Surface waves

A storm always covers a limited part of the ocean surface. As the wind strengthens, waves appear and grow in the area of ​​its action. Some time after the wind has established itself, the waves become statistically stationary. This means that the average height of the waves, their average length and average period do not change. However, the instantaneous states of the water surface in the zone of wind action appear chaotic. At a particular moment in time, this surface is a complex, disorderly alternation of swells, depressions and hills of varying heights and horizontal extent. When moving to subsequent moments, the geometry of the water surface changes in a random, unpredictable way. In view of the above, only a statistical approach is applicable to the study of waves in the zone of their generation by wind. The methods of probability theory and numerous observations made it possible to obtain a number of useful results along this path. The probability distribution of wave heights was found to follow the Rayleigh distribution function. Its integral expression is the formula

Where: h w – wave height with probability of not exceeding F;

h w 0 – average wave height.

Exponent m varies from 4 in deep water to 2 in shallow water. Average wave height h w 0 can be found using additional relationships based on the balance of wave energy. According to observations, during storms the heights of ocean waves often exceed 10 m. During hurricanes, individual waves can reach a height of 20-25 m.

Time T, during which the wave moves along its length l, is called the period of the wave. The average period and average length of waves in the zone of their generation by the wind are expressed, respectively, by empirical formulas that relate these quantities to wind speed:

(97)

(98)

The numerical coefficients in these formulas are dimensional, wind speed w has the dimension m/s.

The longer the wave, the faster it moves through the ocean and the slower its energy dissipates. Therefore, the largest waves that arise in the storm zone can extend beyond this zone and move great distances from the place of their origin. Such waves are called swell waves. When the wind stops, the short waves die out first and after a while only swell waves remain in the area of ​​the ended storm. Swell waves are ordered formations. They look like parallel shafts with a shape close to sinusoidal and follow each other at approximately equal distances.

The correct nature of swell waves makes it possible to describe their properties with sufficient accuracy using hydrodynamic methods. The sine wave profile and its elements are shown in Fig. 56. Letter x indicates the height of the free surface relative to the rest level. When propagating sinusoidal waves x changes along the way X and in time t according to the law

, (99)

Where: a – amplitude (half-height) of waves.

The speed of propagation of sinusoidal waves, in the general case, is expressed by the formula

. (100)

If the depth of the reservoir is large compared to the wavelength, i.e. , That , and formula (100) becomes the following:

. (101)

If, on the contrary, , then , and instead of formula (100) we have

. (102)

Thus, in deep reservoirs, the speed of wave propagation is determined by their length, and in shallow reservoirs, by the depth of the reservoir. The conventional boundary between deep and shallow bodies of water is taken to be a depth equal to half the wavelength: . Above the ocean floor, the ocean is always deep for wind waves, but it becomes "shallow" when tsunami waves propagate through it.

Since the lengths of swell waves can range from several tens to several hundred meters, then, according to formula (101), the speeds of their movement usually lie in the range of 10-20 m/s. This means that swell waves can travel more than 1,500 km in a day.

When approaching the shore, the waves transform. Their ridges become sharper, their hollows become flat. When the water depth is equal to 1.5-2.0 wave heights, the waves break.

If waves in the open ocean or sea, as well as in the open part of a lake or reservoir, propagate along the coast, then they turn around on the coastal shallows.

The wave crests tend to become parallel to the coastline, and the wave speed receives a component directed toward the shore (Fig. 57). This

The phenomenon is called refraction of waves on the coastal shallows. The explanation of wave refraction is given by formula (102). The speed of the wave above the bottom slope turns out to be variable along the crest - the sections of the crest closest to the shore move more slowly, those farther from the shore - faster.

Approaching the shore at an acute angle and breaking, the waves create an along-shore flow of water (see Fig. 57). Alongshore flow velocities can reach 1.0-1.5 m/s. These speeds are sufficient for intensive sediment transport, and alongshore currents move large masses of soil on sea coasts, as well as in the coastal zones of lakes and reservoirs. When a long-shore flow meets the mouth of a bay or bay, it deposits its cargo or part of it here, and the entrances to the bays and bays become shallow after storms.

Ebbs and flows

A tidal wave runs around the world's oceans twice a day. The tidal wave period is equal to half a lunar day: 12 hours 25 minutes, or 44700 s. The greater length of the lunar day compared to the solar day is explained by the fact that the Moon rotates in its orbit in the same direction in which the Earth rotates. Along the great circle of the globe, lying in the plane of the Moon's orbit, the tidal wave moves at an average speed of 450 m/s. This speed cannot be obtained from formula (102), since the ebb and flow of the tides are forced oscillations, and not free, like swell waves or seiches.

The usually observed course of rainfall fluctuations in water level is shown in Fig. 58. The highest level at high tide is called high water PV, the lowest at low tide is called low water MB. Fluctuations in levels are somewhat delayed in relation to the movement of the Moon. The time between the Moon's climax and full water is called the lunar interval. It changes throughout the month and year, as well as across the ocean. When the declination of the Moon is zero (the plane of the Moon's orbit coincides with the plane of the equator), the height of the two semidiurnal high waters is the same. With a non-zero declination (and it varies from 0° to ±28°), the heights of the two high waters are different.

Tidal waves are generated by two celestial bodies - the Sun and the Moon and spread over a spherical surface. These circumstances alone, not to mention the uneven distribution of ocean depths and the irregularity of its boundaries, give rainfall fluctuations an extremely complex character. Manifestations of this complexity include the fact that, along with those shown in Fig. 58 semi-diurnal oscillations, in the ocean, under certain conditions, diurnal oscillations are formed - with one high and one low water per day.

The difference between the height of high water and low water is called the magnitude of the tide. In the open ocean the tide is low. On small oceanic islands it rarely exceeds 1 m. The tide reaches its highest values ​​off the coast of oceans and seas, especially in bays, bays and narrows. Along the maritime borders of the USSR, the highest tide - up to 12 m - is observed in the Penzhenskaya Bay of the Sea of ​​​​Okhotsk. Tides reach values ​​of 8-10 m at the mouth of the Mezen. At the mouths of the large Siberian rivers Ob, Yenisei and Lena, rainfall fluctuations in levels are much weaker than surge fluctuations.

In Western Europe, the highest tides occur on the Atlantic coast of France and off the coast of England. The tide in Bristol Bay reaches 15 m. The highest tides on the globe - up to 18 m - are observed in the Bay of Fundy on the Atlantic coast of Canada.

Let us consider the mechanism of storm fluctuations in ocean level. The forces that cause these fluctuations are called tidal forces. They are caused by the attraction of the Moon and the Sun, but as will now be shown, they are by no means equal to the forces of attraction themselves. In addition to them, centrifugal and Coriolis forces of inertia and friction forces participate in the formation of storm oscillations. The tidal force created by the gravity of the Moon, due to the proximity of the Moon to the Earth, is 2.3 times greater than the tidal force created by the Sun. The absolute values ​​of tidal forces are very small. When referred to a unit of mass, they are measured in hundred-millionths of the acceleration due to gravity on Earth.

To understand the essence of the phenomenon, let us analyze the effect of an attracting body on water in the ocean and take the Sun as such, since the laws of planetary motion around the Sun make it possible to very simply resolve the issue of centrifugal forces caused by this movement (if we took the Moon as an attracting body, then would find that the Earth and Moon rotate around a common center of mass located inside the Earth, and determining centrifugal forces would become very difficult).

Let us accept, without introducing any error into the essence of our reasoning, that the plane of the equator coincides with the plane of the Earth’s orbit, and we highlight in this plane the diameter of the Earth, directed at a given moment in time

on the Sun (Fig. 59). The centrifugal force and the gravitational force of the Sun act along the selected diameter. Due to the laws of planetary rotation, all points of the Earth have the same orbital trajectories and therefore the centrifugal force caused by orbital motion at all points on the globe, and therefore at all points of our diameter, is the same. As for the force of attraction, from the end of the diameter facing the Sun is the zenith point Z- to its other end - the nadir point N it should decrease like , Where r– the distance of the point from the center of the Sun. Based on the smallness of the diameter of the Earth (»13 thousand km) compared to the distance from the Earth to the Sun (149 million km), it is permissible to neglect the nonlinearity of this change and accept that the force of attraction at the zenith will be greater, and at the nadir there will be less force of attraction at center of the Earth by the same amount DF. At the center of the Earth, the gravitational and centrifugal forces are balanced; on the earth’s surface, equilibrium obviously does not work. At the zenith, where the attractive force is greater than the centrifugal force, their resultant DF directed towards the Sun, at nadir - DF directed away from the Sun. Powers ±DF and there are tide-forming ones. The general definition of tidal forces is as follows: the tidal force at a given point on the globe is the vector difference between the force of attraction of a celestial body (Sun or Moon) at a given point and the force of its gravity at the center of the Earth. Ultimately, the inhomogeneity of the gravitational field is responsible for the formation of tides.

The described distribution of tidal forces leads to the fact that at each moment of time the free surface of the World Ocean has two diametrically opposite humps. These humps in the reference frame associated with the Sun hardly change their position during the day, but in the reference frame associated with the rotating Earth, they move against the direction of rotation, creating the effect of two semidiurnal tidal waves.

Qualitatively the same influence on the waters of the ocean and the attraction of the Moon. Since the relative position of the three luminaries - the Sun, the Earth and the Moon - periodically changes, the sum of the two tidal forces also periodically changes, and with it the magnitude of the tides. The most significant is the so-called monthly tide inequality. It is as follows. On the new moon and full moon there are three bodies - the Sun WITH(Fig. 60), Earth 3 and Moon L- located on the same straight line. This state is called astronomical syzygy. The tidal forces of the Moon and the Sun add up during syzygy, and 1-2 days after it the tides reach their greatest magnitude. They are called syzygy. During the first and last quarter of the Moon, the Earth-Moon direction forms a right angle with the Earth-Sun direction. This configuration of three bodies is called astronomical quadrature. With quadrature, the two tide-forming forces do not add up: the axes of the two pairs of humps are perpendicular and soon the tides decrease to minimum values. Such tides are called quadrature.

What has been said in this paragraph can only give a general idea of ​​tides. The theory of tides was studied by many outstanding mechanics and mathematicians (I. Newton, D. Bernoulli, P. Laplace, G. Ery, G. Poincaré, etc.), but this theory cannot be considered complete. The theoretical work carried out and numerous observations made it possible to compile tide maps and reference books, which are widely used in navigation. Maps and directories continue to be updated and updated.

Let us note one of the interesting and still insufficiently studied aspects of the theory of tides - the problem of friction forces developing during the movement of tidal waves. According to available estimates, the power lost to friction in the tidal waves of the World Ocean is a considerable figure: 1.1 × 10 6 MW. Friction between the Earth and tidal waves slows down the rotation of the Earth and is considered the reason for the increase in the length of the day by 0.001 s per century, which is established by astronomical observations.

Surfactants can exist near the free surface of a solid or near the interface between two different bodies. There are five types of surfactants.
Rayleigh waves, theoretically discovered by Rayleigh in 1885, can exist in a solid body near its free surface bordering the vacuum. The phase velocity of such waves is directed parallel to the surface, and the particles of the medium oscillating near it have both transverse, perpendicular to the surface, and longitudinal components of the displacement vector. During their oscillations, these particles describe elliptical trajectories in a plane perpendicular to the surface and passing through the direction of the phase velocity. This plane is called sagittal. The amplitudes of longitudinal and transverse vibrations decrease with distance from the surface into the medium according to exponential laws with different attenuation coefficients. This leads to the fact that the ellipse is deformed and the polarization far from the surface can become linear. The penetration of the Rayleigh wave into the depth of the sound pipe is on the order of the length of the surface wave. If a Rayleigh wave is excited in a piezoelectric, then both inside it and above its surface in a vacuum there will be a slow electric field wave caused by the direct piezoelectric effect.
Waves of Stoneleigh(or Stonley), named after the scientist who discovered them in 1908, differ from Rayleigh waves in that they can exist near the interface of two solid media in acoustic contact. When a Stoneley wave propagates, particles of both media participate in the oscillations. At the same time, just like in a Rayleigh wave, they perform an elliptical movement in the sagittal plane. The penetration depths of Stoneley waves into contacting media are on the order of the surface wave length.
Gulyaev - Bluestein waves(Blyukshtein) were discovered in 1968 in the USSR by Yu.V. Gulyaev. and independently in the US by Bluestein. They have two characteristic features. Firstly, they exist only in piezoelectric crystals near the free boundary and, secondly, the particles of the medium experience purely transverse vibrations in a direction parallel to the surface (“horizontal” polarization). Gulyaev-Blustein waves penetrate into the oscillating medium more deeply than Rayleigh and Stoneley waves. The depth of their penetration into the volume of a solid body is of the order of magnitude λ sound ε / k 2 , where ε is the dielectric constant, k - electromechanical coupling coefficient (see below). Thanks to the direct piezoelectric effect, the Gulyaev-Blustein wave is accompanied by a slow electric field wave in a vacuum above the surface of the piezoelectric.
Waves of Marfeld - Tournois, discovered in 1971, differ from Gulyaev-Blustein waves in that they can exist near the interface of two contacting piezoelectrics. These surfactants are also purely shear and have “horizontal” polarization.
Love waves (1926) spread in a thin (about λ sound) a layer of a substance deposited on a substrate in which the speed of sound is greater than in the layer. These purely shear waves have “horizontal” polarization and penetrate the substrate to a depth of the order of λ sound. They have dispersion; their speed lies between the speeds of sound in the layer and in the substrate.

1.3. Guided and channeled waves. Representatives waveguide Acoustic modes are waves in thin plates or films, both surfaces of which are free, and the thickness is of the order of the elastic wave length. In this case, the plate performs the functions of a planar waveguide, and the waves themselves are essentially normal waves in it. The latter were called Lamb waves after the scientist who discovered them in 1916. The displacement vector in a Lamb wave has both longitudinal and transverse components, with the transverse component being normal to the surfaces of the waveguide.
Other representatives of waveguide modes are normal acoustic waves in thin rods of various profiles (round, rectangular, etc.). Channeled acoustic waves are those waves that can propagate both through channels along grooves and protrusions of various profiles (rectangular, triangular, semicircular, etc.) made on the free (not necessarily flat) surface of a solid body, as well as along the spatial angle formed by two faces sound pipes. For practice, they are attractive because they can be used in acoustic integrated circuits.

2. EQUATIONS DESCRIBING ELECTROMECHANICAL
PROCESSES IN PIEZOELECTRICS

Superficial waves are called guided plane inhomogeneous slow electromagnetic waves of class E or class H, which have dispersion. Guiding systems, along which surface waves propagate, are slowing (impedance) surfaces.

Surface waves have two main features , distinguishing them from all other guided waves.

1.) The amplitudes of the E and H vectors of surface waves decrease exponentially in the direction of the normal to the slowing surfaces along which they propagate.

2.) Surface waves are slow (Vph 1).

The decrease in the amplitudes of the vectors E and H of a surface wave in the direction normal to the surface along which it propagates is not associated with active losses in the medium, but is caused by special phase relationships between the components of the vectors E and H of this wave, due to which the flow of the Poynting vector in a given direction is on average for period =0.

The energy flux density transferred by a surface wave along a guide surface is maximum immediately at this surface and decreases sharply with distance from it. Figuratively speaking, propagating along a guide surface, the wave seems to “stick” to it, which determines the name “surface” for waves of this type.

48.Approximate Leontovich boundary conditions.

Let us assume that a plane electromagnetic wave is incident from air at an angle onto a plane interface with a fairly conducting medium described by the complex refractive index:

From the establishment of the concept of a well-conducting medium, it follows that. The extreme inequality according to Siell's law represents that the angle of refraction must be very small. It can be approximately assumed that a refracted wave enters Medium 2 in the direction of the normal at a different angle of incidence. This is the main physical definition of Leontovich's conditions. According to the above, the equivalent circuit of a metal-like medium takes the form of a homogeneous long line with a characteristic resistance calculated by the general formula

At the beginning of the line in this case (that is, at the interface), the tangential components of the magnetic and electric vectors must satisfy the undoubted relationship that directly follows from the definition of characteristic resistance:

As is known, on the surface of an ideal conductor. A nonzero tangential component appears at the interface in the case of large but finite conductivity. Despite the smallness of this value (since at ), it determines the flow of power into the metal used to heat it.

If the axis z is directed inside Environment 2, and the interface coincides with the plane , then the following conditions must be met at the interface:

With this arrangement of signs, as can be easily verified, the flow of the Poynting vector corresponding to heat losses will always be directed along the positive direction of the z axis. Using Leontovich boundary conditions in the form or in the form, it is necessary to see the tangent component of the magnetic vector.

49. Interference. Interference in thin plates

50. 49. Interference. Interference in Newton's rings

Retarding surfaces

A retarding (impedance) surface is the interface between media on which the tangent components of the vectors E and H of the alternating EM field (existing on both sides of this boundary) are shifted in phase relative to each other by 90°. Due to this, the flow of the Poynting vector in the direction of the normal to the slowing surface on average over period = 0, and the transfer of energy by EM waves is possible only in the direction parallel to such a surface.

When solving boundary problems of electrodynamics, a parameter called surface impedance (surface resistance) is often used to characterize interfaces, which is equal to the ratio of the complex amplitudes of the tangent components of the vectors E and H on this surface.

Complex surface resistance module

Argument (phase) of complex surface resistance

Due to the phase shift between the tangent components of the E and H vectors on the slowing surface, its surface impedance is a purely imaginary quantity .

If Z is positive, then surface waves of class E propagate along the slowing surface.

If Z is negative, then surface waves of class H propagate along the slowing surface.

Flat slowing surfaces can be the interface between two dielectrics having different dielectric constants (air - dielectric), and the interface between a dielectric - a comb metal structure (air - a comb metal structure).

SURFACE ACOUSTIC WAVES(surfactant) - elastic waves, propagating along the free surface of a solid body or along the boundary of a solid body with other media and fading away with distance from the boundaries. There are two types of surfactants: vertical, in which the vector oscillates. The displacement of the particles of the medium in the wave is located in a plane perpendicular to the boundary surface (vertical plane), and with horizontal polarization, in which the displacement vector of the particles of the medium is parallel to the boundary surface and perpendicular to the direction of propagation of the wave.
The simplest and most surfactants with vertical polarization often encountered in practice are Rayleigh waves, propagating along the boundary of a solid body with a rather rarefied gaseous medium. Their energy is localized in a surface layer with a thickness from to where is the wavelength. Particles in a wave move in ellipses, semimajor axis w which is perpendicular to the border, and small And- parallel to the direction of wave propagation (Fig. A). Phase velocity of Rayleigh waves c k 0.9c t, Where c t- phase velocity is flat.

Schematic representation of surface waves of various types (solid shading indicates solid media, intermittent shading indicates liquid; X- direction of wave propagation; and, v And w- components of particle displacement in a given environment; the curves depict the approximate course of change in the displacement amplitude with distance from the interface): A- Rayleigh wave on the free boundary of a solid body; b- a damped wave of the Rayleigh type at the solid-liquid interface (oblique lines in a liquid medium represent the wave fronts of the outgoing wave, their thickness is proportional to the amplitude of the displacements); V- undamped surface wave at the solid-liquid boundary; G- Stoneley wave at the interface between two solid media; d- Love wave at the boundary between a solid half-space and a solid layer.

If a solid body borders a liquid and in the liquid c w is less than the speed c k in a solid body (this is true for almost all real media), then at the boundary of a solid body and a liquid propagation of a damped Rayleigh-type wave is possible. As this wave propagates, it continuously radiates energy into the liquid, forming in it an inhomogeneous wave emanating from the boundary (Fig. 6) . The phase velocity of a given surfactant, accurate to percent, is equal to c k, and coefficient attenuation at a wavelength of ~ 0.1, i.e., along the way the wave attenuates by approximately e once. The depth distribution of displacements in such a wave in a solid is similar to the distribution in a Rayleigh wave.
In addition to the damped surfactant, at the boundary of a liquid and a solid there is always an undamped surfactant running along the boundary with a phase velocity less than the speed c of the wave in the liquid and the longitudinal speeds c l and transverse c t waves in a solid. This surfactant, being a wave with vertical polarization, has a completely different structure and speed than the Rayleigh wave. It consists of a weakly inhomogeneous wave in a liquid, the amplitude of which slowly decreases with distance from the boundary (Fig. V), and two highly inhomogeneous wills in a solid body (longitudinal and transverse). Due to this, the wave energy and particle movement are localized mainly in the liquid rather than in the solid. In practice, this type of wave is rarely used.
If two solid media border each other along a plane and their elastic moduli do not differ much, then the Stoneley surfactant can propagate along the boundary (Fig., d). This wave consists, as it were, of two Rayleigh waves (one in each medium). The vertical and horizontal components of the displacements in each medium decrease with distance from the boundary so that the wave energy is concentrated in two boundary layers of thickness ~ The phase velocity of Stoneley waves is less than the values ​​c l And with t in both boundary environments.
Waves with vertical polarization can propagate at the boundary of a solid half-space with a liquid or solid layer or even with a system of such layers. If the thickness of the layers is much smaller than the wavelength, then the motion in the half-space is approximately the same as in a Rayleigh wave, and the phase velocity of the surfactant is close to c k. In the general case, the motion can be such that the wave energy will be redistributed between the solid half-space and the layers, and the phase velocity will depend on the frequency and thickness of the layers (see. Sound dispersion).
In addition to SAWs with vertical polarization (mainly Rayleigh-type waves), there are waves with horizontal polarization (Love waves), which can propagate at the boundary of a solid half-space with a solid layer (Fig. d). These are purely transverse waves: they have only one displacement component v, and the elastic deformation in the wave is a pure shear. Displacements in the layer (index 1) and in the half-space (index 2) are described as follows. expressions:

Where t- time, - circular frequency,

k- wave number of the Love wave, c t 1 c t 2 are the wave numbers of transverse waves in the layer and half-space, respectively, h- layer thickness, A- arbitrary constant. From the expressions for v 1 And v 2 it can be seen that the displacements in the layer are distributed along a cosine, and in the half-space they decrease exponentially with depth. The depth of wave penetration into the half-space varies from fractions to many depending on the thickness of the layer h, frequency and environmental parameters. The very existence of a Love wave as a surfactant is associated with the presence of a layer in the half-space: when h 0, the depth of penetration of the wave into the half-space tends to infinity and the wave becomes volumetric. Phase speed With Love waves is contained within the limits between the phase velocities of transverse waves in the layer and half-space c t l< с < c t 2 and is determined from the equation

where are the densities of the layer and half-space, respectively, It is clear from the equation that Love waves propagate with dispersion: their phase velocity depends on frequency. At small layer thicknesses, when... That is, the phase velocity of the Love wave tends to the phase velocity of the bulk transverse wave in the half-space. When Love waves exist in the form of several. modifications, each of which corresponds normal wave a certain order.
At the boundaries of crystals, the same types of surfactants can exist as in isotropic solids, only the movement in waves becomes more complicated. At the same time, the anisotropy of a solid can introduce certain properties. changes in wave structure. So, on certain planes of crystals that have piezoelectricity. properties, waves like Love waves, like Rayleigh waves, can exist on a free surface (without the presence of a solid layer). These are similar electrosonic waves of Gulyaev - Blushtein. Along with ordinary Rayleigh waves, in certain crystal samples a damped wave can propagate along the free boundary, emitting energy deep into the crystal (leaky wave). Finally, if the crystal has a piezoelectric effect and there is a flow of electrons in it (piezosemiconductor crystal), then interaction of surface waves with electrons is possible, leading to an amplification of these waves (see. Acoustoelectronic interaction).
Elastic surfactants cannot exist on the free surface of a liquid, but at frequencies in the ultrasonic range and below, surface waves can arise there, in which the determining factors are not elastic forces, but surface tension - this is the so-called. capillary waves (see Waves on the surface of a liquid).
Ultra- and hypersonic surfactants are widely used in technology for comprehensive non-destructive testing of the surface and surface layer of a sample (see. Flaw detection), to create microelectronic circuits for electrical processing. signals, etc. If the surface of a solid sample is free, then Rayleigh waves are used. In cases where the sample is in contact with a liquid, another solid sample, or a solid layer, the Rayleigh waves are replaced by another appropriate type of surfactant.

Lit.: Landau L.D., Lifshits E.M., Theory of Elasticity, 4th ed., M., 1987; Viktorov I.A., Physical foundations of the use of ultrasonic waves of Rayleigh and Lzmba in technology, M., 1966, ch. 1; him, Sound surface waves in solids, M., 1981; Physical acoustics, ed. W. Mason, R. Thurston, trans. from English, vol. 6, M., 1973, ch. 3; Surface acoustic waves, ed. A. Oliner, trans. from English, M., 1981.

I. A. Viktorov.

Surface waves

A typical SAW device, used for example as a bandpass filter. The surface wave is generated on the left by applying an alternating voltage through printed conductors. In this case, electrical energy is converted into mechanical energy. Moving along the surface, the mechanical high-frequency wave changes. On the right - the receiving tracks pick up the signal, and the reverse conversion of mechanical energy into alternating electric current occurs through a load resistor.

Surface acoustic waves(surfactant) - elastic waves propagating along the surface of a solid body or along the boundary with other media. Surfactants are divided into two types: with vertical polarization and with horizontal polarization ( Love waves).

The most common special cases of surface waves include the following:

• Rayleigh waves(or Rayleigh), in the classical sense, propagating along the boundary of an elastic half-space with a vacuum or a fairly rarefied gaseous medium.
• at the solid-liquid interface.
• Stonley Wave
• Love waves- surface waves with horizontal polarization (SH type), which can propagate in the elastic layer structure on an elastic half-space.

Rayleigh waves

Rayleigh waves, theoretically discovered by Rayleigh in 1885, can exist in a solid near its free surface bordering a vacuum. The phase velocity of such waves is directed parallel to the surface, and the particles of the medium oscillating near it have both transverse, perpendicular to the surface, and longitudinal components of the displacement vector. During their oscillations, these particles describe elliptical trajectories in a plane perpendicular to the surface and passing through the direction of the phase velocity. This plane is called sagittal. The amplitudes of longitudinal and transverse vibrations decrease with distance from the surface into the medium according to exponential laws with different attenuation coefficients. This leads to the fact that the ellipse is deformed and the polarization far from the surface can become linear. The penetration of the Rayleigh wave into the depth of the sound pipe is on the order of the length of the surface wave. If a Rayleigh wave is excited in a piezoelectric, then both inside it and above its surface in a vacuum there will be a slow electric field wave caused by the direct piezoelectric effect.

Used in touch displays with surface acoustic waves.

Damped Rayleigh waves

Damped Rayleigh-type waves at the solid-liquid interface.

Continuous wave with vertical polarization

Continuous wave with vertical polarization, running along the boundary of a liquid and a solid with a speed

Stonley Wave

Stonley Wave, propagating along the flat boundary of two solid media, the elastic moduli and density of which do not differ much.

Love waves

Links

• Physical Encyclopedia, vol. 3 - M.: Great Russian Encyclopedia p. 649 and p. 650.

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See what “Surface waves” are in other dictionaries:

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