Mechanical waves abstract in physics. Lesson summary "mechanical waves and their main characteristics." Lesson type Learning new things
LESSON 7/29
Subject. Mechanical waves
Purpose of the lesson: to give students the concept of wave motion as a process of propagation of vibrations in space over time.
Lesson type: lesson on learning new material.
LESSON PLAN
Knowledge control |
1. Energy conversion during oscillations. 2. Forced vibrations. 3. Resonance |
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Demonstrations |
1. Formation and propagation of transverse and longitudinal waves. 2. Fragments of the video “Transverse and Longitudinal Waves” |
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Learning new material |
1. Mechanical waves. 2. Basic characteristics of waves. 3. Interference of waves. 4. Transverse and longitudinal waves |
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Reinforcing the material learned |
1. Qualitative questions. 2. Learning to solve problems |
LEARNING NEW MATERIAL
The sources of waves are oscillating bodies. If such a body is located in any medium, vibrations are transmitted to adjacent particles of the substance. And since particles of matter interact with each other, vibrating particles transmit vibrations to their “neighbors.” As a result, vibrations begin to spread in space. This is how waves arise.
Ø A wave is the process of propagation of oscillations over time.
Mechanical waves in the medium are caused by elastic deformations of the medium. The formation of a wave of one type or another is explained by the presence of force connections between the particles participating in the oscillations.
Any wave carries energy, because a wave is vibrations propagating in space, and any vibrations, as we know, have energy.
Ø A mechanical wave transfers energy, but does not transfer matter.
If the source of the waves performs harmonic oscillations, then each point of the given medium in which the oscillations propagate also performs harmonic oscillations, and with the same frequency as the source of the waves. In this case, the wave has a sinusoidal shape. Such waves are called harmonic. The maximum of a harmonic wave is called its crest.
As an example, consider a wave that runs along a cord when one end of it oscillates under the influence of an external force. If we observe any point on the cord, we will notice that each point oscillates with the same period.
Ø The time period T during which one complete oscillation occurs is called the oscillation period.
A complete oscillation occurs during the time when a body returns from one extreme position to this extreme position.
Ø Oscillation frequency v is a physical quantity equal to the number of oscillations per unit time.
Ø The magnitude of the greatest deviation of particles from the equilibrium position is called the amplitude of the wave.
The period of a wave and its frequency are related by the relation:
The unit of vibration frequency is called hertz (Hz): 1 Hz = 1/s.
Ø The distance between the nearest points of a wave that move the same way is called the wavelength and is denoted by λ.
Since waves are vibrations that propagate in space over time, let’s find out what the speed of propagation of waves is. In a time equal to one period T, each point of the medium carried out exactly one oscillation and returned to the same position. So, the wave has shifted in space by exactly one wavelength. Thus, if we denote the speed of wave propagation , we obtain that the wavelength is equal to:
λ = T.
Since T = 1/v, we find that the wave speed, wavelength and wave frequency are related by the relation:
= λv.
Waves from different sources propagate independently of each other, due to which they pass freely through one another. By superimposing waves with the same lengths, one can observe the strengthening of waves at some points in space and weakening at others.
Ø Mutual amplification or attenuation in space of two or more waves with the same length is called wave interference.
Mechanical waves are transverse and longitudinal:
Transverse wave particles oscillate across the direction of wave propagation (in the direction of energy transfer), and longitudinal wave particles oscillate along the direction of wave propagation.
Ø Waves in which the particles of the medium during oscillations are displaced in a direction perpendicular to the direction of propagation of the wave are called transverse.
Transverse waves can only propagate in solids. The fact is that such waves are caused by shear deformations, and in liquids and gases there are no shear deformations: liquids and gases do not “resist” a change in shape.
Ø Waves in which the particles of the medium during oscillations are displaced along the direction of propagation of the wave are called longitudinal.
An example of a longitudinal wave is a wave that runs along a soft spring when one end of it oscillates under the influence of a periodic external force directed along the spring. Longitudinal waves can propagate in any medium. The relation = λ v and λ = T are valid for both types of waves.
QUESTIONS TO STUDENTS DURING PRESENTATION OF NEW MATERIAL
First level
1. What are mechanical waves?
2. Is the wavelength of the same frequency the same in different media?
3. Where can transverse waves propagate?
4. Where can longitudinal waves propagate?
Second level
1. Are transverse waves possible in liquids and gases?
2. Why do waves transfer energy?
CONSTRUCTION OF LEARNED MATERIAL
WHAT WE LEARNED IN LESSON
· A wave is the process of propagation of oscillations over time.
· The time period T during which one complete oscillation occurs is called the oscillation period.
· Oscillation frequency v is a physical quantity equal to the number of oscillations per unit time.
· The distance between the nearest points of a wave that move the same way is called the wavelength and is denoted by λ.
· Mutual amplification or attenuation in space of two or more waves of the same length is called wave interference.
· Waves in which the particles of the medium during oscillations are displaced in a direction perpendicular to the direction of propagation of the wave are called transverse.
· Waves in which particles of the medium during oscillations are displaced along the direction of propagation of the wave are called longitudinal.
Riv1 No. 10.12; 10.13; 10.14; 10.24.
Riv2 No. 10.30; 10.46; 10.47; 10.48.
Riv3 No. 10.55, 10.56; 10.57.
Municipal autonomous educational institution
"Secondary school No. 1 in Svobodny"
Mechanical waves
9th grade
Teacher: Malikova
Tatyana Viktorovna
The purpose of the lesson :
give students the concept of wave motion as the 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.Review with students the basic concepts that characterize waves.
2.Revise and introduce students to new facts and examples of the use of sound waves. Teach how to fill out the table with examples from speeches during the lesson.
3. Teach students to use interdisciplinary connections to understand the phenomena being studied.
Educational objectives of the lesson:
1. Education of worldview concepts (cause-and-effect relationships in the surrounding world, cognition of the world).
2. Fostering moral attitudes (love of nature, mutual respect).
Developmental objectives 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. Prevalence of wave processes in nature. The different nature of the causes causing wave processes. Definition of a wave. Reasons for the formation of waves in solids and liquids. The main property of waves is the transfer of energy without 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.
Consolidation : presentation demonstration 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: receiving and observing circular and linear waves
Video fragment: circular and linear waves.
We move on to studying the propagation of oscillations. If we are talking about mechanical vibrations, that is, the oscillatory movement of any solid, liquid or gaseous medium, then the propagation of vibrations means the transfer of vibrations from one particle of the medium to another. The transmission of vibrations is due to the fact that adjacent areas of the medium are connected to each other. This connection can be carried out in different ways. It can be caused, in particular, by elastic forces arising as a result of deformation of the medium during its vibrations. As a result, an oscillation caused in some way in one place entails the successive occurrence of oscillations in other places, more and more distant from the original one, 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, caused by the elasticity of the air around us. Thanks to elastic waves, we can hear at a distance. Circles scattering 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 between adjacent sections of the water surface is due not to elasticity, but to gravity or surface tension forces.
Tsunami - huge ocean waves. Everyone has heard about them, but do you know why they are formed?
They arise mainly during underwater earthquakes, when rapid displacements of sections of the seabed occur. They can also occur as a result of explosions of underwater volcanoes and severe landslides.
In the open sea, tsunamis are not only not destructive, but, moreover, they are invisible. The height of tsunami waves does not exceed 1-3 m. If such a wave, which has a huge supply of energy, rapidly sweeps under a ship, then it will only rise smoothly and then fall just as smoothly. And the tsunami wave sweeps across the ocean expanses truly rapidly, at a speed of 700-1000 km/h. For comparison, a modern jet airliner flies at the same speed.
Once a tsunami wave has arisen, it can travel thousands and tens of thousands of kilometers across the ocean, almost without weakening.
While completely safe in the open ocean, such a wave becomes extremely dangerous in the coastal zone. She puts all her unspent enormous energy into a crushing blow to the shore. In this case, the wave speed decreases to 100-200 km/h, while the height increases to tens of meters.
The last tsunami hit Indonesia in December 2004 and killed over 120 thousand people, leaving more than a million people homeless.
That is why it is so important to study these phenomena and, if possible, prevent such tragedies.
Not only sound waves can travel through the air, but also destructive blast waves. Seismic stations record ground vibrations caused by earthquakes occurring thousands of kilometers away. This is only possible because seismic waves - vibrations in the earth's crust - propagate from the site of the earthquake.
Wave phenomena of a completely different nature, namely electromagnetic waves, also play a huge role. Phenomena caused by electromagnetic waves include, for example, light, the importance of which for human life is difficult to overestimate.
In subsequent lessons we will look at the use of electromagnetic waves in more detail. For now, let's return to the study of mechanical waves.
The process of propagation of vibrations 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 relative 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 pulled to the side and returned back, the “bend” will run upward along the cord. Each point of the cord oscillates perpendicular to the direction of propagation of the wave, that is, across the direction of propagation. Therefore, waves of this type are called transverse.
What results in the transfer 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 in this place. Elastic forces appear, striving to destroy the deformation, that is, tensions appear that pull the immediately adjacent section of the cord after the section displaced by our hand. The displacement of this second section causes deformation and tension in the next one, etc. Sections of the cord have mass, and therefore, due to inertia, they do not gain or lose speed under the influence of elastic forces instantly. When we have brought the end of the cord to the greatest deviation to the right and begin to move 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 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 direction of propagation
wave oscillations
The propagation of transverse waves can also be demonstrated using a wave machine. White balls simulate particles of the environment; they can slide along vertical rods. The balls are connected by threads to the disk. As the disk rotates, the balls move in concert along the rods, their movement reminiscent of a wave pattern on the surface of water. Each ball moves up and down without moving to the sides.
Now let’s pay attention to how the two outer balls move; they oscillate with the same period and amplitude, and at the same time they find themselves in the upper and lower positions. 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. Wavelength is denoted by the Greek letter λ.
Now let's try to simulate longitudinal waves. As the disk rotates, the balls oscillate from side to side. Each ball periodically deviates either to the left or to the right from its equilibrium position. As a result of oscillations, the particles either come together, forming a clot, or move apart, creating a vacuum. The direction of the ball's oscillations coincides with the direction of wave propagation. Such waves are called longitudinal.
Of course, for longitudinal waves the definition of wavelength remains in full force.
Direction
wave propagation
direction of vibration
Both longitudinal and transverse waves can only arise in an elastic medium. But in any case? As already mentioned, in a transverse wave the layers shift relative to each other. But elastic shear forces arise only in solid bodies. In liquids and gases, adjacent layers slide freely 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. When volume changes, elastic forces arise in both solids, liquids, and gases. Therefore, longitudinal waves are possible in bodies in any of these states.
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 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, the same thing is easy to detect. If there is a shot in the distance, a locomotive whistle, or a blow to some object, then we first see these phenomena and only after some time we hear the sound. The further the sound source is from us, the greater the delay. The time interval between a flash of lightning and a clap of thunder can sometimes reach several tens of seconds.
In 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 let's return to the types of waves. Longitudinal, transverse... What other waves are there?
Let's watch a fragment of the film
Spherical (circular) waves
Plane (linear) 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 adjacent layer of the medium. From this layer, energy is transferred to the next layer, etc. When a wave meets various bodies, the energy it carries can produce work or be converted into other types of energy.
A striking example of such energy transfer without matter transfer is provided by blast waves. At distances of many tens of meters from the explosion site, where neither fragments nor a stream of hot air reaches, the blast wave knocks out glass, breaks walls, etc., that is, it produces a lot of mechanical work. We can observe these phenomena on television, 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. Now let’s try to repeat everything we learned about waves in this lesson.
Questions for the class + demonstration of a presentation on this topic
And now let's check how much you have mastered the material of today's lesson with the help of a small test.
MINISTRY OF COMMUNICATIONS OF THE USSR
LENINGRAD ELECTROTECHNICAL INSTITUTE OF COMMUNICATIONS NAMED AFTER PROF. M. A. BONCH-BRUEVICH
S. F. Skirko, S. B. Vrasky
OSCILLATIONS
TUTORIAL
LENINGRAD
INTRODUCTION
Oscillatory processes are of fundamental importance not only in macroscopic physics and technology, but also in the laws of microphysics. Despite the fact that the nature of oscillatory phenomena is different, these phenomena have common features and are subject to general laws.
The purpose of this textbook is to help students understand these general patterns for oscillations of a mechanical system and oscillations in an electrical circuit, use a general mathematical apparatus to describe these types of oscillations and apply the method of electromechanical analogies, which greatly simplifies the solution of many issues.
A significant place in the textbook is devoted to tasks, since they develop the skill in using general laws to solve specific issues and make it possible to assess the depth of mastery of theoretical material.
IN At the end of each section, exercises with solutions to typical problems are given and problems for independent solution are recommended.
The tasks given in the textbook for independent solution can also be used in exercises, for tests and independent work and homework.
IN Some sections have tasks, some of which are related to existing laboratory work.
The textbook is intended for students of all faculties of full-time, evening and correspondence departments of the Leningrad Electrotechnical Institute of Communications named after. prof. M. A. Bonch-Bruevich.
They are of particular importance for correspondence students who work on the course independently.
§ 1. HARMONIC VIBRATION Oscillations are processes that repeat exactly or approximately
at regular intervals.
The simplest is harmonic oscillation, described by the equations:
a - amplitude of oscillation - the largest value of the quantity,
The phase of the oscillation, which together with the amplitude determines the value of x at any time,
The initial phase of the oscillation, that is, the phase value at time t=0,
ω - cyclic (circular) frequency, which determines the rate of change of the oscillation phase.
When the oscillation phase changes by 2, the values of sin(+) and cos(+) are repeated, therefore harmonic oscillation is a periodic process.
When f=0, a change in ωt by 2·π will occur in time t=T, that is
2 and |
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Time interval T-period of oscillation. In the moment |
time t, t + 2T, |
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2 + 3T, etc. - x values are the same. |
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Oscillation frequency: |
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Frequency determines the number of vibrations per second.
Unit *ω+ = rad/s; + = glad; [ + = Hz (s-1), [T] = s. By introducing frequency and period into equation (1.1), we obtain:
= ∙ sin(2 ∙ |
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1 This can be the charge of the capacitor, the current strength in the circuit, the angle of deflection of the pendulum, the coordinate of the point, etc.
Rice. 1.1
If is the distance of the oscillating point from the equilibrium position, then the speed of movement of this point can be found by differentiating x with respect to t. Let us agree to denote the derivative with respect to ℓ by, then
Cos(+) . |
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From (1.6) it is clear that the speed of a point performing a harmonic oscillation also performs a simple harmonic oscillation.
Speed amplitude
i.e., it depends on the displacement amplitude and on the oscillation frequency ω or ѵ, and therefore on the oscillation period T.
From a comparison of (1.1) and (1.6) it is clear that the argument (+) is the same in both equations, but is expressed through sine, and through cosine.
If we take the second derivative of time, we obtain an expression for the acceleration of a point, which we denote by
Comparing (1.8) with (1.9), we see that acceleration is directly related to displacement
= −2 |
acceleration is proportional to the displacement (from the equilibrium position) and is directed against (minus sign) the displacement, i.e., directed towards the equilibrium position. This property of acceleration allows us to state: a body performs simple harmonic oscillatory motion if the force acting on it is directly proportional to the displacement of the body from the equilibrium position and is directed against the displacement.
In Fig. 1.1 shows graphs of the dependence of the displacement x of a point on the equilibrium position,
velocity and acceleration of a point versus time.
Exercises
1.1. What are the possible values of the initial phase if the initial displacement is x 0 = -0.15 cm, and the initial speed x0 = 26 cm/s.
Solution: If the displacement is negative and the speed is positive, as specified by the condition, then the oscillation phase lies in the fourth quarter of the period, that is, between 270° and 360° (between -90° and 0°).
Solution: Using (1.1) and (1.6) and putting t = 0 in them, according to the condition we have a system of equations:
2cos; |
−0.15 = ∙ 2 ∙ 5 cos , |
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from which we determine and. |
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1.3. The oscillations of a material point are given in the form |
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Write the vibration equation in terms of cosine. |
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1.4. The oscillations of a material point are given in the form |
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Write the equation of oscillations in terms of sine.
Problems to solve independently
GEOMETRICAL METHOD OF REPRESENTATION OF OSCILLATIONS USING V e c t o r a m p l i t u d y .
In Fig. Figure 1.2 shows an axis from an arbitrary point of which a radius is drawn - a vector numerically equal to the amplitude. This vector rotates uniformly with angular velocity counterclockwise.
If at t = 0 the radius vector made an angle with the horizontal axis, then at time t this angle is equal to +.
In this case, the projection of the end of the vector onto the axis has the coordinate
This equation differs from (1.11) in the initial phase.
Conclusion. A harmonic oscillation can be represented by the movement of the projection onto a certain axis of the end of the amplitude vector, drawn from an arbitrary point on the axis and uniformly rotating relative to this point. In this case, the modulus a of the vector is included in the equation of harmonic oscillation as amplitude, angular velocity as cyclic frequency, and the angle that determines the position of the radius - vector at the moment the time begins to count, as the initial phase.
REPRESENTATION OF HARMONIC OSCILLATIONS
Equation (1.14) has the character of an identity. Therefore, harmonic oscillation
Asin(+), or = acos(+),
can be represented as the real part of a complex number
= (+).
If you perform mathematical operations on complex numbers, and then separate the real part from the imaginary part, you will get the same result as when operating on the corresponding trigonometric functions. This allows you to replace relatively cumbersome trigonometric transformations with simpler operations on exponential functions.
§ 2 FREE VIBRATIONS OF THE SYSTEM WITHOUT DAMPING
Free vibrations are those that occur in a system brought out of equilibrium by an external influence.
and left to its own devices. Undamped oscillations are those with constant amplitude.
Let's consider two problems:
1. Free vibrations without damping of the mechanical system.
2. Free oscillations without attenuation in the electrical circuit.
When studying solutions to these problems, pay attention to the fact that the equations describing the processes in these systems turn out to be the same, which makes it possible to use the method of analogies.
1. Mechanical system
The system consists of a body of mass connected to a fixed wall by a spring. The body moves along a horizontal plane absolutely, without friction. The mass of the spring is negligible
compared to body weight.
In Fig. 2.1, this system is depicted in the equilibrium position in Fig. 2.1, with the body unbalanced.
The force that must be applied to a spring to stretch it depends on the properties of the spring.
where is the elastic constant of the spring.
Thus, the mechanical system under consideration is a linear elastic system without friction.
After the action of the external force ceases (according to the condition, the system is removed from the state of equilibrium and left to itself), an elastic restoring force acts on the body from the side of the spring, equal in magnitude and
opposite in direction to external force |
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return = −. |
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Applying Newton's second law |
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we obtain the differential equation of the body's own motion
This is a linear (and enters into the equation to the first degree), homogeneous (the equation does not contain a free term) second-order differential equation with constant coefficients.
The linearity of the equation occurs due to the linear relationship between the force f and the deformation of the spring.
Since the restoring force satisfies condition (1.10), it can be argued that the system performs a harmonic oscillation with a cyclic
frequency = |
Which directly follows from equation (1.10) and (2.3). |
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We write the solution to equation (2.4) in the form |
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Substitution by (2.5) and into equation (2.4) turns (2.4) into an identity. Therefore, equation (2.5) is a solution to equation (2.4).
Conclusion: an elastic system, being taken out of equilibrium and left to itself, performs a harmonic oscillation with a cyclic frequency
depending on the parameters of the system and called the natural cyclic frequency.
Natural frequency and natural period of oscillation of such a system
(2.5), just like (1.1), includes two more quantities: amplitude and initial phase. These quantities were not in the original differential equation (2.4). They appear as a result of double integration as arbitrary constants. So, the properties of the system do not determine either the amplitude or the phase of its own oscillations. The amplitude of the oscillations depends on the maximum displacement caused by the external force; the initial phase of the oscillations depends on the choice of the time reference point. Thus, the amplitude and initial phase of oscillations depend on the initial conditions.
2. Electrical circuit
Let's consider the second example of free oscillations - oscillations in an electrical circuit consisting of capacitance C and inductance L (Fig. 2.2).
Loop resistance R = 0 (the condition is as unrealistic as the absence of friction in the previous problem).
Let's take the following procedure:
1. With the key open, we charge the capacitor
some charge to a potential difference. This corresponds to the system being taken out of equilibrium.
2. Turn off the source (it is not shown in the figure)
And We close the key S. The system is left to its own devices. The capacitor tends to the position balance-he
discharges. The charge and potential difference across a capacitor changes over time
Current flows in the circuit |
Also changing over time. |
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In this case, a self-inductive emf appears in the inductance
ε ind |
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At each moment, Kirhoff’s second law must be valid: the algebraic sum of voltage drops, potential differences and electromotive forces in a closed circuit is equal to zero
Equation (2.12) is a differential equation describing free oscillation in the circuit. It is in every way similar to the differential equation (2.4) discussed above for the proper motion of a body in an elastic system. The mathematical solution of this equation cannot be other than the mathematical solution (2.4), only instead of the variable it is necessary to put the variable q - the charge of the capacitor, instead of the mass to put the inductance L and instead of the elastic constant
Natural frequency
Own period
The current strength is determined as the derivative of the charge with respect to time =, i.e. current in an electrical circuit is analogous to speed in a mechanical system
In Fig. Figure 2.3 (similar to Fig. 1.1 for an elastic system) shows a charge oscillation and a current oscillation, advancing the charge oscillation in phase by 90°.
The potential difference between the plates of the capacitor also performs a harmonic oscillation:
Both systems considered - mechanical and electrical - are described by the same equation - a second-order linear equation. The linearity of this equation reflects the characteristic properties of systems. It stems from the linear dependence of force and deformation expressed in (2.1), and the linear dependence of the voltage on the capacitor on the charge of the capacitor, expressed in (2.10), and
Induction emf from = expressed in (2.11).
The analogy in the description of elastic and electrical systems established above will turn out to be very useful in further acquaintance with oscillations. Here is a table in which
One line contains quantities that are similarly described mathematically.
11.1. Mechanical vibrations– the movement of bodies or particles of bodies, with varying degrees of repeatability in time. Main characteristics: oscillation amplitude and period (frequency).
11.2. Sources of mechanical vibrations– unbalanced forces from various bodies or parts of bodies.
11.3. Amplitude of mechanical vibrations– the greatest displacement of the body from the equilibrium position. The amplitude unit is 1 meter (1 m).
11.4. Oscillation period- the time during which an oscillating body will complete one complete oscillation (forward and backward, passing through the equilibrium position twice). The period unit is 1 second (1 s).
11.5. Oscillation frequency– physical quantity reciprocal to the period. The unit is 1 hertz (1 Hz = 1/s). Characterizes the number of oscillations performed by a body or particle per unit of time.
11.6. Thread pendulum– a physical model that includes a weightless inextensible thread and a body whose dimensions are negligible compared to the length of the thread, located in a force field, usually the gravitational field of the Earth or another celestial body.
11.7. Period of small oscillations of a thread pendulum is proportional to the square root of the length of the thread and inversely proportional to the square root of the coefficient of gravity.
11.8. Spring pendulum– a physical model that includes a weightless spring and a body attached to it. The presence of a gravitational field is not mandatory; such a pendulum can oscillate both vertically and along any other direction.
11.9. Period of small oscillations of a spring pendulum is directly proportional to the square root of the body mass and inversely proportional to the square root of the spring stiffness coefficient.
11.10. In relation to oscillating bodies, free, undamped, damped, forced oscillations and self-oscillations are distinguished.
11.11. Mechanical wave– the phenomenon of propagation of mechanical vibrations in space (in an elastic medium) over time. A wave is characterized by the speed of energy transfer and wavelength.
11.12. Wavelength– the distance between the nearest wave particles that are in the same state. The unit is 1 meter (1 m).
11.13. Wave speed is defined as the ratio of the wavelength to the period of oscillation of its particles. The unit is 1 meter per second (1 m/s).
11.14. Properties of mechanical waves: reflection, refraction and diffraction at the interface between two media with different mechanical properties, as well as interference of two or more waves.
11.15. Sound waves (sound)– these are mechanical vibrations of particles of an elastic medium with frequencies in the range of 16 Hz - 20 kHz. The frequency of sound emitted by a body depends on the elasticity (stiffness) and size of the body.
11.16. Electromagnetic vibrations– a collective concept that includes, depending on the situation, changes in charge, current, voltage, and intensity of the electric and magnetic fields.
11.17. Sources of electromagnetic vibrations– induction generators, oscillatory circuits, molecules, atoms, atomic nuclei (that is, all objects where there are moving charges).
11.18. Oscillatory circuit– an electrical circuit consisting of a capacitor and an inductor. The circuit is designed to generate high frequency alternating electric current.
11.19. Amplitude of electromagnetic oscillations– the greatest change in the observed physical quantity characterizing the processes in the oscillatory circuit and the space around it.
11.20. Period of electromagnetic oscillations– the shortest time during which the values of all quantities characterizing electromagnetic oscillations in the circuit and the space around it return to their previous values. The period unit is 1 second (1 s).
11.21. Electromagnetic frequency– physical quantity reciprocal to the period. The unit is 1 hertz (1 Hz = 1/s). Characterizes the number of fluctuations of values per unit of time.
11.22. By analogy with mechanical oscillations, in relation to electromagnetic oscillations, free, undamped, damped, forced oscillations and self-oscillations are distinguished.
11.23. Electromagnetic field– a set of electric and magnetic fields propagating in space, constantly changing and transforming into each other – an electromagnetic wave. Speed in vacuum and air is 300,000 km/s.
11.24. Electromagnetic wavelength is defined as the distance over which the oscillations spread during one period. By analogy with mechanical oscillations, it can be calculated by multiplying the wave speed and the period of electromagnetic oscillations.
11.25. Antenna– an open oscillatory circuit used to emit or receive electromagnetic (radio) waves. The length of the antenna should be longer, the longer the wavelength.
11.26. Properties of electromagnetic waves: reflection, refraction and diffraction at the interface between two media with different electrical properties and interference of two or more waves.
11.27. Radio transmission principles: the presence of a high-frequency carrier frequency generator, an amplitude or frequency modulator, and a transmitting antenna. Principles of radio reception: the presence of a receiving antenna, tuning circuit, demodulator.
11.28. Principles of television coincide with the principles of radio communication with the addition of the following two: electronic scanning with a frequency of about 25 Hz of the screen on which the transmitted image is located and synchronous element-by-element transmission of the video signal to the video monitor.
Lesson type: lesson of communicating new knowledge.
Target: introduce the concepts of wave length and speed, teach students to apply formulas to find wave length and speed.
Tasks:
familiarize students with the origin of the term “wavelength, wave speed”
be able to compare types of waves and draw conclusions
obtain the relationship between wave speed, wavelength and frequency
introduce a new concept: wavelength
teach students to apply formulas to find wavelength and speed
be able to analyze a graph, compare, draw conclusions
Technical means:
Personal Computer
-multimedia projector
-
Lesson plan:
1. Organization of the beginning of the lesson.
2. Updating students' knowledge.
3. Assimilation of new knowledge.
4. Consolidation of new knowledge.
5. Summing up the lesson.
1. Organization of the beginning of the lesson. Greetings.
- Good afternoon Let's greet each other. To do this, just smile at each other. I hope that today there will be a friendly atmosphere throughout the lesson. And to relieve anxiety and tension
Slide No. 2 (picture 1)
let's change our mood
- Slide No. 2 (picture 2)
What concept did we learn about in the last lesson? (Wave)
Question: what is a wave? (Oscillations that propagate in space over time are called waves)
Question : what quantities characterize oscillatory motion? (Amplitude, period and frequency)
Question: But will these quantities be characteristics of the wave? (Yes)
Question: Why? (wave - oscillations)
Question: what are we going to study in class today? (study wave characteristics)
Absolutely everything in this world happens with some . Bodies do not move instantly, it takes time. Waves are no exception, no matter in what medium they propagate. If you throw a stone into the water of a lake, the resulting waves will not reach the shore immediately. It takes time for waves to travel a certain distance; therefore, we can talk about the speed of wave propagation.
There is another important characteristic: wavelength.
Today we will introduce a new concept: wavelength. And we get the relationship between the speed of wave propagation, wavelength and frequency.
2. Updating students' knowledge.
In this lesson we continue to study mechanical waves
If you throw a stone into the water, circles will run from the place of disturbance. Ridges and troughs will alternate. These circles will reach the shore.
- Slide No. 3
A big boy came and threw a big stone. A little boy came and threw a small stone.
Question: will the waves be different? (Yes)
Question: how? (Height)
Question: What do you call the height of the ridge? (Amplitude of fluctuation)
Question: What is the name of the time it takes a wave to travel from one oscillation to the next? (Oscillation period)
Question: what is the source of wave motion?(The source of wave motion is vibrations of body particles interconnected by elastic forces)
Question: particles vibrate. Does substance transfer occur? (NO)
Question: What is being transmitted? (ENERGY)
Waves observed in nature are oftentransfer enormous energy
Exercise: Raise your right hand and show how to dance a wave- Slide No. 4
Question: where does the wave travel? (Right)
Question: how does the elbow move? (Up and down, that is, across the wave)Question: What are these waves called? (Such waves are called transverse)
- Slide No. 5
Question - Definition: waves in which particles of the medium oscillate perpendicular to the direction of propagation of the wave are calledtransverse .
- Slide No. 6
Question: what wave was shown? (Longitudinal)
Question - Definition: waves in which vibrations of particles of the medium occur in the direction of propagation of the wave are calledlongitudinal .
- Slide No. 7
Question: how is it different from a transverse wave? (There are no ridges and troughs, but there are condensations and rarefactions)
Question: There are bodies in solid, liquid and gaseous states. What waves can propagate in what bodies?
Answer 1:In solids Longitudinal and transverse waves are possible, since elastic deformations of shear, tension and compression are possible in solids
Answer 2:In liquids and gases Only longitudinal waves are possible, since there are no elastic shear deformations in liquids and gases
3. Assimilation of new knowledge. Exercise : draw a wave in your notebook- Slide No. 8
- Slide No. 9
Write in your notebook: The shortest distance between two points that oscillate in the same phase is called the wavelength (λ).
- Slide No. 10
Question: what value is the same for these points if this is a wave motion? (Period)
Writing in a notebook : wavelength is the distance over which a wave propagates in a time equal to the period of oscillation at its source. It is equal to the distance between adjacent crests or troughs in a transverse wave and between adjacent condensations or depressions in a longitudinal wave.
- Slide No. 11
Question: What formula will we use to calculate λ?
Clue: What is λ? This distance...
Question: What is the formula for calculating distance? Speed x time
Question: What time? (Period)
we obtain the formula for the speed of wave propagation.- Slide No. 12
Write off the formula.
Independently obtain formulas for finding wave speed.
Question: What does the speed of wave propagation depend on?
Clue: Two identical stones were dropped from the same height. One in water and the other in vegetable oil. Will the waves travel at the same speed?
Write in your notebook: The speed of wave propagation depends on the elastic properties of the substance and its density
4. Consolidation of new knowledge.
teach students to use formulas to find wavelength and speed.
Problem solving:
1 . The figure shows a graph of oscillations of a wave propagating at a speed of 2 m/s. What are the amplitude, period, frequency and wavelength.- Slide No. 13
- Slide No. 14
2 . A boat rocks on waves traveling at a speed of 2.5 m/s. The distance between the two nearest wave crests is 8 m. Determine the period of oscillation of the boat.
3 . The wave propagates at a speed of 300 m/s, oscillation frequency is 260 Hz. Determine the distance between adjacent points that are in the same phases.
4 . 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?
5. Summing up the lesson.
What new did we learn in the lesson?
What have we learned?
How has your mood changed?
Reflection
Please look at the cards that are on the tables. And determine your mood! At the end of the lesson, leave your mood card on my desk!
6. Information about homework.§33, ex. 28
Final words from the teacher:
I want to wish you less hesitation in your life. Walk confidently along the path of knowledge.