Lesson Objectives:
educational:
- formation of the concept of "mechanical wave";
- consideration of the conditions for the occurrence of two types of waves;
- wave characteristics;
developing:
- development of the ability to apply knowledge in specific situations;
educational:
- education of cognitive interest;
- positive motivation for learning;
- accuracy in completing assignments.
Type of lesson: a lesson in the formation of new knowledge.
Equipment:
for demos: rubber cord, glass of water, pipette, Wave Machine layout, computer, multimedia projector, Waves presentation.
During the classes
1. Organizational moment.
Announcement of the topic and objectives of the lesson.
2. Actualization of basic knowledge
Test
Option number 1
. Swing movement.B. The movement of a ball falling to the Earth,
2. Which of the following vibrations are free?
B. Loudspeaker cone vibration during loudspeaker operation.
3. The body oscillation frequency is 2000 Hz. What is the period of oscillation?
4. The equation x=0.4 cos 5nt is given. Determine the amplitude, period of oscillation.
5. A load suspended on a thread makes small oscillations. Considering the oscillations to be undamped, indicate the correct answers.
. The longer the thread, the greater the oscillation frequency.B. When the load passes the equilibrium position, the speed of the load is maximum.
B. The load is moving periodically.
Option number 2
1. Which of the following movements are mechanical vibrations?
. Movement of tree branches.B. The movement of raindrops on the ground.
B. The movement of a sounding guitar string.
2. Which of the following vibrations are forced?
. Oscillations of a load on a spring after a single deviation from its equilibrium position.B. The movement of the piston in the cylinder of an internal combustion engine.
B. Fluctuations of the load on the thread, once taken away from the equilibrium position and released.
3. Body oscillation period 0.01 s. What is the oscillation frequency?
4. The body performs a harmonic oscillation according to the law \u003d 20 sin nt. Determine the amplitude, period of oscillation.
5. A weight suspended on a spring makes small oscillations in the vertical direction. Considering the oscillations to be undamped, indicate the correct answers.
. The greater the stiffness of the spring, the longer the period of oscillation.B. The period of oscillation depends on the amplitude.
B. The speed of the load changes periodically over time.
3. Formation of new knowledge.
The basic physical model of matter is a set of moving and interacting atoms and molecules. The use of this model makes it possible to explain, using the molecular-kinetic theory, the properties of various states of matter and the physical mechanism of energy and momentum transfer in these media. In this case, under the medium we can understand gas, liquid, solid body.
Let us consider a method of energy transfer without transfer of matter as a result of successive transfer of energy and momentum along a chain between adjacent particles of the medium interacting with each other.
wave process is the process of energy transfer without the transfer of matter.
Demonstration of experience:
We attach a rubber cord to the ceiling and with a sharp movement of the hand make its free end oscillate. As a result of external action on the medium, a perturbation arises in it - the deviation of the particles of the medium from the equilibrium position;
Follow the propagation of waves on the surface of the water in the glass, creating them with drops of water falling from their pipettes.
A mechanical wave is a perturbation that propagates in an elastic medium from point to point (gas, liquid, solid).
Acquaintance with the mechanism of wave formation on the “Wave Machine” layout. At the same time, the oscillatory motion of particles and the propagation of oscillatory motion should be taken into account.
There are longitudinal and transverse waves.
Longitudinal - waves in which the particles of the medium oscillate along the direction wave propagation. (Gases, liquids, solids). It is observed when a nail is hammered in, a longitudinal impulse sweeps along the nail, driving it deeper.
Transverse - waves in which particles oscillate perpendicular to the direction of wave propagation (solid bodies). It is observed in a rope, one end of which comes into oscillatory motion.
A traveling wave, the main property of which is the transfer of energy without the transfer of matter: electromagnetic radiation The sun warms the Earth, the waves of the ocean wash away the shores.
Wave characteristics.
Wavelength - the distance traveled by a wave in one period of oscillation of its particles. At a distance of a wavelength, adjacent crests or troughs are located in a transverse wave or thickening or rarefaction in a longitudinal wave.
λ is the wavelength.
Wave speed - the speed of movement of crests and troughs in a transverse wave and thickening and rarefaction in a longitudinal wave.
v – wave speed
Familiarity with formulas for determining the wavelength:
λ = v / v
v- frequency
T- period
Formation of skills and abilities.
Problem solving.
1. The boy carries buckets of water on the yoke, the period of free oscillations of which is 1.6 s. At what speed of the boy's movement will the water begin to splash out especially strongly if the length of his step is 65 cm?
2. A wave propagates over the water surface in a lake with a speed of 8 m/s. What is the period and frequency of oscillations of the buoy if the wavelength is 3 m?
3. The wavelength in the oceans can reach 400 m, and the period is 14.5 s. Determine the propagation speed of such a wave.
Lesson results.
1. What is a wave?
2. What is the process of wave formation?
3. What waves do we perceive while in the classroom?
4. Does the matter of the medium transfer during the formation of waves?
5. List the characteristics of the waves.
6. How are speed, wavelength and frequency related?
Homework:
P.31-33 (textbook Physics-9)
No. 439,438 (Rymkevich A.P.)
OK-9 Propagation of vibrations in an elastic medium
wave motion- mechanical waves, i.e., waves that propagate only in matter (sea, sound, waves in a string, earthquake waves). The sources of the waves are vibrations of the vibrator.
Vibrator- oscillating body. Creates vibrations in an elastic medium.
wave called oscillations that propagate in space over time.
wave surface- locus of points of the medium oscillating in the same phases
L 
uch- a line, the tangent to which at each point coincides with the direction of wave propagation.
The reason for the appearance of waves in an elastic medium
If the vibrator oscillates in an elastic medium, then it acts on the particles of the medium, forcing them to perform forced oscillations. Due to the forces of interaction between the particles of the medium, vibrations are transmitted from one particle to another.
T 
wave types
transverse waves
Waves in which the oscillations of the particles of the medium occur in a plane perpendicular to the direction of wave propagation. Occur in solids and on the surface of the hearth.
P 
rodal waves
Oscillations occur along the propagation of the wave. They can occur in gases, liquids and solids.
surface waves
AT 
waves that propagate at the interface between two media. Waves on the border between water and air. If a λ
less than the depth of the reservoir, then each particle of water on the surface and near it moves along an ellipse, i.e. is a combination of vibrations in the longitudinal and transverse directions. At the bottom, a purely longitudinal movement is observed.
plane waves
Waves whose wave surfaces are planes perpendicular to the direction of wave propagation.
With 
pheric waves
Waves whose wave surfaces are spheres. The spheres of wave surfaces are concentric.
Characteristics of wave motion
Wavelength
The shortest distance between two races oscillating in the same phase is called the wavelength. Depends only on the medium in which the wave propagates, at equal frequencies of the vibrator.
Frequency
Frequency ν wave motion depends only on the frequency of the vibrator.
Wave propagation speed
Speed v= λν
. As 
, then 
. However, the speed of wave propagation depends on the type of substance and its state; from ν
and λ
, does not depend.
In an ideal gas 
, where R- gas constant; M- molar mass; T- absolute temperature; γ
- constant for a given gas; ρ
is the density of the substance.
In solids transverse waves
, where N- shear modulus; longitudinal waves 
, where Q- all-round compression module. In solid rods 
where E- Young's modulus.
In solids, both transverse and longitudinal waves propagate with different velocities. This is the basis for determining the epicenter of an earthquake.
Plane wave equation
His kind x=x 0 sin ωt(t−l/v) = x 0 sin( ωt−kl), where k= 2π /λ - wave number; l- the distance traveled by the wave from the vibrator to the considered point BUT.
Time lag of oscillations of medium points: 
.
Phase delay of medium point oscillations: 
.
Phase difference of two oscillating points: ∆ φ =φ 2 −φ 1 = 2π (l 2 −l 1)/λ .
wave energy
Waves carry energy from one vibrating particle to another. Particles perform only oscillatory motions, but do not move with the wave: E=E to + E P,
where E k is the kinetic energy of the oscillating particle; E n - potential energy of elastic deformation of the medium.
To some extent V elastic medium in which a wave propagates with an amplitude X 0 and cyclic frequency ω
, there is an average energy W equal to 
, where m- mass of the selected volume of the medium.
Wave intensity
The physical quantity, which is equal to the energy transferred by a wave per unit of time through a unit surface area perpendicular to the direction of wave propagation, is called the intensity of the wave: 
. It is known that W and j~
.
Wave power
If a S is the transverse area of the surface through which the energy is transferred by the wave, and j is the intensity of the wave, then the power of the wave is equal to: p=jS.
OK-10 Sound waves
At 
The elastic waves that cause the sensation of sound in humans are called sound waves.
16 –2∙10 4 Hz - audible sounds;
less than 16 Hz - infrasounds;
more than 2∙10 4 Hz - ultrasounds.
O 
An obligatory condition for the occurrence of a sound wave is the presence of an elastic medium.
M 
The mechanism of occurrence of a sound wave is similar to the occurrence of a mechanical wave in an elastic medium. While oscillating in an elastic medium, the vibrator acts on the particles of the medium.
Sound is created by long-term periodic sources of sound. For example, musical: string, tuning fork, whistle, singing.
Noise is created by long-term, but not periodic sources of sound: rain, sea, crowd.
Sound speed
Depends on the medium and its state, as for any mechanical wave:
.
At t= 0°Сv water = 1430 m/s, v steel = 5000 m/s, v air = 331 m/s.
Sound wave receivers
1. Artificial: the microphone converts mechanical sound vibrations in electrical. Are characterized by sensitivity σ
:
,σ
depends on ν
w.v. .
2. Natural: ear.
Its sensitivity perceives sound at ∆ p= 10 −6 Pa.
The lower the frequency ν sound wave, the lower the sensitivity σ ear. If a ν w.v. decreases from 1000 to 100 Hz, then σ the ear is reduced by 1000 times.
Exceptional selectivity: the conductor captures the sounds of individual instruments.
Physical characteristics of sound
objective
1. Sound pressure is the pressure exerted by a sound wave on an obstacle in front of it.
2. The spectrum of sound is the decomposition of a complex sound wave into its component frequencies.
3.
Intensity sound wave: 
, where S- surface area; W- sound wave energy; t- time; 
.
subjective
Volume, like pitch, sound is related to the sensation that arises in the human mind, as well as to the intensity of the wave.
The human ear is capable of perceiving sounds with an intensity of 10 −12 (hearing threshold) to 1 
(pain threshold).
G 
Loudness is not directly proportional to intensity. To get a sound twice as loud, you need to increase the intensity by 10 times. A wave with an intensity of 10 −2 W/m 2 sounds 4 times louder than a wave with an intensity of 10 −4 W/m 2 . Because of this relationship between objective perceived loudness and sound intensity, a logarithmic scale is used.
The unit of this scale is the bel (B) or decibel (dB), (1 dB = 0.1 B), named after the physicist Heinrich Bel. The loudness level is expressed in bels: 
, where I 0 = 10 −12 
hearing threshold (averaged).
E 
if I= 10 −2 
, then 
.
Loud sounds are harmful to our body. The sanitary norm is 30–40 dB. This is the volume of a calm, quiet conversation.
Noise disease: high blood pressure, nervous irritability, hearing loss, fatigue, poor sleep.
Intensity and loudness of sound from various sources: jet aircraft - 140 dB, 100 W/m 2 ; rock music indoors - 120 dB, 1 W / m 2; normal conversation (50 cm from it) - 65 dB, 3.2 ∙ 10 −6 W / m 2.
Pitch depends on the oscillation frequency: than > ν , the higher the sound.
T 
sound tone allows you to distinguish between two sounds of the same pitch and volume made by different instruments. It depends on the spectral composition.
Ultrasound
Applicable: echo sounder for determining the depth of the sea, preparation of emulsions (water, oil), washing of parts, tanning of leather, detection of defects in metal products, in medicine, etc.
It spreads over considerable distances in solids and liquids. Carries much more energy than a sound wave.
wave called vibrations that propagate in space over time. For the emergence and propagation of waves, the following conditions are necessary: a source of oscillations and an elastic medium.
There are two types of waves: transverse and longitudinal. transverse they call such a wave in which particles oscillate perpendicularly (i.e., across) to the direction of wave propagation. Longitudinal called such a wave in which the particles oscillate in the direction (i.e. along) of the wave propagation.
Characteristics of the oscillatory process:
1. Displacement - deviation of the oscillating point from the equilibrium position at a given time (m).
2. Amplitude - the largest displacement from the equilibrium position (m).
3. Period T is the time it takes for one complete oscillation (s).
4. Frequency - the number of complete oscillations per unit of time (Hz, s -1).
5. Cyclic (circular) frequency - the number of complete oscillations per unit of time (seconds) ().
6. Oscillation phase - a physical quantity that determines the displacement at a given time ( glad). The phase of oscillations at the initial moment of time is called the initial phase.
Harmonic vibrations - fluctuations in which changes physical quantities occurs according to the law of sine or cosine (harmonic law).
or 
, .
Oscillation amplitude, - oscillation frequency, - initial phases of oscillations, 
- oscillation phase.
Forced vibrations- undamped oscillations of the system, which are caused by the action of an external periodic force.
Resonance– phenomena of an increase in the amplitude of oscillations when the frequency of the driving force approaches the frequency of forced oscillations.
Types of wave processes: mechanical waves, electromagnetic waves(Unlike mechanical ones, they can propagate in a vacuum).
Mathematical pendulum – material point suspended on a weightless inextensible thread.
Spring pendulum. .
Sound – oscillatory motion of particles of an elastic medium, propagating in the form of waves.
Oscillations excited at any point in the medium (solid, liquid or gaseous) propagate in it with a finite speed, depending on the properties of the medium, being transmitted from one point of the medium to another. The farther the particle of the medium is located from the source of oscillations, the later it will begin to oscillate. In other words, the entrained particles will lag behind in phase those particles that entrain them.
When studying the propagation of oscillations, the discrete (molecular) structure of the medium is not taken into account. The medium is considered as continuous, i.e. continuously distributed in space and possessing elastic properties.
So, An oscillating body placed in an elastic medium is a source of oscillations that propagate from it in all directions. The process of propagation of oscillations in a medium is called wave.
When a wave propagates, the particles of the medium do not move along with the wave, but oscillate around their equilibrium positions. Together with the wave, only the state is transmitted from particle to particle oscillatory motion and energy. So basic property of all waves,regardless of their nature,is the transfer of energy without the transfer of matter.
Waves happen transverse (vibrations occur in a plane perpendicular to the direction of propagation) and longitudinal (concentration and rarefaction of particles of the medium occurs in the direction of propagation).
where υ is the wave propagation velocity, is the period, ν is the frequency. From here, the speed of wave propagation can be found by the formula:
| . | (5.1.2) |
The locus of points oscillating in the same phase is called wave surface. The wave surface can be drawn through any point in space covered by the wave process, i.e. there are an infinite number of wave surfaces. The wave surfaces remain stationary (they pass through the equilibrium position of particles oscillating in the same phase). There is only one wavefront, and it moves all the time.
Wave surfaces can be of any shape. In the simplest cases, wave surfaces have the form plane or spheres, respectively, the waves are called flat or spherical . In a plane wave, the wave surfaces are a system of planes parallel to each other; in a spherical wave, they are a system of concentric spheres.
A medium is called elastic if there are interaction forces between its particles that prevent any deformation of this medium. When a body oscillates in an elastic medium, it acts on the particles of the medium adjacent to the body and causes them to perform forced oscillations. The medium near the oscillating body is deformed, and elastic forces arise in it. These forces act on particles of the medium that are more and more distant from the body, taking them out of their equilibrium position. Gradually, all particles of the medium are involved in oscillatory motion.
The bodies that cause elastic waves propagating in the medium are wave sources(oscillating tuning forks, strings of musical instruments).
elastic waves called mechanical perturbations (deformations) produced by sources that propagate in an elastic medium. Elastic waves cannot propagate in a vacuum.
When describing the wave process, the medium is considered continuous and continuous, and its particles are infinitesimal volume elements (sufficiently small compared to the wavelength), in which there are a large number of molecules. When a wave propagates in a continuous medium, the particles of the medium participating in the oscillations have certain oscillation phases at each moment of time.
The locus of points of the medium, oscillating in the same phases, forms wave surface.
The wave surface that separates the oscillating particles of the medium from particles that have not yet begun to oscillate is called the wave front. Depending on the shape of the wave front, waves are plane, spherical, etc.
A line drawn perpendicular to the wave front in the direction of wave propagation is called a beam. The beam indicates the direction of wave propagation.;;
AT plane wave wave surfaces are planes perpendicular to the direction of wave propagation (Fig. 15.1). Plane waves can be obtained on the surface of water in a flat bath by means of vibrations of a flat rod.
In a spherical wave, the wave surfaces are concentric spheres. A spherical wave can be created by a ball pulsating in a homogeneous elastic medium. Such a wave propagates with the same speed in all directions. The rays are the radii of the spheres (Fig. 15.2).