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Wavelength is the propagation speed of waves presentation. Lesson Development: Wavelength

During the lesson, you will be able to independently study the topic “Wavelength. Wave propagation speed. In this lesson, you will learn about the special characteristics of waves. First of all, you will learn what a wavelength is. We will look at its definition, how it is labeled and measured. Then we will also look at the propagation speed of the wave in detail.

To begin with, let's remember that mechanical wave is an oscillation that propagates over time in an elastic medium. Since this is an oscillation, the wave will have all the characteristics that correspond to the oscillation: amplitude, oscillation period and frequency.

In addition, the wave has its own special characteristics. One of these characteristics is wavelength. Wavelength is denoted by the Greek letter (lambda, or they say "lambda") and is measured in meters. We list the characteristics of the wave:

What is a wavelength?

Wavelength - this is the smallest distance between particles that oscillate with the same phase.

Rice. 1. Wavelength, wave amplitude

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

Also, the wavelength can be called the distance traveled by the wave in one period of particle oscillation (Fig. 2).

Rice. 2. Wavelength

The next characteristic is the speed of wave propagation (or simply the speed of the wave). Wave speed It is denoted in the same way as any other speed by a letter and is measured in. How to clearly explain what is the speed of the wave? The easiest way to do this is with a transverse wave as an example.

transverse wave is a wave in which perturbations are oriented perpendicular to the direction of its propagation (Fig. 3).

Rice. 3. Shear wave

Imagine a seagull flying over the crest of a wave. Its flight speed over the crest will be the speed of the wave itself (Fig. 4).

Rice. 4. To the determination of the wave speed

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

Speed ​​can be defined as the ratio of the wavelength, the distance traveled by the wave in one period, to the period of oscillation of the particles of the medium in which the wave propagates. In addition, remember that the period is related to the frequency as follows:

Then we get a relation that relates the speed, wavelength and frequency of oscillations: .

We know that a wave arises as a result of the action of external forces. It is important to note that when a wave passes from one medium to another, its characteristics change: the speed of the waves, the wavelength. But the oscillation frequency remains the same.

Bibliography

  1. Sokolovich Yu.A., Bogdanova G.S. Physics: a reference book with examples of problem solving. - 2nd edition redistribution. - X .: Vesta: publishing house "Ranok", 2005. - 464 p.
  2. Peryshkin A.V., Gutnik E.M., Physics. Grade 9: textbook for general education. institutions / A.V. Peryshkin, E.M. Gutnik. - 14th ed., stereotype. - M.: Bustard, 2009. - 300 p.
  1. Internet portal "eduspb" ()
  2. Internet portal "eduspb" ()
  3. Internet portal "class-fizika.narod.ru" ()

Homework

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Slides captions:

Story. Let's remember how a wave arises. (From the material of the last lesson) ... Let's draw a wave and associate a coordinate system with it. If the displacement of particles from the equilibrium position is plotted along the vertical axis, and the distance over which the wave propagates along the horizontal axis, then the following characteristics of the wave can be shown: amplitude and wavelength. Amplitude - the maximum displacement of particles from the equilibrium position. Wavelength - the distance between the nearest points that oscillate in the same phases. Wavelength is denoted by the Greek letter λ ("lambda"). [λ ]=[m] Let's build another graph of the wave, where we show the displacement along the vertical axis, and the propagation time of the wave along the horizontal axis, then you can see the wave period on the graph, i.e. the time of one complete oscillation. [T]=[s] Since the oscillation period is related to the frequency by dependence Т=1/ ν , then the wavelength can be expressed in terms of wave speed and frequency: λ= V/ ν V=λ / Т V= λν

1. In the oceans, the wavelength reaches 300 m, and the oscillation period is 15 s. Determine the propagation speed of such a wave Answer 20 m/s.

Answer: 0.17 m. 2. Determine the length of the sound wave in the air if the frequency of the sound source is 2000 Hz. The speed of sound in air is 340 m/s.

Answer: 0.3 Hz. 3. The distance between the nearest wave crests in the sea is 10 m. What is the frequency of wave impacts on the hull of the boat if the wave speed is 3 m/s.

Answer: 6.6 m. 4. 6 crests of waves passed by a stationary observer in 20 s, starting from the first one. What is the wavelength and period of oscillation if the wave speed is 2 m/s?

Answer: 3 m/s. The period of oscillation of water particles is 2 s, and the distance between adjacent wave crests is 6 m. Determine the propagation velocity of these waves.

LESSON ANALYSIS

The lesson was held in the 9th grade in the amount 28 person. Lesson on the topic “Wavelength. The speed of wave propagation" is eighth lesson in physics “Mechanical oscillations and waves. Sound" . Therefore, students need to form the basic concepts, definitions and terms in this lesson.
The lesson took into account the triune didactic goal: educational, developing, upbringing.
I set an educational goal to familiarize students with the origin of the term "wavelength, wave speed."
As a developing goal, I set the formation of students' clear ideas about the conditions for wave propagation; development of logical and theoretical thinking, imagination, memory in solving problems and consolidating ZUNs.
I have set as an educational goal : to form a conscientious attitude to educational work, positive motivation for learning; contribute to the education of humanity, discipline, aesthetic perception of the world.
The type of lesson is combined, because this topic is eighth lesson in the section “Mechanical vibrations and waves. Sound".
In the lesson, I provided for a logical connection when explaining new material: consistency, accessibility, understandability. The main methods of the lesson were: verbal (explanation of the topic), visual (demonstrations, computer simulation), practical (problem solving, test tasks).
When fixing the ZUNs of students, I used the solution of problems at the blackboard with an explanation. I believe that the triune didactic goal of the lesson has been achieved. Then I summed up the lesson and explained the homework.

I believe that all the objectives of the lesson were successfully implemented, the methods and techniques of teaching were chosen rationally, taking into account the level of training of students. Various methods of organizing work in the lesson were used (group work in pairs, under the guidance of a teacher, individual). However, when planning this lesson in the future, I will try to add more differentiated tasks. For example, when solving problems, it was possible to distribute individual tasks for working with graphs for each student. But in this lesson, a differentiated approach was implemented both during preliminary preparation for the lesson and during the lesson (all questions and tasks were selected in such a way that the goals and objectives were implemented in relation to both the class as a whole and each child individually).


"Tasks"

2

1. The distance between the nearest wave crests in the sea is 20m. How fast does the wave travel. If the period of particle oscillations in a wave is 10 s?

2 . The fisherman noticed that in 5s the float made 10 oscillations on the waves, and the distance between adjacent wave humps was 1m. What is the speed of wave propagation?

3. The oscillation frequency in the wave is 10000 Hz, and the wavelength is 2 mm. Determine the speed of the wave.

4. The wavelength is 2 m, and the speed of its propagation is 400 m/s. Define. How many complete oscillations does this wave make in 0.1 s.

_______________________________________________________________________________________________

1. The distance between the nearest wave crests in the sea is 20m. How fast does the wave travel. If the period of particle oscillations in a wave is 10 s?

2 . The fisherman noticed that in 5s the float made 10 oscillations on the waves, and the distance between adjacent wave humps was 1m. What is the speed of wave propagation?

3. The oscillation frequency in the wave is 10000 Hz, and the wavelength is 2 mm. Determine the speed of the wave.

4. The wavelength is 2 m, and the speed of its propagation is 400 m/s. Define. How many complete oscillations does this wave make in 0.1 s.

_______________________________________________________________________________________________

1. The distance between the nearest wave crests in the sea is 20m. How fast does the wave travel. If the period of particle oscillations in a wave is 10 s?

2 . The fisherman noticed that in 5s the float made 10 oscillations on the waves, and the distance between adjacent wave humps was 1m. What is the speed of wave propagation?

3. The oscillation frequency in the wave is 10000 Hz, and the wavelength is 2 mm. Determine the speed of the wave.

4. The wavelength is 2 m, and the speed of its propagation is 400 m/s. Define. How many complete oscillations does this wave make in 0.1 s.

View document content
"lesson"

Lesson topic:

Lesson type:a lesson in communicating new knowledge.

Target: introduce the concepts of wave length and speed, teach students to apply formulas for finding the length and speed of a wave.

Tasks:

    to acquaint students with the origin of the term "wavelength, wave speed"

    be able to compare types of waves and draw conclusions

    get the relationship between wave propagation speed, wavelength and frequency

    introduce a new concept: wavelength

    teach students to apply formulas for finding the length and speed of a wave

    be able to analyze the graph, compare, draw conclusions

Technical means:

Personal Computer
- multimedia projector
- PowerPoint presentation for the lesson

Lesson plan:

1. Organization of the beginning of the lesson.
2. Actualization of students' knowledge.
3. Assimilation of new knowledge.
4. Consolidation of new knowledge.
5. Summing up the lesson.
6. Information about homework.

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 a friendly atmosphere will be present throughout the lesson today. To relieve anxiety and tension .(surf sound)

What concept did we learn in the last lesson? (Wave)

Question: what is a wave? ( Perturbations propagating in space, moving away from their place of origin, are called a wave)

Question: what quantities characterize the oscillatory motion? (amplitude, period and frequency)

Question: But will these quantities be characteristics of the wave? (Yes)

Question: Why? (wave - fluctuations)

Question: what are we going to study today in the lesson? (study the characteristics of the wave)

Absolutely everything in this world happens with some kind ofspeed. Bodies don't 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 the lake, then the resulting waves will not reach the shore immediately. It takes time to move waves over a certain distance, therefore, we can talk about the speed of wave propagation.

There is another important characteristic is the wavelength.

Today we will get acquainted with this concept. And we get the relationship between the speed of wave propagation, wavelength and frequency.

2. Actualization of students' knowledge.

And so we continue to study mechanical waves.

If you throw a stone into the water, then circles will run from the place of disturbance. There will be alternating ridges and valleys. These circles will reach the shore.

A big boy came and threw a big stone. A little boy came and threw a little stone.

Question: will the waves be different? (Yes)

Question: how? (height)

Question: what is the height of the crest? (vibration amplitude)

Question: What is the time it takes for a wave to go from one wave to the next? (Wobbling period)

Question: particles oscillate. Does material transfer take place? (No)

Question: What is transmitted? (Energy)

Waves observed in nature are often carry great energy.

I would like to invite someone who wants to study the material about the tsunami and tell us about this phenomenon in the next lesson.

1 slide

Question: what are these waves called? (Such waves are called transverse)

Question- Definition: waves in which the particles of the medium oscillate perpendicular to the direction of wave propagation are called transverse.

2 slide

Question: what wave was shown? (Longitudinal)

Question- Definition: waves in which the particles of the medium oscillate in the direction of wave propagation are called longitudinal.

3 slide

Question: How is it different from a transverse wave? (There are no ridges and troughs, but there are thickening and rarefaction)

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.

Open your notebooks and write down the topic of the lesson:

4 slide

5 slide

Let us consider in more detail the process of transferring vibrations from point to point during the propagation of a transverse wave. To do this, let us turn to the figure, which shows the various stages of the process of propagation of a transverse wave at time intervals equal to ¼T.

Figure a) shows a chain of numbered balls. This is a model: the balls symbolize the particles of the environment. We will assume that between the balls, as well as between the particles of the medium, there are interaction forces, in particular, with a small distance of the balls from each other, an attractive force arises.

Scheme of the process of propagation in space of a transverse wave

If you bring the first ball into an oscillatory motion, i.e., make it move up and down from the equilibrium position, then due to the interaction forces, each ball in the chain will repeat the movement of the first one, but with some delay (phase shift). This delay will be greater, the farther the given ball is from the first ball. So, for example, it can be seen that the fourth ball lags behind the first one by 1/4 of the oscillation (Fig. b). After all, when the first ball has passed 1/4 of the path of a complete oscillation, deviating as much as possible upwards, the fourth ball is just starting to move from the equilibrium position. The movement of the seventh ball lags behind the movement of the first by 1/2 oscillation (Fig. c), the tenth - by 3/4 oscillation (Fig. d). The thirteenth ball lags behind the first one by one complete oscillation (Fig. e), i.e., it is in the same phases with it. The movements of these two balls are exactly the same (Fig. e).

Notebook entry: (λ).

6 slide

Wavelength is denoted by the Greek letter λ ("lambda"). The distance between the first and thirteenth balls (see e), the second and fourteenth, the third and fifteenth, and so on, i.e. between all balls closest to each other, oscillating in the same phases, will be equal to the wavelength λ.

Question: what is the same value for these points, if it is a wave motion? (Period)

7 slide

Writing in a notebook: wavelength is the distance over which a wave propagates in a time equal to the period of oscillation in its source. It is equal to the distance between adjacent crests or troughs in a transverse wave and between adjacent thickenings or rarefaction in a longitudinal wave.

Clue: What is λ? This distance...

Question: What is the formula for calculating distance? Speed ​​multiplied by time

Question: What time? (Period)

we get the formula for the wavelength.

where λ is the wave speed, V is its speed, T is the period.

Since the period of oscillations is related to their frequency by the dependence Т = 1/ν, the wavelength can be expressed in terms of wave speed and frequency:

Thus, the wavelength depends on the frequency (or period) of oscillations of the source that generates this wave, and on the speed of wave propagation.

Write down the formula.

Independently obtain formulas for finding the wave speed.

V = λ/T and V = λν.

8 slide

The formulas for finding the wave speed are valid for both transverse and longitudinal waves. The wavelength λ, during the propagation of longitudinal waves, can be represented using a figure. It shows (in section) a pipe with a piston. The piston oscillates with a small amplitude along the pipe. Its movements are transmitted to the adjacent layers of air filling the pipe. The oscillatory process gradually spreads to the right, forming rarefaction and condensation in the air. The figure shows examples of two segments corresponding to the wavelength λ. Obviously, points 1 and 2 are the points closest to each other, oscillating in the same phases. The same can be said about points 3 and 4.

Question: What determines the speed of wave propagation?

Clue: Two identical stones are dropped from the same height. One in water and the other in vegetable oil. Will the waves propagate at the same speed?

Notebook entry: The speed of wave propagation depends on the elastic properties of the substance and its density.

4. Consolidation of new knowledge.

teach students to apply formulas to find the length and speed of a wave.

Problem solving:

1. The distance between the nearest wave crests in the sea is 20m. How fast does the wave travel. If the period of particle oscillations in a wave is 10 s?

Given: Solution

λ =20 m V = λ/T=20 m: 10 s = 2 m/s

Find: V . Answer: V = 2 m/s

2 . The fisherman noticed that in 5s the float made 10 oscillations on the waves, and the distance between adjacent wave humps was 1m. What is the speed of wave propagation?

Given: Solution

t \u003d 5 s T \u003d t / N \u003d 5 s: 10 \u003d 0.5 s

N = 10 V = λ/T=1 m: 0.5 s = 2 m/s

Find: V . Answer: V = 2 m/s

3. The oscillation frequency in the wave is 10000 Hz, and the wavelength is 2 mm. Determine the speed of the wave.

Given: SI Solution

λ =2 mm 0.002 m λ \u003d VT, T \u003d 1 / ν, λ \u003d V / ν, then V \u003d λν \u003d 0.002 m * 10000 Hz \u003d

ʋ= 10000 Hz = 20 m/s

Find: V . Answer: V = 20 m/s

4. The wavelength is 2 m, and the speed of its propagation is 400 m/s. Define. How many complete oscillations does this wave make in 0.1 s.

Given: Solution

V =400 m/s λ = VT =› T = λ / V then n = Δt /T = V / λ* Δt =400 m/s* 0.1 s /2m=20

∆t = 0.1 s

Find: n . Answer: n = 20

5. Summing up the lesson.

    What new did we learn in the lesson?

    What have we learned?

    How has your mood changed?

Reflection

Look at the cards on the tables. And define your mood! At the end of the lesson, leave your mood card on my desk!

6. Information about homework.

§33, ex. 28

Final word from the teacher:

I want to wish you less hesitation in your life. Walk the path of knowledge with confidence.

View presentation content
"Wavelength"





Wavelength. Wave propagation speed



λ("lambda" ) - wavelength

[λ] = m

The distance between the points closest to each other, oscillating in the same phases, is called the wavelength


Wavelength called the distance over which a wave propagates in a time equal to the period of oscillation in its source. It is equal to the distance between adjacent crests or troughs in a transverse wave and between adjacent thickenings or rarefaction in a longitudinal wave.


Checking homework

  • 1. Specify signs of oscillatory motion.
  • 2. How many times does the body pass through the equilibrium position in a time equal to the period of oscillation?
  • 3. What is the name of the period of time after which the movement repeats?
  • 4. Which of the following movements are mechanical vibrations?
  • A. Swing movement.
  • B. The movement of a ball falling to the ground.
  • C. The movement of a sounding guitar string
Checking homework
  • Are these types of movements oscillatory:
  • movement of the second hand of a clock
  • bow movement
  • the movement of the earth around the sun
  • movement of insect wings
Solve the rebus and try to formulate the topic of the lesson) wave motion.
  • Wavelength.
A wave is an oscillation that travels through space over time.
  • Waves are generated by oscillating bodies that create a deformation of the medium in the surrounding space.
What does a wave look like?
  • depression
  • Mechanical waves can propagate only in some medium (substance): in a gas, in a liquid, in a solid.
  • A mechanical wave cannot arise in a vacuum.
Wavelength
  • Wavelength
  • λ = With/ν.
  • Wave speed
Units of measurement in the SI system:
  • wavelength [lambda] = 1 m wave propagation speed
  • [ v ] = 1m/s oscillation period [ T ] = 1c oscillation frequency [ nu ] = 1 Hz
GIA-2010-4. Sound waves can propagate
  • 1) only in gases
  • 2) only in liquids
  • 3) only in solids
  • 4) in gases, liquids and solids
GIA-2010-4. The period of oscillation of a mathematical pendulum can be greatly reduced by
  • 1) increase the mass of the pendulum load
  • 2) reduce the pendulum load volume
  • 3) reducing the length of the pendulum
  • 4) decrease in the amplitude of the pendulum oscillations
GIA-2010-4. The figure shows a cord along which a transverse wave propagates at some point in time. The distance between which points is half the wavelength? GIA-2010-4. The figure shows the profile of a wave propagating through water. The distance between which points in the figure is equal to the wavelength?
  • 1 – 2
  • 1 – 3
  • 1 – 4
  • 2 - 5
GIA-2010-6. Two other tuning forks are brought in turn to the sounding tuning fork. The second tuning fork and the accuracy is the same as the first. The third one is tuned to a lower frequency. Which of the tuning forks will begin to sound with a greater amplitude?
  • second
  • third
  • both tuning forks will sound the same
  • none of them
GIA-2010-6. The speaker is connected to the output of the sound generator. Oscillation frequency 170 Hz. Determine the length of a sound wave in air, knowing that the speed of a sound wave in air is 340 m/s.
  • 57,800 m

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