in any? As already mentioned, in a transverse wave, the layers are shifted relative to each other. But elastic forces in shear arise only in solids. In liquids and gases, adjacent layers freely slide over each other without the appearance of elastic forces. And since there are no elastic forces, then the formation of transverse waves is impossible.
In a longitudinal wave, sections of the medium experience compression and rarefaction, that is, they change their volume. Elastic forces with a change in volume arise both in solids, and in liquids, and in gases. Therefore, longitudinal waves are possible in bodies that are in any of these states.
The simplest observations convince us that the propagation of mechanical waves does not occur instantaneously. Everyone has seen how gradually and evenly the circles on the water expand or how the waves of the sea run. Here we directly see that the propagation of vibrations from one place to another takes a certain time. But for sound waves, which are invisible under normal conditions, it is easy to detect the same thing. If in the distance there was a shot, a whistle of a locomotive, a blow to some object, then we first see these phenomena and only after some time hear the sound. The farther away from us the sound source, the greater the delay. The time interval between a flash of lightning and a thunderclap can sometimes reach up to several tens of seconds.
For a time equal to one period, the wave propagates over a distance equal to the wavelength, so its speed is determined by the formula:
v=λ /T or v=λν
Task: the fisherman noticed that in 10 seconds the float makes 20 oscillations on the waves, and the distance between adjacent wave crests is 1.2 m. What is the speed of wave propagation?
Given: Solution:
λ=1.2 m T=t/N v=λN/t
v-? v=1.2*20/10=2.4 m/s
Now back to the types of waves. Longitudinal, transverse ... And what other waves are there?
Let's watch a movie clip
Spherical (circular) waves
Plane (linear) waves
The propagation of a mechanical wave, which is a successive transfer of motion from one section of the medium to another, means thereby the transfer of energy. This energy is delivered by the wave source when it sets in motion the layer of the medium adjacent to it. From this layer, energy is transferred to the next layer, and so on. When a wave encounters various bodies, the energy it carries can produce work or be converted into other forms of energy.
Explosive waves give us a vivid example of such energy transfer without transfer of matter. At distances of many tens of meters from the explosion site, where neither fragments nor a stream of hot air reach, the blast wave knocks out glass, breaks walls, etc., that is, it produces a lot of mechanical work. We can observe these phenomena on TV, for example, in war films.
The transfer of energy by a wave is one of the properties of waves. What other properties are inherent in waves?
reflection
refraction
interference
diffraction
But we will talk about all this in the next lesson. And now let's try to repeat everything that we learned about waves in this lesson.
Questions to the class + demonstration of a presentation on this topic
And now let's check how well you learned the material of today's lesson with the help of a small test.
The purpose of the lesson: to form ideas about the process of propagation of mechanical waves; enter the physical characteristics of the waves: length, speed.
During the classes
Checking homework by frontal survey
1. How are waves formed? What is a wave?
2. What waves are called transverse? Give examples.
3. What waves are called longitudinal? Give examples.
4. How is wave motion related to energy transfer?
Learning new material
1. Consider how a transverse wave propagates along a rubber cord.
2. Let's divide the cord into sections, each of which has its own mass and elasticity. When deformation begins, the elastic force can be detected in any section of the cord.
The elastic force tends to the initial position of the cord. But since each section has inertia, the oscillations do not stop in the equilibrium position, but continue to move until the elastic forces stop this section.
In the figure, we see the positions of the balls at certain points in time, which are separated from each other by a quarter of the period of oscillation. The vectors of the speeds of movement of the sections, at the corresponding points in time, are shown by arrows
3. Instead of a rubber cord, you can take a chain of metal balls suspended on threads. In such a model, the elastic and inertial properties are separated: the mass is concentrated in the balls, and the elasticity in the springs. P 
4. The figure shows longitudinal waves propagating in space in the form of condensation and rarefaction of particles.
5. The wavelength and its speed are the physical characteristics of the wave process.
In one period, the wave propagates over a distance, which we will denote - λ is the wavelength.
The distance between 2 points closest to each other, oscillating in the same phases, is called the wavelength.
6. The speed of a wave is equal to the product of the wavelength and the frequency of oscillations.
7. V = λ/T; since Т= 1/ν, then V=λ ν
8. Periodicity of two kinds can be observed when a wave propagates along a filament.
Firstly, each particle in the cord makes vibrations. If the oscillations are harmonic, then the frequency and amplitude are the same at all points and the oscillations will differ only in phases.
Secondly, the waveform is repeated through segments whose length is equal to - λ. 
The figure shows the wave profile at a given time. As time passes, this whole picture moves at a speed V from left to right. After a time Δt, the wave will have the form shown in the same figure. The formula V= λ·ν is valid for both longitudinal and transverse waves.
Consolidation of the studied material
Problem #435
Given: V= λ/T; T= λ/V T= 3/6 = 0.5 s
Mechanical (or elastic) waves are called mechanical perturbations (deformations) propagating in an elastic medium. The bodies that, acting on an elastic medium, cause these perturbations, are called sources of elastic waves.
The medium is called elastic, and the deformations caused by external influences are called elastic deformations if they completely disappear after the termination of these influences. At sufficiently small deformations, all solid bodies can practically be considered elastic.
Gas has volumetric elasticity, i.e. the ability to resist a change in its volume.
According to Hooke's law for volumetric deformation
, where
– change in gas pressure with a small change in its volume;
is the volumetric elasticity modulus of the gas.
For an ideal gas, the value depends on the type of thermodynamic process. With a very slow change in gas volume, the process can be considered isothermal, and with a very fast one, it can be considered adiabatic.
In the first case pV = const and after differentiation we get.
In the second case pV γ = const and
Liquids and gases have only volumetric elasticity.
Solid bodies, in addition to bulk elasticity, have shape elasticity, which manifests itself in their resistance to shear deformation.
Unlike other types of mechanical motion of a medium (for example, its flow), the propagation of elastic waves in a medium is not associated with the transfer of matter.
An elastic wave is called longitudinal if the particles of the medium oscillate in the direction of wave propagation. Longitudinal waves are associated with volumetric deformation of the medium and therefore can propagate in any medium - solid, liquid and gaseous. An example of such waves are sound (acoustic) waves.
Audible sound - 16 Hz< ν < 20 кГц
Infrasound - ν<16 Гц
Ultrasound – ν > 20 kHz
Hypersound – ν >1 GHz.
An elastic wave is called a transverse wave if the particles of the medium oscillate, remaining in planes perpendicular to the direction of wave propagation. Transverse waves are associated with the shear deformation of an elastic medium and, therefore, can only propagate in solids. For example, waves propagating along the strings of musical instruments.
Surface waves are waves propagating along the free surface of a liquid (or the interface between two immiscible liquids).
The equation of an elastic wave is the dependence on the coordinates and time of scalar or vector quantities characterizing the oscillations of the medium during the passage of the considered wave in it.
For waves in a solid body, such a quantity can be the displacement vector of a particle of the medium from the equilibrium position or its three projections on the coordinate axes. In a gas or liquid, the overpressure of an oscillating medium is usually used.
A line, the tangent to which at each of its points coincides with the direction of wave propagation, i.e. with the direction of energy transfer by a wave is called a beam. In a homogeneous medium, the rays have the form of straight lines.
An elastic wave is called harmonic if the particle oscillations corresponding to it are harmonic. The frequency of these oscillations is called the wave frequency.
The wave surface or wave front is the locus of points at which the phase of the oscillations has the same value. In a homogeneous isotropic medium, the wave surfaces are orthogonal to the rays.
A wave is called flat if its wave surfaces are a set of planes parallel to each other.
In a plane wave propagating along the OX axis, all quantities ξ characterizing the oscillatory motion of the medium depend only on the time t and the coordinate x of the point M of the medium. If there is no absorption of waves in the medium, then oscillations in TM differ from oscillations at the origin O, occurring according to the law, only in that they are shifted in time by x/υ, where υ is the phase velocity of the wave.
The phase velocity of a wave is the speed of movement in the space of points of the surface corresponding to any fixed value of the phase.
For shear waves
a) along a stretched string, where
F is the string tension force;
ρ is the density of the string material;
S is the cross-sectional area of the string.
B) in an isotropic solid, where
G is the shear modulus of the medium;
ρ is the density of the medium.
For longitudinal waves
a) in a thin rod, where
Е – Young's modulus of the rod material;
ρ is the density of the rod material.
B) in liquid and gas, where
χ is the volumetric elasticity modulus of the medium;
ρ is the density of the unperturbed medium.
B) in an ideal gas, where
γ is the gas adiabatic index;
M is the molar mass of the gas;
T is the gas temperature.
For a plane harmonic wave propagating in a nonabsorbing medium along the positive direction of the OX axis, the elastic wave equation has the form
or
The distance λ \u003d υ.T, over which a harmonic wave propagates in a time equal to the oscillation period, is called the wavelength (the distance between the two nearest points of the medium at which the phase difference of the oscillations is 2π.
Another characteristic of a harmonic wave is the wave number k, which shows how many wavelengths fit on a segment of length 2π:
, then
.
A wave vector is a vector whose modulus is equal to the wave number k and directed along the beam at the considered point M of the medium.
For a plane wave propagating along the ОХ, therefore, where is the radius vector t.M.
Thus
.
The wave equation can also be written using the Euler formula for complex numbers, in an exponential form that is convenient for differentiation
, where.
Only the real part of the complex quantity has physical meaning, i.e. . Using to find any characteristic of the wave, after performing all mathematical operations, it is necessary to discard the imaginary part of the resulting complex expression.
A wave is called spherical if its wave surfaces look like concentric spheres. The center of these spheres is called the center of the wave.
Divergent spherical wave equation
, where
r is the distance from the wave center to the t.M.
For a harmonic spherical wave
and,
Where A(r) is the wave amplitude; φо is the initial phase of oscillations in the center of the wave.
Real sources of waves can be considered point (sources of spherical waves) if the distance r from the source of oscillations to the considered points of the medium is much larger than the size of the source.
If r is very large, then any small sections of the wave surfaces can be considered flat.
In a homogeneous, isotropic, non-absorbing medium, plane and spherical waves are described by a partial differential equation, which is called the wave equation.
, where
is the Laplace operator or Laplacian.
