Wave energy converters
Wave profile tracking transducers
In this class of converters, we will focus first on the development of Professor at the University of Edinburgh Stephen Salter, named after the creator of the Salter duck. Technical name such a converter is an oscillating wing. The shape of the converter ensures maximum power extraction (Fig. 9).
Waves coming from the left cause the duck to oscillate. Cylindrical shape opposite surface ensures that the wave does not propagate to the right when the weft oscillates around its axis. Power can be removed from the axis of the oscillatory system in such a way as to ensure a minimum of energy reflection. Reflecting and transmitting only a small part of the wave energy (approximately 5%), this device has a very high conversion efficiency in a wide range of exciting frequencies (Fig. 10).
Initially, Salter created a prototype of a fairly narrow-band frequency device. In a wave pool, it absorbed up to 90% of the incident energy. The first tests in conditions close to sea conditions were carried out in May 1977 on Lake. Loch Ness. 50-meter garland of 20-meter "ducks" total mass 16 t was launched and tested for 4 months at various wave conditions. In December of the same year, this model, 1/10 of the future size of the ocean converter, was again launched and produced the first current. During 3 months of one of the harshest winter periods, the model of the first English wave power plant operated with an efficiency of about 50%.
Salter's further developments are aimed at providing the duck with the ability to withstand impacts maximum waves and create an anchored garland of transducers in the form of a fairly flexible line. It is assumed that the characteristic size of a real duck will be approximately 0.1 liters, which corresponds to 10 m for 100-meter Atlantic waves. A string of ducks several kilometers long is expected to be installed in the area with the most intense waves to the west of the Hebrides. The power of the entire station will be approximately 100 MW.
The most serious shortcomings for Salter's ducks were the following:
The need to transfer slow oscillatory motion to the generator drive;
The need to remove power from a long-distance device floating at a considerable depth;
Due to the high sensitivity of the system to the direction of waves, it is necessary to monitor changes in their direction to obtain high conversion efficiency;
Difficulties during assembly and installation due to the complexity of the “duck” surface shape.
Another variant of a wave converter with a swinging element is the Cockerell contour raft. His model, also 1/10 the size, was tested in the same year as the Salter duck in the Solent Strait near Southampton. A contour raft is a multi-link system of hinged sections (Fig. 11). Like the canard, it is mounted perpendicular to the wave front and tracks its profile.
Detailed laboratory tests on a 1/100 scale model of the raft showed that its efficiency was about 45%. This is lower than that of Salter’s “duck” (but the raft attracts another advantage: the proximity of the design to traditional shipbuilding ones). The production of such rafts will not require the creation of new ones. industrial enterprises and will increase employment in the shipbuilding industry.
Converters using the energy of an oscillating water column
When a wave hits a partially submerged cavity open under water, the column of liquid in the cavity oscillates, causing pressure changes in the gas above the liquid. The cavity may be connected to the atmosphere through a turbine. The flow may be controlled to flow through the turbine in one direction, or a Wells turbine may be used. At least two examples are already known commercial use devices based on this principle are signal buoys introduced in Japan by Masuda (Fig. 12) and in the UK by employees of Queen's University Belfast. A larger device, connected to the grid for the first time, was built in Toftestollen (Norway) by Kvaernor Brug A/S. The basic operating principle of an oscillating column is shown in Fig. 13. At Toftestollen it is used in a 500-kilowatt plant built on the edge of a cliff. In addition, the UK National Electrical Laboratory (NEL) offers a direct-mount design. seabed. The main advantage of devices based on the principle of an oscillating water column is that the air speed in front of the turbine can be significantly increased by reducing the flow area of the channel. This makes it possible to combine slow wave motion with high-frequency turbine rotation. In addition, here it is possible to remove the generating device from the zone of direct influence of salty sea water.
Underwater devices
The advantages of subsea devices are that these devices avoid the effects of storms on the transducers. However, their use increases the difficulties associated with energy extraction and maintenance.
As an example, we can consider a “Bristol cylinder” type converter, which belongs to the group of devices operating under the influence of high-speed pressure in a wave. An air-filled floating body (cylinder) having average density 0.6-0.8 t/m 3, fixed under water on supports installed on the ground. The cylinder oscillates in the wave, moving along an elliptical path and activating hydraulic pumps mounted in the supports and converting the energy of the cylinder movement. The liquid they pump can be supplied through pipelines to a generator station common to several cylinders. One of the advantages of the "Bristol cylinder" idea is that once tuned to the optimal frequency, it does not reflect energy from other frequencies, but allows it to propagate further where it can be absorbed by other transducers, such as cylinders with a different frequency.
The transmission of motion from the executive motor to the output link of the electromechanical module can be ensured using various motion converters (gears), the structure and design features of which depend on the type of engine, the type of movement of the working element and the method of their location. Motion converters have a significant impact on the quality of operation of the electromechanical system as a whole.
When designing electromechanical modules, the type of motion converter is selected based on the complexity of its design, efficiency, backlash in transmission, overall dimensions, weight, self-braking properties, rigidity, ease of layout, manufacturability, cost, etc.
Purpose and classification of motion converters
Motion converters are designed to convert one type of movement into another, matching the speeds and torques of the engine and the working element. To transform motion, gear, worm, chain, belt and friction transmissions, as well as screw-nut transmissions are used (Fig. 4.1). Due to the fact that the angular speed of rotation of electric motors, as a rule, is much higher than the speeds of the working bodies of electromechanical modules, reduction gears are used in motion converters.
Rice. 4.1. Classification of mechanical gears
motion converters
Gears
The most common motion converters are gears - mechanisms that transmit or convert motion using gearing with changing angular velocities and torques. Such transmissions are used to convert rotational movement between shafts with parallel ones (Fig. 4.2, a-d), intersecting (Fig. 4.2, e-z) axes, as well as for converting rotational motion into translational motion, and vice versa (Fig. 4.2, d).
Rice. 4.2. Main types of gears:
A– cylindrical with straight teeth; b– cylindrical with oblique teeth; V– cylindrical with chevron teeth; G– cylindrical internal gearing with straight teeth; d- rack and pinion transmission; e– conical with straight teeth; and– conical with tangential teeth; h– conical with circular teeth;
The kinematic diagram of cylindrical and bevel gears is shown in Fig. 4.3. The gear ratio can be found from the ratio of the number of input teeth z 1 and day off z 2 gears
The main characteristics of mechanical transmissions are the power on the shafts and W, angular velocities and in s -1, (or rotation speed and in min -1), moments of forces and in , gear ratio and efficiency. . Expressions describing the relationships between the main characteristics of gears have the form 
or and , (4.2)
, (4.3)
Or , (4.4)
or when highlighting the moment of transmission losses in the form
. (4.6)
It should also be noted that bringing the moments of inertia of an element of an electromechanical module rotating at a speed or translationally moving at a speed to speed can be performed based on the law of conservation of kinetic energy
or 
(4.7)
according to the expression
Or , (4.8)
where is the mass of a translationally moving body; – radius of reduction to the shaft with speed
For a rack and pinion transmission, when converting rotational motion into translational motion, the linear speed of the rack will be determined as
, , (4.10)
gear ratio
, , (4.11)
where is the gear diameter in mm.
The rack and pinion gear ratio can be in the range of 10…200 m -1. Efficiency cylindrical gears is 0.95...0.99.
In Fig. Figure 4.4 shows a diagram of a planetary gear. Planetary gears are gears in which geometric axis at least one gear is movable. The main elements of the planetary gear are:
Sun gear 1 (located in the center);
Carrier 2 , rigidly fixing the axes of several planetary gears relative to each other same size 3 (satellites) meshed with the sun gear;
Ring gear 4 (epicycle), which has internal engagement with planetary gears.
When using a planetary gear as a gearbox, one of its three main elements is fixed motionless, the other element is used as a drive, and the third as a driven.
In the case when the driver 2 fixed (), and power is supplied through the sun gear 1 , planetary gears 3 will rotate in place at a speed determined by the ratio of the number of their teeth relative to the sun gear
Rotation of planetary gears 3 transmitted to the ring gear 4 . If a ring gear has teeth, it will rotate at a speed
As a result, if the carrier is locked, then the overall gear ratio of the system will be equal to
If the ring gear () is fixed and the power is supplied to the carrier, then the gear ratio to the sun gear will be greater than unity and will be
Planetary gears are most widely used in automobile differentials and in summing links of kinematic circuits of metal-cutting machines. IN modern devices cascades of several planetary gears can be used to obtain a wide range of gear ratios. Many automatic car transmissions operate on this principle.
The advantages of planetary gears compared to conventional cylindrical or bevel gears are their smaller dimensions and weight. Disadvantages: increased manufacturing accuracy, larger number rolling bearings.
To obtain large gear ratios (up to 90,000), wave transmissions are used (see Fig. 4.5). The wave transmission consists of a rigid fixed element - a gear 1
with internal teeth, motionless relative to the gear housing; flexible element - thin-walled elastic gear with external teeth 2
connected to the output shaft; wave generator - cam 3
, eccentric or other mechanism that stretches a flexible element until pairs of engagement with a fixed element are formed at two (or more) points. The number of teeth of the flexible wheel is several less number teeth of the fixed element.
The operating principle of wave gear transmission is illustrated in Fig. 4.6. For example, if the number of teeth of a flexible wheel is 200, and the fixed element is 202, and there is a two-wave transmission (two protrusions on the wave generator), when the generator rotates clockwise, the first tooth of the flexible wheel will enter the first cavity of the rigid one, the second into the second, etc. up to the two hundredth tooth and two hundredth cavity. On the next revolution, the first tooth of the flexible wheel will enter the two hundred and first cavity, the second - into the two hundred and second, and the third - into the first cavity of the rigid wheel. Thus, in one full turn wave generator, the flexible wheel will move relative to the rigid one by only 2 teeth.
The gear ratio of wave transmission from the wave generator shaft to the flexible wheel shaft is equal to
where , – respectively, the number of teeth of the rigid and flexible gears.
The main disadvantage of such gearboxes is low efficiency. (no more than 70...80%), and also high requirements to the precision of manufacturing and the properties of the materials used.
Worm-gear
A worm gear is a mechanism for transmitting rotation between intersecting (usually mutually perpendicular) shafts. When the worm rotates 1
(Fig. 4.7) its turns smoothly engage with the gear teeth 2
and bring the latter into rotation.
The driving link of a worm gear is a worm, and the driven link is a worm wheel. Distinctive feature worm gear is the presence of a self-locking effect, i.e. impossibility of reverse power transfer from the wheel to the worm.
The gear ratio of the worm gear depends on the number of worm passes:
| over | |||
and number of wheel teeth
The main disadvantage of worm gears is their low efficiency. – 70...80%. For this reason, they are used to transmit small and medium powers, usually up to 50 kW, less often up to 200 kW.
Flexible transmissions
Flexible gears are designed to transmit rotary motion and convert rotary motion into translational motion and vice versa. Flexible transmissions include belt, chain and cable.
Belt drives
The mechanism for transmitting rotation using a flexible element (belt) due to friction forces (for toothed belts - engagement forces) is called a belt drive. The belt drive (see Fig. 4.8) consists of a drive 1 and slave 2 pulleys and the belt put on them 3 . The mechanism may also include a tensioning device 4 and fencing (not shown in Fig. 4.8).
Gear ratio determined by the ratio of the diameters of the driven and driving pulleys and, as a rule, taking into account the elastic sliding of the belt along the pulleys
, (4.16)
which is usually taken at .
Efficiency belt drive is 90...95%
The main advantages are: the ability to work with high speeds, smooth and quiet operation, simplicity of design and low cost. The disadvantages of belt transmission are: significant forces acting on the shafts and supports, variability of the transmission ratio, and short service life of the belts.
Chain transmission
A chain drive (Fig. 4.9) is a mechanism for transmitting rotation between parallel shafts using sprocket wheels rigidly attached to the shafts, through which a closed drive chain is thrown.
The gear ratio of the chain drive is determined by the ratio of the number of teeth of the driven and driving sprockets
average speed chain is determined by dependence
Where R– chain pitch, mm.
Chain drives are universal, simple and economical. Compared to gear drives, they are less sensitive to inaccuracies in the location of shafts and shock loads, allow virtually unlimited center-to-center distances, and provide a simpler layout. Compared to belt drives, they are characterized by the following advantages: the absence of pretension and associated additional loads on shafts and bearings; high power transmission at both high and low speeds; maintaining satisfactory performance at high and low temperatures; adaptation to any design changes by removing or adding links.
The disadvantages of chain drives include: uneven running, which increases as the number of sprocket teeth decreases and the link pitch increases; increased noise and chain wear due to incorrect choice of design, careless installation and poor maintenance; the need for lubrication and elimination of sagging of the idle branch as the chain wears out.
Cable transmission
In a cable transmission, the transformation of rotational motion into translational motion and vice versa between links (drive 1
and slave 2
) is carried out using a cable 3
(Fig. 4.10). Cables are made of steel wire (usually galvanized).
During operation of a cable transmission, individual wires of the cable are subject to stretching, bending, torsion and crushing. From the condition of limiting the bending stress in the cable, the minimum diameter of the pulleys is found according to the condition
, (4.19)
A) and the rolling screw nut (Fig. 4.11, b). The main transmission elements are: screw 1 and nut 2 .
In a sliding pair to increase efficiency. to reduce friction losses, steel balls are placed between these elements 3
. When the screw (nut) rotates, the balls roll along the screw surfaces screw and nut and transmit rotation from screw to nut, or from nut to screw. The speed of movement of the balls differs from the speed of the screw and nut, therefore, in order to ensure continuous circulation of the balls, the ends of the working part of the thread are connected by a return channel.
The screw-nut transmission ratio is determined as, m -1:
, , (4.21)
where linear speed screw (nut) can be calculated according to the dependence
, (4.22)
Where R– thread pitch, mm; To– number of thread starts.
In industrially manufactured screw-nut gears, the gear ratio is 300…2000 .
Efficiency the rolling screw-nut transmission is 0.85...0.95, and the sliding screw nut is 0.25...0.6.
The advantage of the transmission is high precision of movement and low metal consumption. The disadvantage is low efficiency. in sliding gears and the complexity of manufacturing rolling gears.
1. Formulate a definition for motion transducers. Which mechanical transmissions Do you know motion converters? Name the main characteristics of mechanical transmissions.
2. Remember the main advantages and disadvantages of all mechanical transmissions known to you.
3. List the main types of gears. Explain the principle of operation of a planetary gear.
4. What is the self-locking effect of the worm gear?
Waves surround us everywhere, as we live in a world of movements and sounds. What is the nature of the wave process, what is the essence of the theory of wave processes? Let's look at this using experimental examples.
The concept of waves in physics
A common concept for many processes is the presence of sound. By definition, sound is the result of rapid oscillatory movements, which are created by air or other medium perceived by our auditory organs. Knowing this definition, we can proceed to consider the concept of “wave process”. There are a number of experiments that allow us to clearly examine this phenomenon.
The wave processes studied in physics can be observed in the form of radio waves, sound waves, compression waves when used vocal cords. They spread through the air.
For visual definition concepts throw a stone into a puddle and characterize the spread of effects. This is an example It occurs due to the rise and fall of a liquid.
Acoustics
An entire section called “Acoustics” is devoted to the study of the properties of sound in physics. Let's figure out what it characterizes. Let's focus on phenomena and processes in which everything is not yet clear, on problems that are still waiting to be solved.
Acoustics, like other branches of physics, still has many unsolved mysteries. They have yet to be discovered. Let us consider the wave process in acoustics.
Sound
This concept is associated with the presence that are produced by particles of the medium. Sound is a series of oscillatory processes associated with the occurrence of waves. In the process of formation in the environment of compression and rarefaction, a wave process arises.
Wavelength indicators depend on the nature of the medium where oscillatory processes take place. Almost all phenomena that occur in nature are associated with the presence of sound vibrations and sound waves that propagate in the medium.
Examples of determining the wave process in nature
These movements can inform about the phenomenon of the wave process. High frequency sound waves can spread over thousands of kilometers, for example, if a volcanic eruption occurs.
During an earthquake, strong acoustic and geoacoustic vibrations occur, which can be recorded with special sound receivers.
During an underwater earthquake, an interesting and terrible phenomenon- tsunami, which is huge wave, which arose during powerful underground or underwater manifestations of the elements.
Thanks to acoustics, you can get information that a tsunami is approaching. Many of these phenomena have been known for a long time. But still some concepts of physics require careful study. Therefore, to explore mysteries that have not yet been solved, it is sound waves that come to the rescue.
Tectonic theory
In the 18th century, the “catastrophe hypothesis” was born. At that time, the concepts of “element” and “regularity” were not connected. Then they discovered that the age of the bottom of the world's oceans is much younger than the land, and this surface is constantly renewed.
It was at this time, thanks to a new look at the earth, that the crazy hypothesis grew into the theory of “Lithospheric Plate Tectonics,” which states that the earth’s mantle moves and the firmament floats. This process is similar to the movement of an eternal ice drift.
To understand the described process, it is important to free yourself from stereotypes and habitual views, to realize other types of being.
Further advances in science
Geological life on earth has its own time and state of matter. Science has managed to recreate the likeness. At the bottom of the ocean there is a continuous movement, during which ruptures and the formation of rift ridges occur when new substance from the depths of the earth rises to the surface and gradually cools.
At this time, processes occur on land when on the surface earth's mantle floating colossal plates of the lithosphere - the upper stone shell of the earth, which carries continents and the seabed.
There are about ten such plates. The mantle is restless, so lithospheric plates start to move. IN laboratory conditions the process has the appearance of an elegant experience.
In nature, this threatens with a geological catastrophe - an earthquake. The reason is global convection processes that occur in the depths of the earth. The result of the seething will be a tsunami.
Japan
Among other seismically dangerous areas of the earth, Japan occupies a special place; this chain of islands is called the “belt of fire.”
By closely monitoring the breathing of the earth's surface, one can predict the impending catastrophe. To study oscillatory processes, an ultra-deep drilling rig was introduced into the thickness of the earth. It penetrated to a depth of 12 km and allowed scientists to draw conclusions about the presence of certain rocks inside the earth.
The speed of an electromagnetic wave is studied in physics lessons in the 9th grade. They show an experiment with weights located on equal distance from each other. They are connected by identical springs of the usual type.
If you move the first weight to the right by a certain distance, the second one remains in the same position for some time, but the spring already begins to compress.
Definition of "wave"
Since such a process has occurred, an elastic force has arisen that will push the second weight. It will receive acceleration, after some time it will pick up speed, move in this direction and compress the spring between the second and third weights. In turn, the third will receive acceleration, begin to accelerate, shift and affect the fourth spring. And so the process will occur on all elements of the system.
In this case, the displacement of the second load will occur later in time than the first. The effect always lags behind the cause.
Also, the displacement of the second load will entail the displacement of the third. This process tends to spread to the right.
If the first load begins to oscillate harmonic law, then this process will spread to the second weight, but with a delayed reaction. Therefore, if you make the first weight oscillate, you can get an oscillation that will spread in space over time. This is the definition of a wave.
Types of waves
Let's imagine a substance that consists of atoms, they are:
- have mass - like the weights proposed in the experiment;
- join together to form a solid by chemical bonds(as considered in the experiment with a spring).
It follows that matter is a system that resembles a model from experience. It can spread. This process is associated with the emergence of elastic forces. Such waves are often called “elastic”.
There are two types of elastic waves. To determine them, you can take a long spring, secure it on one side and stretch it to the right. This way you can see that the direction of wave propagation is along the spring. The particles of the medium are displaced in the same direction.
In such a wave, the nature of the direction of vibration of the particles coincides with the direction of propagation of the wave. This concept called "longitudinal wave".
If you stretch a spring and give it time to come to rest, and then suddenly change its position in the vertical direction, you will see that the wave propagates along the spring and is reflected many times.
But the direction of particle oscillation is now vertical, and the wave propagation is horizontal. This is a transverse wave. It can only exist in solids.
Electromagnetic wave speed different types is different. Seismologists successfully use this property to determine the distance to earthquake sources.
When a wave propagates, particles oscillate along or across, but this is not accompanied by the transfer of matter, but only by movement. This is stated in the 9th grade Physics textbook.
Characteristics of the wave equation
Wave equation in physical science- a type of linear hyperbolic differential equation. It is also used for other areas that are covered by the theoretical one of the equations that are used for calculations mathematical physics. In particular, they describe gravitational waves. Used to describe processes:
- in acoustics, as a rule, linear type;
- in electrodynamics.
Wave processes are displayed in the calculation for the multidimensional case of a homogeneous wave equation.
Difference between wave and oscillation
Remarkable discoveries come from thinking about an ordinary phenomenon. Galileo used his own heartbeat as the standard of time. Thus, the constancy of the process of oscillation of a pendulum was discovered - one of the fundamental principles of mechanics. It is absolutely only for mathematical pendulum- an ideal oscillatory system, which is characterized by:
To bring a system out of equilibrium, a condition for the occurrence of oscillations is necessary. In this case, a certain energy is communicated. Various oscillatory systems required different kinds energy.
Oscillation is a process that is characterized by constant repetition of movements or states of a system during certain periods of time. Visual demonstration oscillatory process is an example of a swinging pendulum.
Oscillatory and wave processes are observed in almost all natural phenomena.
The wave has the function of disturbing or changing the state of the medium, propagated in space and carrying energy without the need to transfer the substance. This distinctive property wave processes, they have been studied in physics for a long time. When researching, you can isolate the wavelength.
Sound waves can exist in all spheres; they do not exist only in a vacuum. Special properties possess electromagnetic waves. They can exist everywhere, even in a vacuum.
The energy of a wave depends on its amplitude. A circular wave, propagating from a source, dissipates energy in space, so its amplitude quickly decreases.
A linear wave has interesting properties. Its energy is not dissipated in space, so the amplitude of such waves decreases only due to the force of friction.
The direction of wave propagation is depicted by rays - lines that are perpendicular to the wave front.
The angle between the incident ray and the normal is Between the normal and the reflected ray - the angle of reflection. The equality of these angles is maintained at any position of the obstacle relative to the wave front.
When waves moving in a direction meet opposite directions, a standing wave may form.
Results
Particles of the medium between neighboring nodes standing wave oscillate in the same phase. These are the parameters of the wave process recorded in wave equations. When waves meet, both increases and decreases in their amplitudes can be observed.
Knowing the main characteristics of the wave process, it is possible to determine the amplitude of the resulting wave at a given point. Let us establish in what phase the wave from the first and second sources will arrive at this point. Moreover, the phases are opposite.
If the stroke difference is odd number half-waves, the amplitude of the resulting wave at this point will be minimal. If the path difference is zero or an integer number of wavelengths, an increase in the amplitude of the resulting wave will be observed at the meeting point. This is when waves from two sources are added.
Frequency electromagnetic waves fixed in modern technology. The receiving device must detect weak electromagnetic waves. If you install a reflector, more wave energy will enter the receiver. The reflector system is installed so that it creates the maximum signal at the receiving device.
The characteristics of the wave process underlie modern ideas about the nature of light and the structure of matter. Thus, when studying them using a 9th grade physics textbook, you can successfully learn to solve problems in the field of mechanics.
In this chapter we will discuss a new phenomenon - waves. Waves are often discussed a lot in physics, and we must concentrate our attention on this issue not only because we are going to consider special example waves - sound - but also because wave processes have other numerous applications in all areas of physics.
While studying the harmonic oscillator, we have already noted that there are examples of both mechanical oscillating systems and electrical ones. Waves are closely related to oscillatory systems, but wave motion is not only oscillation in this place, depending on time, but also movement in space.
We've already actually studied waves. When we talked about wave properties light, we turned Special attention to spatial interference of waves of the same frequency from various sources located in different places. There are two more important phenomena, which we did not mention and which are characteristic of both light, i.e. electromagnetic waves, and any other form of wave motion. The first of them is the phenomenon of interference, but not in space, but in time. When we listen to sounds from two sources at once, and their frequencies are slightly different, we receive either the crests of both waves, or the crest of one wave and the trough of the other (Fig. 47.1). The sound either increases or decreases, beats occur, or, in other words, interference occurs in time. The second phenomenon is wave motion in a closed volume, when waves are reflected from one or the other wall.
Fig. 47.1. Interference of sound over time from two sources with slightly different frequencies results in beats.
All these effects could, of course, be considered using the example of electromagnetic waves. We did not do this for the reason that in one example we would not feel general phenomena characteristic of a variety of processes. To emphasize the generality of the concept of waves beyond the framework of electrodynamics, we will consider here another example - sound waves.
There is another example - sea waves running onto the shore, or small water ripples. In addition, there are two types of elastic waves in solids: compression waves (or longitudinal waves), in which the particles of the body oscillate back and forth in the direction of wave propagation ( sound vibrations in gas of exactly this type), and transverse waves, when the particles of a body oscillate perpendicular to the direction of motion of the wave. During earthquakes, as a result of the movement of a section of the earth's crust, elastic waves both types.
And finally, there is another type of waves that gives us modern physics. These are waves that determine the amplitude of the probability of finding a particle in a given place - “matter waves”, which we have already talked about. Their frequency is proportional to energy, and their wave number is proportional to momentum. These waves are found in quantum mechanics.
In this chapter we will consider only those waves whose speed does not depend on the wavelength. An example of such waves is the propagation of light in a vacuum. The speed of light in this case is the same for radio waves, for blue and green light, and in general for light of any wavelength. That is why, when we described wave phenomena, at first we did not notice the very fact of wave propagation. Instead, we said that if we transfer a charge to a certain point, then the electric field at a distance will be proportional to the acceleration of the charge, but not at the moment of time, but at an earlier moment of time. Therefore the distribution electric field in space at some point in time, shown in Fig. 47.2, after a while it will move a distance. Expressed mathematically, we can say that in the one-dimensional case we are considering, the electric field is a function of . From this it is clear that when it turns out to be a function only of . If you take more late moment time and slightly increase we get the same field value. For example, if the field maximum occurs at and at time , then the position of the maximum at time is found from the equality
We see that such a function corresponds to wave propagation.
So, the function describes the wave. We can write down everything that has been said briefly like this:
If . Of course, there is also another possibility when the source emits waves not to the right, as indicated in Fig. 47.2, and to the left, so that the waves will move towards negative ones. Then the propagation of the wave would be described by the function .
Fig. 47.2. Approximate distribution of the electric field at some point in time (a) and the electric field after a period of time (b).
It may also happen that several waves are simultaneously moving in space, and then the electric field is the sum of all fields and they all propagate independently. This property of electric fields can be expressed as follows: let it correspond to one wave, and a to another, then their sum also describes a certain wave. This statement is called the principle of superposition. This is also true for sound waves.
We know well that sounds are perceived in the sequence in which they are created by the source. What if high frequencies spread faster than low ones, then instead of the sounds of music we would hear a sharp and abrupt noise. Likewise, if red light were traveling faster than blue light, the flash of white light would appear red, then white, and finally blue. We know very well that this does not actually happen. Both sound and light move through air at speeds that are almost independent of frequency. Examples of wave motion where this principle does not apply will be discussed in Chapter. 48.
For light (electromagnetic waves), we have obtained a formula that determines the electric field at a given point, which arises when the charge is accelerated. It would seem that all that remains for us now is to determine in a similar way some characteristic of air, say pressure at given distance from the source through the movement of the source, and take into account the delay in sound propagation.
In the case of light, this approach was acceptable, since all our knowledge boiled down to the fact that a charge in one place acts with some force on a charge in another place. The details of the propagation of interaction from one point to another were completely unimportant. But sound, as we know, travels through the air from a source to the ear, and it is natural to ask what the air pressure is at any given moment. In addition, I would like to know exactly how the air moves.
In the case of electricity, we could believe in the rule, since we had not yet studied the laws of electricity, but for sound this is not so. It is not enough for us to formulate the law determining the propagation of sound pressure in the air; this process must be explained on the basis of the laws of mechanics. In short, sound is part of mechanics and must be explained using Newton's laws. The propagation of sound from one point to another is simply a consequence of the mechanics and properties of gases, if sound propagates in a gas, or the properties of liquids and solids, if sound passes through these media. Later we will also derive the properties of light and its wave motion from the laws of electrodynamics.
Wave energy is a branch of energy associated with obtaining energy from sea waves. The resulting energy can be used for desalination, pumping water and generating electricity.
The first patent for a device to obtain energy from sea waves was issued in 1799 in Paris. The first wave energy capture device was built there in 1910.
Wave energy received particular attention during the 1973 oil crisis. The development of new devices was carried out by scientists from the Norwegian Institute of Technology, University of Bristol and Lancaster University.
After oil prices stabilized, research funding decreased.
The first experimental wave power plant was built in Portugal, it has a capacity of about 2 MW.
The main elements of the power plant are three Pelamis P-750 converters, which bend under the influence of waves. Special pistons supply oil to hydraulic motors that drive electric generators.
In the future, it is planned to expand the power plant through the construction of new converters.
According to scientists, the total potential of wave energy around the world is about 2 TW. The most promising are: West Coast Europe, Australia, New Zealand, north coast Great Britain. And also some coasts in North and South America.
The problems that the use of wave energy may cause are under study. Wave energy can have Negative influence on local flora and fauna. Also wave converters cause noise, which can negatively affect fishing.
Various converters are used to produce wave electricity, here are some of them:
The Pacific Northwest Cooperative is funding a buoy-based wave park in Oregon. The vibrations of the buoy from the waves are transmitted to a special generator. Electricity is transmitted using an underwater transmission line. Buoys are designed to be installed at a distance of 8 miles from shore.
A wave power station with WaveRoller converters was built in Finland. They are small rafts with an anchor. Under the influence of waves, they swing, transferring energy to the piston pump.
In Denmark, a power plant with Dragon type converters was built in 2003. They represent artificial reservoirs in the middle of the ocean, located above the water level. Returning under the influence of gravity, the water passes through hydraulic turbines.
Currently, wave energy is being developed by some countries.
