2. Types of vibrations
Definition. Free vibrations- these are oscillations that occur in a system under the influence of internal forces after it has been removed from an equilibrium position (after a short-term action of an external force).
Examples of free vibrations: vibrations of free pendulums, vibrations of a guitar string after a strike, etc.
Definition. Forced vibrations- These are oscillations that occur under the influence of an external periodically changing force.
Examples of forced oscillations: vibrations of the speaker membrane, piston in the cylinder of the internal combustion chamber, etc.
Definition. Resonance– this is the phenomenon of a sharp increase in the amplitude of vibrations of a body, when the natural frequency of vibrations of the system coincides with the frequency of vibrations of the external force.
Comment. The natural frequency is determined by the parameters of the oscillatory system.
Examples of resonance: a bridge that could collapse if soldiers marched across it while marching in lockstep; a crystal glass bursting from the singer’s voice, etc.
Definition. Self-oscillations– undamped oscillations that exist in the system due to the supply of energy from an external source regulated by the system itself.
Examples of self-oscillations: oscillations of a pendulum in a clock with weights, oscillations of an electric bell, etc.
Comment. The oscillations of the pendulums under consideration are harmonic.
Definition. Math pendulum is a system that is a material point on a long weightless inextensible thread that performs free small oscillations under the action of the resultant force of gravity and the tension force of the thread.
– period of oscillation of a mathematical pendulum, s
Where l is the length of the thread, m
Notes:
1) The period formula is correct provided that the thread is much longer than the linear dimensions of the load and that the vibrations are small;
2) The period does not depend on the mass of the load and the amplitude of oscillations;
3) The period depends on the length of the thread (heating/cooling) and on the acceleration of gravity (mountainous areas, latitude).
Definition. Spring pendulum– an oscillatory system consisting of a body mounted on an elastic spring, which performs free small oscillations.
Comment. In the simplest case, vibrations in the horizontal plane along the surface are considered without taking into account friction forces.
– period of oscillation of the spring pendulum, s
Where m is the mass of the load, kg
k – spring stiffness, N/m
Notes:
1) The period formula is correct provided that the fluctuations are small;
2) The period does not depend on the amplitude of oscillations;
3) The period depends on the mass of the load and the stiffness of the spring.
Energy conversion during harmonic vibrations:
1) Mathematical pendulum: ;
2) Spring pendulum (horizontal) 
.
4. Mechanical waves
Comment. If, having arisen in one place, mechanical vibrations spread to neighboring regions of space filled with matter, then they speak of wave motion.
Definition. Mechanical wave is the process of propagation of mechanical vibrations in any medium.
Types of waves:
1) Transverse waves– these are waves in which the direction of vibration is perpendicular to the direction of propagation of the wave.
Examples of transverse waves: waves on the water, waves in the whip, etc.
2) Longitudinal waves– these are waves in which the direction of vibration is parallel to the direction of propagation of the wave.
Example of longitudinal waves: sound waves.
Definition. Wavelength() – the minimum distance between two points of a wave with the same oscillation phase, i.e. in a simplified formulation, this is the distance between adjacent wave crests or troughs. It is also the distance that a wave travels in one oscillation period.
– wavelength, m
Where υ – wave propagation speed, m/s
T – oscillation period, s
ν – oscillation frequency, Hz
Definition. Sound waves (sound)– mechanical longitudinal elastic waves propagating in the medium.
Ranges of sound waves (by frequency):
1) Infrasound:, may have adverse effects on the human body;
2) Audible sound: 
;
3) Ultrasound: frequency is more than 20,000 Hz, some animals are sensitive to ultrasound, bats use it for orientation in space, it is used in echolocation and ultrasound technology in medicine.
Notes:
1) Sound speed– this is the speed of transmission of an elastic wave in a medium; as a rule, the more dense the substance, the greater it is. Speed of sound in air;
2) Sound volume characterized by the amplitude and frequency of vibrations of particles of an elastic medium;
3) Pitch of sound is determined by the frequency of oscillations of particles of an elastic medium.
Definition. Echolocation– technology for measuring distances to objects using sound emission and recording the time delay before receiving its echo, i.e. reflection of sound from the interface between media. Typically, this technology uses ultrasound.
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 connection 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.
