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 wavelength is. We will look at its definition, how it is designated and measured. Then we will also take a closer look at the speed of wave propagation.
To begin with, let us remember that mechanical wave is a vibration that propagates over time in an elastic medium. Since it is an oscillation, the wave will have all the characteristics that correspond to an oscillation: amplitude, oscillation period and frequency.
In addition, the wave has its own special characteristics. One of these characteristics is wavelength. The wavelength is denoted by the Greek letter (lambda, or they say “lambda”) and is measured in meters. Let us list the characteristics of the wave:
What is wavelength?
Wavelength - this is the smallest distance between particles vibrating with the same phase.
Rice. 1. Wavelength, wave amplitude
It is more difficult to talk about wavelength in a longitudinal wave, because there it is much more difficult to observe particles that perform the same vibrations. But there is also a characteristic - wavelength, which determines the distance between two particles performing the same vibration, vibration with the same phase.
Also, the wavelength can be called the distance traveled by the wave during one period of oscillation of the particle (Fig. 2).
Rice. 2. Wavelength
Next characteristic is the speed of wave propagation (or simply wave speed). Wave speed denoted in the same way as any other speed, by a letter and measured in . How to clearly explain what wave speed is? The easiest way to do this is using a transverse wave as an example.
Transverse wave is a wave in which disturbances are oriented perpendicular to the direction of its propagation (Fig. 3).
Rice. 3. Transverse 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 determine the wave speed
Wave speed depends on what the density of the medium is, what the forces of interaction between the particles of this medium are. Let's write down the relationship between wave speed, wave length and wave period: .
Velocity can be defined as the ratio of the wavelength, the distance traveled by the wave in one period, to the period of vibration of the particles of the medium in which the wave propagates. In addition, remember that the period is related to frequency by the following relationship:
Then we get a relationship that connects speed, wavelength and oscillation frequency: .
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
- Sokolovich Yu.A., Bogdanova G.S. Physics: a reference book with examples of problem solving. - 2nd edition repartition. - X.: Vesta: publishing house "Ranok", 2005. - 464 p.
- Peryshkin A.V., Gutnik E.M., Physics. 9th grade: textbook for general education. institutions / A.V. Peryshkin, E.M. Gutnik. - 14th ed., stereotype. - M.: Bustard, 2009. - 300 p.
- Internet portal "eduspb" ()
- Internet portal "eduspb" ()
- Internet portal “class-fizika.narod.ru” ()
Homework
Questions.
1. What is wavelength called?
The wavelength is the distance between two nearest points oscillating in the same phases.
2. What letter indicates wavelength?
Wavelength is denoted by the Greek letter λ (lambda).
3. How long does it take for the oscillatory process to spread over a distance? equal to length waves?
The oscillatory process propagates over a distance equal to the wavelength λ during the period of complete oscillation T.
5. The distance between which points is equal to the length of the longitudinal wave shown in Figure 69?
The length of the longitudinal wave in Figure 69 is equal to the distance between points 1 and 2 (wave maximum) and 3 and 4 (wave minimum).
Exercises.
1. At what speed does a wave propagate in the ocean if the wavelength is 270 m and the oscillation period is 13.5 s?
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2. Determine the wavelength at a frequency of 200 Hz if the wave speed is 340 m/s.
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3. A boat rocks on waves traveling at a speed of 1.5 m/s. The distance between the two nearest wave crests is 6 m. Determine the period of oscillation of the boat.
> Wavelength, frequency in relation to speed
Characteristic waves – length, speed and frequency. Learn what wave graph frequency is, phase and group velocity, wave propagation, and amplitude.
Waves are characterized by frequency, length and amplitude. There are also two types of speed: phase and group.
Learning Objective
- Consider the main characteristic properties of waves.
Main points
- Wavelength is a spatial period.
- Frequency – the number of cycles per time period. Cannot be mixed with corner frequency.
- Phase velocity can be defined as the product of length and frequency.
Terms
- Wave speed – absolute indicator the speed at which the phase of any frequency component of a wave passes.
- Frequency is the ratio of the number of periodic phenomena to the time interval: f = n/t.
Example
If we consider visible light, we can display it as electromagnetic wave. It will be represented by electric and magnetic fields, shifting in the environment. Frequency is defined as color: 4 × 10 14 Hz (red), 8 × 10 14 Hz (purple), and everything else in between. Wavelength exists in inverse proportion to frequency: the higher the frequency, the shorter the length.
Properties of waves
Waves are characterized by their properties. The amplitude represents half the distance from crest to trough. You can also notice the wavelength - the spatial period (from crest to crest), denoted by the letter λ.
Frequency is the number of cycles completed over a certain time period. In the form of a formula:
The red wave is endowed with a low-frequency sine, so few repetitions of cycles are observed. But the purple one high frequency. Notice that time increases horizontally
f = 1/T (T is the oscillation period).
Frequency and wavelength can also be related to each other in relation to the "speed" of the wave. We get:
v = fλ (v is the wave speed or phase speed with which the wave phase propagates in space).
There is also a wave's group velocity, which is the rate at which the overall shape of wave amplitudes (modulation or wave envelope) propagates through space.
Before you is a wave with group (positive) and phase (negative) velocities, moving in different directions
Municipal budget educational institution
Marininskaya secondary school No. 16
Public lesson in physics in 9th grade on the topic
« Wavelength. Wave speed »
Taught the lesson: physics teacher
Borodenko Nadezhda Stepanovna
Lesson topic: “Wavelength. Wave propagation speed"
The purpose of the lesson: repeat the reasons for the propagation of transverse and longitudinal waves; study the vibration of a single particle, as well as the vibration of particles with different phases; introduce the concepts of wavelength and speed, teach students to apply formulas to find wavelength and speed.
Methodological tasks:
Educational :
Introducing students to the origin of the term “wavelength, wave speed”;
show students the phenomenon of wave propagation, and also prove with the help of experiments the propagation of two types of waves: transverse and longitudinal.
Developmental :
Promote the development of speech, thinking, cognitive and general labor skills;
Promote mastery of scientific research methods: analysis and synthesis.
Educational :
- to form a conscientious attitude towards educational work, positive motivation for learning, and communication skills; contribute to the education of humanity, discipline, and aesthetic perception of the world.
Lesson type : combined lesson.
Demos:
1. Oscillation of a single particle.
2. Vibration of two particles with different phases.
3. Propagation of transverse and longitudinal waves.
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.
6. Information about homework, execution instruction.
DURING THE CLASSES
I. Organizational stage
II. Frontal survey
What are waves?
What is the main general property traveling waves of any nature?
What are the main causes of the wave?
What waves are called longitudinal; transverse? Give examples.
In what medium can elastic longitudinal and transverse waves propagate?
III. Learning new knowledge
We have become acquainted with such a physical concept as a mechanical wave. Please repeat again: what is a wave? – physical process, associated with the propagation of oscillations in space over time.
A wave is an oscillation that, when propagating, does not carry matter with it. Waves transfer energy from one point in space to another.
Let's imagine that we have a system of balls connected by elastic springs and located along the x axis. When point 0 oscillates along the y-axis with frequency w according to the equation
y = A cos wt,
each point of this system will also oscillate perpendicular to the x-axis, but with some phase lag.
Fig 1
This delay is due to the fact that the propagation of oscillations through the system occurs at a certain finite speed
v
and depends on the stiffness of the springs connecting the balls. The displacement of a ball located at a distance x from point 0 at any time t will be exactly the same as the displacement of the first ball at an earlier time. Since each of the balls is characterized by the distance x at which it is located from point 0, its displacement from the equilibrium position during the passage of the wave.
Any physical process is always described by a number of characteristics, the values of which allow us to more deeply understand the content of the process. What characteristics do you think can describe the wave process?
These include wave speed (), wavelength ( ), amplitude of oscillations in the wave (A), period of oscillations (T) and frequency of oscillations ().
The speed of mechanical waves, depending on the type of waves and elastic properties of the media, can vary from hundreds of meters per second to 10-12 nm/s
- The distance that a wave travels in a time equal to the oscillation period T is called wavelength and is designated by the letter .
It is quite obvious that for a specific medium the wavelength must be a specific value
= · T
Since the oscillation period is related to the oscillation frequency by the ratio:
T = , then or =
Each quantity in the SI system is expressed:
-
wavelength(m) meter;
T – wave oscillation period (s) second;
– wave oscillation frequency (Hz) Hertz;
– wave propagation speed (m/s);
A - amplitude of oscillations in the wave (m) meter
Let us represent the wave graphically as oscillations that move in space over time. Wave length:= 1000m. The oscillation period is 0.4 s. Wave speed:
= /T=2500 m. What is the amplitude of oscillations in the wave?
It should be noted that the oscillation frequency in the wave always coincides with the oscillation frequency of the wave source.
In this case, the elastic properties of the medium do not affect the vibration frequency of the particles. Only when a wave passes from one medium to another does the speed and wavelength change, and the frequency of particle oscillations remains constant.
When waves propagate, energy is transferred without transferring matter.
IV. Consolidation of new knowledge
What is the period of a wave? Frequency, wavelength?
Write a formula relating the speed of wave propagation to wavelength and frequency or period
V. Problem solving
1.The oscillation frequency in the wave is 10000 Hz, and the wavelength is 2 mm. Determine the speed of the wave.
Given:10000 Hz
2mm
C AND
0.002m
Solution:
0.002m 10000 Hz= 2 m/s
Answer: =2 m/s
2. Determine the wavelength at a frequency of 200 Hz if the wave speed is 340 m/s.
200 Hz
340 m/s
C AND
Solution:
= /
340/200 =1.7 m
Answer: =1.7 m
(Physical education)
They quickly stood up and smiled.
Higher, we reached higher.
Come on, straighten your shoulders,
Raise, lower.
Turn right, turn left,
Touch your hands with your knees.
Up hand and down hand.
They pulled them lightly.
We quickly changed hands!
We're not bored today.
(One straight arm up, the other down, change hands with a jerk.)
Squat with clapping:
Down - clap and up - clap.
We stretch our legs and arms,
We know for sure that it will be good.
(Squats, clapping hands above your head.)
We twist - we turn our heads,
We stretch our neck. Stop!
(Rotate your head right and left.)
And we walk on the spot,
We raise our legs higher.
(Walk in place, raising your legs high.)
Stretched, stretched
Up and to the sides, forward.
(Stretching - arms up, to the sides, forward.)
And everyone returned to their desks -
We have a lesson again.
(Children sit at their desks.)
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?
Under wave speed understand the speed of propagation of disturbance. For example, a blow to the end of a steel rod causes local compression in it, which then spreads along the rod at a speed of about 5 km/s.
The speed of a wave is determined by the properties of the medium in which the wave propagates. When a wave passes from one medium to another, its speed changes.
Wavelength is the distance over which a wave propagates in a time equal to the period of oscillation in it.
Since the speed of a wave is a constant value (for a given medium), the distance traveled by the wave is equal to the product of the speed and the time of its propagation. Thus, to find the wavelength, you need to multiply the speed of the wave by the period of oscillation in it:
Where v— wave speed, T- period of oscillations in the wave, λ (greek letter lambda) - wavelength.
The formula expresses the relationship between wavelength and its speed and period. Considering that the period of oscillation in a wave is inversely proportional to the frequency v, i.e. T= 1/ v, we can obtain a formula expressing the relationship between wavelength and its speed and frequency:
,
where
The resulting formula shows that the wave speed is equal to the product of the wavelength and the frequency of oscillations in it.
Wavelength is the spatial period of the wave. In the wave graph (fig. above), the wavelength is defined as the distance between the two nearest harmonic points traveling wave, being in the same oscillation phase. These are like instant photographs of waves in an oscillating elastic medium at moments in time t And t + Δt. Axis X coincides with the direction of wave propagation, displacements are plotted on the ordinate axis s vibrating particles of the medium.
The frequency of oscillations in the wave coincides with the frequency of oscillations of the source, since the oscillations of particles in the medium are forced and do not depend on the properties of the medium in which the wave propagates. When a wave passes from one medium to another, its frequency does not change, only the speed and wavelength change.