The properties of the medium through which ultrasound passes is determined. Section II Physics of Ultrasound

Dmitry Levkin

Ultrasound - mechanical vibrations above the range of frequencies audible to the human ear (usually 20 kHz). Ultrasonic vibrations travel in a waveform, similar to the propagation of light. However, unlike light waves, which can travel in a vacuum, ultrasound requires an elastic medium such as a gas, liquid, or solid.

, (3)

For transverse waves, it is determined by the formula

Sound dispersion - dependence of the phase velocity of monochromatic sound waves on their frequency. The dispersion of the speed of sound can be due to both the physical properties of the medium and the presence of foreign inclusions in it and the presence of the boundaries of the body in which the sound wave propagates.

Varieties of ultrasonic waves

Most ultrasound methods use either longitudinal or shear waves. There are also other forms of ultrasound propagation, including surface waves and Lamb waves.

Longitudinal ultrasonic waves - waves, the direction of propagation of which coincides with the direction of displacements and velocities of the particles of the medium.

Transverse ultrasonic waves - waves propagating in a direction perpendicular to the plane in which the directions of displacements and velocities of body particles lie, the same as shear waves.

Surface (Rayleigh) ultrasonic waves have an elliptical movement of particles and spread over the surface of the material. Their speed is approximately 90% of the shear wave propagation speed, and their penetration deep into the material is equal to approximately one wavelength.

Lamb wave - an elastic wave propagating in a solid plate (layer) with free boundaries, in which the vibrational displacement of particles occurs both in the direction of wave propagation and perpendicular to the plane of the plate. Lamb waves are one of the types of normal waves in an elastic waveguide - in a plate with free boundaries. Because these waves must satisfy not only the equations of the theory of elasticity, but also the boundary conditions on the surface of the plate; the pattern of motion in them and their properties are more complex than those of waves in unbounded solids.

Visualization of ultrasonic waves

For a plane sinusoidal traveling wave, the ultrasound intensity I is determined by the formula

, (5)

IN spherical traveling wave the intensity of ultrasound is inversely proportional to the square of the distance from the source. IN standing wave I \u003d 0, i.e., there is no sound energy flow on average. Ultrasound intensity in harmonic plane traveling wave equal to the energy density of the sound wave times the speed of sound. The flow of sound energy is characterized by the so-called by the Umov vector - the vector of the energy flux density of the sound wave, which can be represented as the product of the ultrasound intensity by the wave normal vector, i.e., the unit vector perpendicular to the wave front. If the sound field is a superposition of harmonic waves of different frequencies, then additivity of the components takes place for the vector of the mean density of the sound energy flux.

For emitters creating a plane wave, they talk about radiation intensityunderstanding by this specific power of the emitter, i.e., the radiated sound power per unit area of \u200b\u200bthe radiating surface.

Sound intensity is measured in SI units in W / m 2. In ultrasound technology, the range of changes in the intensity of ultrasound is very large - from threshold values \u200b\u200bof ~ 10 -12 W / m 2 to hundreds of kW / m 2 in the focus of ultrasonic concentrators.

Table 1 - Properties of some common materials

Material	Density, kg / m 3	Longitudinal wave speed, m / s	Shear wave speed, m / s	, 10 3 kg / (m 2 * s)
Acrylic	1180	2670	-	3,15
Air	0,1	330	-	0,00033
Aluminum	2700	6320	3130	17,064
Brass	8100	4430	2120	35,883
Copper	8900	4700	2260	41,830
Glass	3600	4260	2560	15,336
Nickel	8800	5630	2960	49,544
Polyamide (nylon)	1100	2620	1080	2,882
Steel (low alloy)	7850	5940	3250	46,629
Titanium	4540	6230	3180	26,284
Tungsten	19100	5460	2620	104,286
Water (293K)	1000	1480	-	1,480

Attenuation of ultrasound

One of the main characteristics of ultrasound is its attenuation. Attenuation of ultrasound Is a decrease in the amplitude and, therefore, of the sound wave as it propagates. Attenuation of ultrasound occurs for a number of reasons. The main ones are:

The first of these reasons is associated with the fact that as the wave propagates from a point or spherical source, the energy emitted by the source is distributed over the increasing surface of the wave front and, accordingly, the energy flux through the unit surface decreases, i.e. ... For a spherical wave, the wave surface of which grows with a distance r from the source as r 2, the wave amplitude decreases proportionally, and for a cylindrical wave - proportionally.

The attenuation coefficient is expressed either in decibels per meter (dB / m) or in nepers per meter (Np / m).

For a plane wave, the attenuation coefficient in amplitude with distance is determined by the formula

, (6)

The attenuation coefficient versus time is determined

, (7)

To measure the coefficient, the unit dB / m is also used, in this case

, (8)

A decibel (dB) is a logarithmic unit for measuring the ratio of energies or powers in acoustics.

, (9)

• where A 1 is the amplitude of the first signal,
• A 2 - amplitude of the second signal

Then the relationship between the units of measurement (dB / m) and (1 / m) will be:

Reflection of ultrasound from the interface

When a sound wave hits the interface between the media, part of the energy will be reflected into the first medium, and the rest of the energy will pass into the second medium. The ratio between the reflected energy and the energy passing into the second medium is determined by the wave impedances of the first and second medium. In the absence of dispersion of the speed of sound wave impedance does not depend on the waveform and is expressed by the formula:

The reflection and transmission coefficients will be determined as follows

, (12)

, (13)

• where D is the sound pressure transmission coefficient

It should also be noted that if the second medium is acoustically softer, i.e. Z 1\u003e Z 2, then upon reflection the phase of the wave changes by 180˚.

The transmission coefficient of energy from one medium to another is determined by the ratio of the intensity of the wave passing into the second medium to the intensity of the incident wave

, (14)

Interference and diffraction of ultrasonic waves

Sound interference - non-uniformity of the spatial distribution of the amplitude of the resulting sound wave, depending on the relationship between the phases of the waves, added at one point or another in space. When harmonic waves of the same frequency are added, the resulting spatial distribution of amplitudes forms a time-independent interference pattern, which corresponds to a change in the phase difference of the constituent waves when passing from point to point. For two interfering waves, this pattern on the plane has the form of alternating bands of amplification and attenuation of the amplitude of the quantity characterizing the sound field (for example, sound pressure). For two plane waves, the stripes are rectilinear with the amplitude varying across the stripes according to the change in the phase difference. An important special case of interference is the addition of a plane wave with its reflection from a plane boundary; in this case, a standing wave is formed with the planes of nodes and antinodes located parallel to the border.

Sound diffraction - the deviation of the behavior of sound from the laws of geometric acoustics, due to the wave nature of sound. The result of sound diffraction is the divergence of ultrasonic beams when moving away from the emitter or after passing through a hole in the screen, bending of sound waves into the shadow region behind obstacles that are large in comparison with the wavelength, the absence of a shadow behind obstacles that are small in comparison with the wavelength, etc. n. Sound fields created by the diffraction of the initial wave by obstacles placed in the medium, by inhomogeneities of the medium itself, as well as by irregularities and inhomogeneities of the boundaries of the medium, are called scattered fields. For objects on which sound diffraction occurs, large compared to the wavelength, the degree of deviations from the geometric pattern depends on the value of the wave parameter

, (15)

• where D is the diameter of the object (for example, the diameter of an ultrasonic emitter or obstacle),
• r is the distance of the observation point from this object

Ultrasound emitters

Ultrasound emitters - devices used to excite ultrasonic vibrations and waves in gaseous, liquid and solid media. Ultrasound emitters convert energy of any other kind into energy.

The most widely used as ultrasound emitters are electroacoustic transducers... In the overwhelming majority of ultrasound emitters of this type, namely in piezoelectric transducers , magnetostrictive transducers, electrodynamic emitters, electromagnetic and electrostatic emitters, electrical energy is converted into vibration energy of any solid body (emitting plate, rod, diaphragm, etc.), which emits acoustic waves into the environment. All of these transducers are, as a rule, linear, and, therefore, the oscillations of the radiating system reproduce in shape the exciting electrical signal; only at very high amplitudes of oscillations near the upper limit of the dynamic range of the ultrasound emitter can nonlinear distortions occur.

In converters designed to emit a monochromatic wave, the phenomenon is used resonance: they operate on one of the natural oscillations of a mechanical oscillatory system, the frequency of which is tuned by an electric oscillator that excites the converter. Electroacoustic transducers that do not have a solid-state emitting system are used relatively rarely as ultrasound emitters; these include, for example, ultrasound emitters based on an electric discharge in a liquid or on electrostriction of a liquid.

Ultrasound transducer characteristics

The main characteristics of ultrasound emitters are their frequency spectrumemitted sound power, radiation directivity... In the case of monofrequency radiation, the main characteristics are operating frequency the ultrasound emitter and its frequency band, the boundaries of which are determined by the drop in the radiated power by two times compared to its value at the frequency of maximum radiation. For resonant electroacoustic transducers, the operating frequency is natural frequency f 0 of the converter, and the width of the line Δf is determined by its quality factor Q.

Ultrasound emitters (electroacoustic transducers) are characterized by sensitivity, electroacoustic efficiency and their own electrical impedance.

Ultrasound transducer sensitivity - the ratio of the sound pressure at the maximum of the directivity characteristic at a certain distance from the emitter (most often at a distance of 1 m) to the electric voltage on it or to the current flowing in it. This characteristic applies to ultrasound emitters used in audible alarms, sonar and other similar devices. For emitters for technological purposes, used, for example, in ultrasonic cleaning, coagulation, exposure to chemical processes, the main characteristic is power. Along with the total radiated power, estimated in W, ultrasound emitters characterize specific power, that is, the average power per unit area of \u200b\u200bthe radiating surface, or the average radiation intensity in the near field, estimated in W / m2.

The efficiency of electroacoustic transducers emitting acoustic energy into the sounding environment is characterized by their value electroacoustic efficiency, which is the ratio of the emitted acoustic power to the consumed electrical power. In acoustoelectronics, to assess the efficiency of ultrasound emitters, the so-called electrical loss factor is used, which is equal to the ratio (in dB) of electrical power to acoustic power. The efficiency of ultrasonic instruments used in ultrasonic welding, machining, and the like is characterized by the so-called efficiency factor, which is the ratio of the square of the amplitude of the vibrational displacement at the working end of the concentrator to the electrical power consumed by the transducer. Sometimes the effective electromechanical coupling coefficient is used to characterize the energy conversion in ultrasound emitters.

Sound field of the emitter

The sound field of the transducer is divided into two zones: the near zone and the far zone. Near zone this is the area just in front of the transducer where the echo amplitude passes through a series of highs and lows. The near zone ends at the last maximum, which is located at a distance N from the transducer. It is known that the location of the last maximum is the natural focus of the transducer. Far zone this is the area behind N where the sound field pressure gradually decreases to zero.

The position of the last maximum N on the acoustic axis, in turn, depends on the diameter and wavelength and for a disk circular radiator is expressed by the formula

, (17)

However, since D is usually much larger, the equation can be simplified and reduced to the form

The characteristics of the sound field are determined by the design of the ultrasonic transducer. Consequently, the sound propagation in the investigated area and the sensor sensitivity depend on its shape.

Application of ultrasound

The various applications of ultrasound, in which its various features are used, can be conditionally divided into three directions. associated with the receipt of information by means of ultrasonic waves, - with an active effect on the substance and - with the processing and transmission of signals (directions are listed in the order of their historical formation). For each specific application, ultrasound of a certain frequency range is used.

Ultrasound - elastic sound vibrations of high frequency. The human ear perceives elastic waves propagating in the medium with a frequency of up to approximately 16-20 kHz; vibrations with a higher frequency are ultrasound (out of earshot). Usually the ultrasonic range is considered to be the frequency range from 20,000 to billion Hz. Sound vibrations with a higher frequency are called hypersound. In liquids and solids, sound vibrations can reach 1000 GHz

Although scientists have known about the existence of ultrasound for a long time, its practical use in science, technology and industry began relatively recently. Now ultrasound is widely used in various fields of physics, technology, chemistry and medicine.

Ultrasound Sources

The frequency of ultrahigh-frequency ultrasonic waves used in industry and biology is in the range of the order of several MHz. The focusing of such beams is usually carried out using special sound lenses and mirrors. An ultrasonic beam with the required parameters can be obtained using an appropriate transducer. The most common ceramic transducers are barium titanite. In cases where the power of the ultrasound beam is of primary importance, mechanical ultrasound sources are usually used. Initially, all ultrasonic waves were received mechanically (tuning forks, whistles, sirens).

In nature, ultrasound occurs both as a component of many natural noises (in the noise of the wind, waterfall, rain, in the noise of pebbles rolled by the sea surf, in the sounds accompanying lightning discharges, etc.), and among the sounds of the animal world. Some animals use ultrasonic waves to detect obstacles, orientation in space.

Ultrasound emitters can be divided into two large groups. The first includes emitters-generators; vibrations in them are excited due to the presence of obstacles in the path of a constant flow - a jet of gas or liquid. The second group of emitters is electro-acoustic transducers; they convert the already specified fluctuations of an electric voltage or current into a mechanical vibration of a solid, which emits acoustic waves into the environment. Examples of emitters: Galton whistle, liquid and ultrasonic whistle, siren.

Propagation of ultrasound.

The propagation of ultrasound is the process of movement in space and time of disturbances that take place in a sound wave.

A sound wave propagates in a substance in a gaseous, liquid or solid state in the same direction in which the particles of this substance are displaced, that is, it causes deformation of the medium. Deformation consists in the fact that there is a successive expansion and compression of certain volumes of the medium, and the distance between two adjacent areas corresponds to the length of the ultrasonic wave. The greater the specific acoustic resistance of the medium, the greater the degree of compression and discharge of the medium at a given vibration amplitude.

Particles of the medium participating in the transfer of wave energy vibrate about their equilibrium position. The speed at which particles vibrate around their mean equilibrium position is called vibrational.

speed.

Diffraction, interference

When ultrasonic waves propagate, the phenomena of diffraction, interference and reflection are possible.

Diffraction (wave bending around obstacles) occurs when the ultrasonic wavelength is comparable (or greater) to the size of the obstacle in the path. If the obstacle is large compared to the acoustic wavelength, then there is no diffraction phenomenon.

With the simultaneous movement of several ultrasonic waves in the tissue at a certain point of the medium, a superposition of these waves can occur. Such superposition of waves on each other is collectively called interference. If, in the process of passing through a biological object, ultrasonic waves intersect, then at a certain point in the biological environment there is an increase or decrease in vibrations. The result of the interference will depend on the spatial relationship of the phases of ultrasonic vibrations at a given point in the medium. If ultrasonic waves reach a certain area of \u200b\u200bthe medium in the same phases (in phase), then the displacements of the particles have the same signs and interference in such conditions contributes to an increase in the amplitude of ultrasonic vibrations. If ultrasonic waves arrive at a specific area in antiphase, then the displacement of particles will be accompanied by different signs, which leads to a decrease in the amplitude of ultrasonic vibrations.

Interference plays an important role in assessing the phenomena occurring in the tissues around the ultrasound transmitter. Interference is of particular importance when ultrasonic waves propagate in opposite directions after they are reflected from an obstacle.

Absorption of ultrasonic waves

If the medium in which ultrasound propagates has viscosity and thermal conductivity, or there are other processes of internal friction in it, then during wave propagation, sound is absorbed, that is, with distance from the source, the amplitude of ultrasonic vibrations becomes smaller, as well as the energy that they carry. The medium in which the ultrasound propagates, interacts with the energy passing through it and absorbs part of it. The predominant part of the absorbed energy is converted into heat, the smaller part causes irreversible structural changes in the transmitting substance. Absorption is the result of friction of particles against each other, in different media it is different. Absorption also depends on the frequency of ultrasonic vibrations. In theory, absorption is proportional to the square of the frequency.

The magnitude of absorption can be characterized by the absorption coefficient, which shows how the intensity of ultrasound changes in the irradiated medium. It increases with increasing frequency. The intensity of ultrasonic vibrations in the medium decreases exponentially. This process is due to internal friction, thermal conductivity of the absorbing medium and its structure. It is roughly characterized by the size of the semi-absorbing layer, which shows at what depth the intensity of the oscillations is halved (more precisely, 2.718 times or 63%). According to Palman, at a frequency of 0.8 MHz, the average values \u200b\u200bof the semi-absorbing layer for some tissues are as follows: adipose tissue - 6.8 cm; muscle - 3.6 cm; adipose and muscle tissue together - 4.9 cm. With an increase in the frequency of ultrasound, the size of the semi-absorbing layer decreases. So, at a frequency of 2.4 MHz, the intensity of ultrasound passing through adipose and muscle tissue is halved at a depth of 1.5 cm.

In addition, an abnormal absorption of the energy of ultrasonic vibrations in some frequency ranges is possible - it depends on the characteristics of the molecular structure of this tissue. It is known that 2/3 of the ultrasound energy is attenuated at the molecular level and 1/3 at the level of microscopic tissue structures.

Depth of penetration of ultrasonic waves

The depth of penetration of ultrasound is understood as the depth at which the intensity is reduced by half. This value is inversely proportional to absorption: the stronger the medium absorbs ultrasound, the smaller the distance at which the ultrasound intensity is attenuated by half.

Scattering of ultrasonic waves

If there are inhomogeneities in the medium, then sound scattering occurs, which can significantly change the simple picture of ultrasound propagation and, ultimately, also cause wave attenuation in the original direction of propagation.

Refraction of ultrasonic waves

Since the acoustic resistance of human soft tissues does not differ much from the resistance of water, it can be assumed that at the interface between the media (epidermis - dermis - fascia - muscle), refraction of ultrasonic waves will be observed.

Reflection of ultrasonic waves

Ultrasound diagnostics is based on the phenomenon of reflection. Reflection occurs in the border areas of skin and fat, fat and muscle, muscle and bone. If, during propagation, ultrasound hits an obstacle, then reflection occurs, if the obstacle is small, then the ultrasound seems to flow around it. The inhomogeneities of the organism do not cause significant deviations, since in comparison with the wavelength (2 mm), their dimensions (0.1-0.2 mm) can be neglected. If ultrasound on its way encounters organs larger than the wavelength, then the ultrasound is refracted and reflected. The strongest reflection is observed at the boundaries of the bone - the surrounding tissues and tissues - air. Air has a low density and almost complete reflection of ultrasound is observed. Reflection of ultrasonic waves is observed at the border of the muscle - periosteum - bone, on the surface of hollow organs.

Traveling and standing ultrasonic waves

If during the propagation of ultrasonic waves in the medium they are not reflected, traveling waves are formed. As a result of energy losses, the oscillatory motions of the particles of the medium gradually damp, and the further the particles are located from the emitting surface, the smaller the amplitude of their oscillations. If on the path of propagation of ultrasonic waves there are tissues with different specific acoustic impedances, then to one degree or another there is a reflection of ultrasonic waves from the boundary section. The superimposition of incident and reflected ultrasonic waves can result in standing waves. For the occurrence of standing waves, the distance from the surface of the emitter to the reflecting surface must be a multiple of half the wavelength.

Oscillations and waves... Oscillations are called multiple repetitions of the same or close to the same processes. The process of propagation of oscillations in a medium is called wave. The line indicating the direction of propagation of the wave is called the ray, and the boundary defining the oscillating particles from the particles of the medium that have not yet begun to oscillate is called the wave front.

The time during which a complete cycle of oscillations is completed is called the period T and is measured in seconds. The value ƒ \u003d 1 / T, which shows how many times the vibration is repeated per second, is called frequency and is measured in s -1.

The quantity ω, showing the number of full revolutions of a point in a circle in 2T s, is called the angular frequency ω \u003d 2 π / T \u003d 2 π ƒ and is measured in radians per second (rad / s).

The phase of the wave is a parameter showing how much of the period has passed since the beginning of the last cycle of oscillations.

Wavelength λ is the minimum distance between two points oscillating in the same phase. Wavelength is related to frequency ƒ and speed with the ratio: λ \u003d s / ƒ. A plane wave propagating along the horizontal X axis is described by the formula:

u \u003d U cоs (ω t - kх),

where k \u003d 2 π / λ. - wave number; U is the vibration amplitude.

The formula shows that the value of u changes periodically in time and space.

The displacement of particles from the equilibrium position u and the acoustic pressure p are used as the quantity changing during the oscillations.

In ultrasonic (US) flaw detection, vibrations with a frequency of 0.5 ... 15 MHz (length of a longitudinal wave in steel 0.4 ... 12 mm) and a displacement amplitude of 10 -11 ... 10 -4 mm (occurring in steel at a frequency of 2 MHz, acoustic stresses 10 ... 10 8 Pa).

The intensity of wave I is equal to I \u003d р 2 / (2ρс),

where ρ is the density of the medium in which the wave propagates.

The intensity of the waves used for control is very low (~ 10 -5 W / m 2). During flaw detection, not the intensity, but the amplitude of the waves A is recorded. Usually, the attenuation of the amplitude A "is measured relative to the amplitude of the oscillations A o (probe pulse) excited in the product, ie the ratio A" / A o. For this, logarithmic units of decibels (dB) are used, i.e. A "/ A about \u003d 20 Ig A" / A about.

Types of waves. Several types of waves are distinguished depending on the direction of particle oscillation relative to the beam.

A longitudinal wave is called a wave in which the oscillatory motion of individual particles occurs in the same direction in which the wave propagates (Fig. 1).

A longitudinal wave is characterized by the fact that in the medium areas of compression and rarefaction, or high and low pressure, or high and low density alternate. Therefore, they are also called pressure, density or compression waves. Longitudinal can spread in solids, liquids, gases.

Figure: 1. Oscillation of particles in a medium v \u200b\u200bin a longitudinal wave.

Shear (transverse) is called such a wave in which individual particles vibrate in a direction perpendicular to the direction of wave propagation. In this case, the distance between the individual vibration planes remains unchanged (Fig. 2).

Figure: 2. Oscillation of particles of a medium v \u200b\u200bin a transverse wave.

Longitudinal and transverse waves, which have received the generalized name "bulk waves", can exist in an unlimited medium. These are the most widely used for ultrasonic flaw detection.

The speed of propagation of a sound wave c is the speed of propagation of a certain state in a material medium (for example, compression or rarefaction for a longitudinal wave). The speed of sound for different types of waves is different, moreover, for transverse and longitudinal waves it is a characteristic of the medium, independent of the parameters of the ultrasonic wave.

The speed of propagation of a longitudinal wave in an unbounded solid is determined by the expression

where E is Young's modulus, defined as the ratio between the magnitude of the tensile force applied to a certain rod and the resulting deformation; v - Poisson's ratio, which is the ratio of the change in the width of the rod to the change in its length, if the rod is stretched along its length; ρ is the density of the material.

Shear wave velocity In an unbounded solid is expressed as follows:

Since v ≈ 0.3 in metals, there is a relation between the longitudinal and transverse waves

c t ≈ 0.55 s l.

Surface waves (Rayleigh waves) are elastic waves propagating along the free (or weakly loaded) boundary of a solid and rapidly decaying with depth. A surface wave is a combination of P and S waves. Particles in a surface wave oscillate along an elliptical trajectory (Fig. 3). The major axis of the ellipse is thus perpendicular to the border.

Since the longitudinal component entering the surface wave decays with depth faster than the transverse one, the elongation of the ellipse changes with depth.

The surface wave has a speed with s \u003d (0.87 + 1.12v) / (1 + v)

For metals with s ≈ 0.93 s t ≈ 0.51 s l.

Depending on the geometric shape of the front, the following types of waves are distinguished:

• spherical - a sound wave at a short distance from a point sound source;
• cylindrical - a sound wave at a short distance from the sound source, which is a long cylinder of small diameter;
• flat - it can be emitted by an endlessly vibrating plane.

The pressure in a spherical or plane sound wave is determined by the ratio:

where v is the value of the vibrational speed.

The quantity ρс \u003d z is called acoustic impedance or acoustic impedance.

Figure: 3. Oscillation of particles of a medium v \u200b\u200bin a surface wave.

If the acoustic impedance is large, then the medium is called hard, if the impedance is low, it is called soft (air, water).

Normal (waves in plates), are called elastic waves propagating in a solid plate (layer) with free or weakly loaded boundaries.

Normal waves come in two polarizations: vertical and horizontal. Of the two types of waves, the Lamb waves are the most widely used in practice - normal waves with vertical polarization. They arise as a result of resonance in the interaction of the incident wave with the multiply reflected waves inside the plate.

To understand the physical essence of waves in plates, let us consider the issue of the formation of normal waves in a liquid layer (Fig. 4).

Figure: 4. To the question of the appearance of normal will in a layer of liquid.

Let a plane wave fall on a layer of thickness h from the outside at an angle β. The AD line shows the front of the falling wave. As a result of refraction at the boundary, a wave with a CB front appears in the layer, propagating at an angle α and undergoing multiple reflections in the layer.

At a certain angle of incidence β, the wave reflected from the lower surface coincides in phase with the direct wave coming from the upper surface. This is the condition for the appearance of normal waves. The angle a at which such a phenomenon occurs can be found from the formula

h cos α \u003d n λ 2/2

Here n is an integer; λ 2 is the wavelength in the layer.

For a solid layer, the essence of the phenomenon (resonance of bulk waves at oblique incidence) remains. However, the conditions for the formation of normal waves are very complicated due to the presence of longitudinal and transverse waves in the plate. Different types of waves existing at different values \u200b\u200bof n are called normal wave modes. Ultrasonic waves with odd values n are called symmetric, since the movement of particles in them is symmetric about the axis of the plate. Waves with even values \u200b\u200bof n are called antisymmetric (fig. 5).

Figure: 5. Oscillation of particles of a medium v \u200b\u200bin a normal wave.

Head waves. In real conditions of ultrasonic testing with an inclined transducer, the ultrasonic wave front of the emitting piezoelectric element has a non-planar shape. From the emitter, the axis of which is oriented at the first critical angle to the interface, longitudinal waves with angles slightly smaller and slightly larger than the first critical also fall on the boundary. In this case, a number of types of ultrasonic waves are excited in the steel.

An inhomogeneous longitudinal-surface wave propagates along the surface (Fig. 6). This wave, consisting of the surface and bulk components, is also called leaky or creeping. Particles in this wave move along trajectories in the form of ellipses, close to circles. The phase velocity of the outgoing wave c in slightly exceeds the velocity of the longitudinal wave (for steel with c \u003d 1.04 c l).

These waves exist at a depth approximately equal to the wavelength, and quickly decay during propagation: the wave amplitude decays 2.7 times faster at a distance of 1.75λ. along the surface. The attenuation is due to the fact that at each point of the interface, shear waves are generated at an angle α t2 equal to the third critical angle, called lateral waves. This angle is determined from the ratio

sin α t2 \u003d (c t2 - c l2)

for steel α t2 \u003d 33.5 °.

Figure: 6. Acoustic field of the head wave transducer: PEP - piezoelectric transducer.

In addition to the flowing out, a head wave is also excited, which has been widely used in the practice of ultrasonic testing. The head wave is called a longitudinal-subsurface wave, excited when an ultrasonic beam falls on the interface at an angle close to the first critical one. The speed of this wave is equal to the speed of the longitudinal wave. The head wave reaches its amplitude value under the surface along the beam with an angle of entry of 78 °.

Figure: 7. The amplitude of the head wave reflection depending on the depth of the flat-bottom holes.

The head wave, like the outgoing one, generates lateral transverse ultrasonic waves at the third critical angle to the interface. Simultaneously with the excitation of the longitudinal-surface wave, a reverse longitudinal-surface wave is formed - the propagation of an elastic disturbance in the direction opposite to the direct radiation. Its amplitude is ~ 100 times less than the amplitude of the forward wave.

The head wave is insensitive to surface irregularities and reacts only to defects lying under the surface. The attenuation of the amplitude of the longitudinal-subsurface wave along a ray of any direction occurs as in a conventional bulk longitudinal wave, i.e. proportional to l / r, where r is the distance along the ray.

In fig. 7 shows the change in the amplitude of the echo from flat-bottomed holes located at different depths. The sensitivity to defects near the surface is close to zero. The maximum amplitude at a distance of 20 mm is achieved for flat-bottom holes located at a depth of 6 mm.

Other related pages

1. The speed of propagation of ultrasound depends on the temperature and pressure in the pipeline. The speed of ultrasound at various values \u200b\u200bof water temperature and atmospheric pressure is given in Table E.1.

Table E.1

Alexandrov A.A., Trakhtengerts M.S. Thermophysical properties of water at atmospheric pressure. M. Publishing house of standards, 1977, 100s. (State service of standard reference data. Ser. Monographs).

2. When using a flow meter to measure the flow and volume of water in water and heat supply systems, the ultrasound speed is determined according to the table. E.2 by the method of linear interpolation in temperature and pressure in accordance with the formula:

where c (t, P) is the ultrasound velocity in the liquid flowing through the pipeline, m / s;

c (t1) is the tabular value of the ultrasound velocity at a temperature lower than the measured one, m / s;

c (t2) - tabular value of the ultrasound velocity at a temperature higher than the measured one, m / s;

c (P1) is the tabular value of the ultrasound velocity at a pressure lower than the measured one, m / s;

c (P2) is the tabular value of the ultrasound velocity at a pressure greater than the measured one, m / s;

t is the temperature of the water in the pipeline, ºС;

P is the water pressure in the pipeline, MPa;

t1, t2 - tabular values \u200b\u200bof temperatures, ºС;

P1, P2 - tabular values \u200b\u200bof pressures, MPa;

NOTE.

1. The values \u200b\u200bof c (t1) and c (t2) are determined according to the table. D.1. The values \u200b\u200bof c (P1) and c (P2) are determined from the data in Table. D 2. at a temperature closest to the temperature of the water in the pipeline.

2. Measurements of temperature and pressure of water in the pipeline should be performed with an error of no more than ± 0.5 ºС and ± 0.5 MPa, respectively.

Table E.2

Continuation of table E.2

Alexandrov A.A., Larkin D.K. Experimental determination of the speed of ultrasound in a wide range of temperatures and pressures. Heat Power Engineering Journal, No. 2, 1976, p. 75.

3. In the absence of tables of the dependence of the speed of ultrasound on the temperature of the liquid, the speed of ultrasound can be determined using the device shown in Fig.D.1. Immediately before measuring the ultrasound velocity, the body of the device (steel bracket) is immersed in the liquid under investigation, and the thickness gauge is adjusted to measure the ultrasound velocity. The ultrasonic thickness gauge then directly measures the ultrasound velocity.

To measure the ultrasound velocity in a liquid, it is also possible to use a US-12 IM (SHO 2.048.045 TO) device or other types of thickness gauges.

Fig.D.1. Device for measuring the speed of ultrasound in a liquid.

Longitudinal mechanical waves with vibration frequencies above 20 kHz are called ultrasound. Like sound waves, an ultrasonic wave is an alternation of condensations and discharges of the medium. In every medium, the speed of propagation of both sound and ultrasound is the same. In view of this, the length of ultrasonic waves in air is less than 17 mM (V \u003d λ * ν; Vair \u003d 330 m / s).

Sources of ultrasound are special electromechanical emitters. One type of emitters work on the basis of the phenomenon of magnetostriction, when the dimensions of some bodies (for example, a nickel rod) change in an alternating magnetic field. Such emitters make it possible to obtain vibrations with frequencies from 20 to 80 kHz. From an alternating current source with the indicated frequencies, the voltage is applied to the nickel rod, the longitudinal dimension of the rod changes with the frequency of the alternating current, and an ultrasonic wave is emitted from the lateral faces of the sample (Fig. 4).

The second type of emitters works on the basis of the piezoelectric effect, when the dimensions of some bodies - ferroelectric materials - change in an alternating electric field. For this type of emitters, higher frequency oscillations can be obtained - up to 500 MHz. From an alternating current source, voltage is also applied to the lateral faces of the rod made of ferroelectric (quartz, tourmaline), the longitudinal size of the rod changes with the frequency of the alternating current, and an ultrasonic wave is emitted from the lateral faces of the sample (Fig. 5). In both the first and second cases, ultrasound is emitted due to vibrations of the lateral faces of the rod, in the latter case, these faces are metallized to supply current to the sample.

Ultrasound receivers operate on the principle of the inverse phenomena of magnetostriction and piezoelectric effect: an ultrasonic wave causes fluctuations in the linear dimensions of bodies when the bodies are in the field of an ultrasonic wave, fluctuations in dimensions are accompanied by the appearance of either an alternating magnetic or alternating electric field in the material. These fields, appearing in the corresponding sensor, are registered by some indicator, for example, an oscilloscope. The more intense the ultrasound, the greater the amplitude of mechanical vibrations of the sample - sensor, and the greater the amplitude of the arising alternating magnetic or electric fields.

Features of ultrasound.

As mentioned above, in each medium, the propagation speed of both sound and ultrasound is the same. The most important feature of ultrasound is the narrowness of the ultrasound beam, which allows you to act on any objects locally... In inhomogeneous media with fine inhomogeneities, when the sizes of inclusions are approximately equal but larger than the wavelength (L ≈ λ), the phenomenon of diffraction takes place. If the size of the inclusions is much larger than the wavelength (L \u003e\u003e λ), the ultrasound propagation is straightforward. In this case, it is possible to obtain ultrasonic shadows from such inclusions, which is used in various types of diagnostics, both technical and medical. An important theoretical moment when using ultrasound is the passage of ultrasound from one medium to another. Such a characteristic of the waves as the frequency does not change. On the contrary, the speed and wavelength can change in this case. So in water the speed of acoustic waves is 1400 m / s, when in air - 330 m / s. The penetration of ultrasound into another medium is characterized by the penetration coefficient (β). It is defined as the ratio of the intensity of the wave that entered the second medium to the intensity of the incident wave: β \u003d I 2 / I 1 - Fig 6. This coefficient depends on the ratio of the acoustic impedances of the two media. Acoustic impedance is the product of the density of a medium by the speed of propagation of waves in a given medium: Z 1 \u003d ρ 1 * V 1, Z 2 \u003d ρ 2 * V 2. The penetration coefficient is the highest - close to unity, if the acoustic impedances of the two media are approximately equal: ρ 1 * V 1,≈ ρ 2 * V 2... If the impedance of the second medium is much greater than the first, the penetration coefficient is negligible. In general, the coefficient β is calculated by the formula:

For the transition of ultrasound from air to human skin β \u003d 0.08%, for the transition from glycerol to skin β \u003d 99.7%.

Absorption of ultrasound in various media.

In homogeneous media, ultrasound is absorbed, like any type of radiation, according to the exponential function law:

The L 'value is called the half-absorption layer - this is the distance at which the wave intensity is halved. The half-absorption layer depends on the frequency of the ultrasound and the tissue itself - the object. With an increase in frequency, the value of L 1/2 decreases. For various tissues of the body, the following values \u200b\u200bof the degree of absorption of ultrasound take place:

Substance	Water	Blood	Cartilage	Bone
L '	300 cm	2 - 8 cm	0.24 cm	0.05 cm

The action of ultrasound on body tissues.

There are three types of ultrasound action:

Mechanical,

Thermal,

Chemical.

The degree of influence of one type or another is determined by the intensity. In this regard, medicine is distinguished three levels of ultrasound intensities:

1 level - up to 1.5 W / cm 2,

Level 2 - from 1.5 to 3 W / cm 2,

Level 3 - from 3 to 10 W / cm 2.

All three types of ultrasound action on tissues are associated with the phenomenon of cavitation - these are short-term (half of the oscillation periods of the particles of the medium) the appearance of microscopic cavities in the places where the medium is discharged. These cavities are filled with liquid vapors, and in the high-pressure phase (the other half of the oscillation period of the medium particles), the resulting cavities collapse. At high wave intensities, the collapse of cavities with liquid vapors in them can lead to a destructive mechanical effect. Naturally, the collapse of microcavities is accompanied by a thermal effect. The chemical action of ultrasound is also associated with the process of collapse of microcavities, since in this case the particles of the medium reach high speeds of translational motion, which can cause the phenomenon of ionization, rupture of chemical bonds, and the formation of radicals. The formed radicals can interact with proteins, lpids, nucleic acids and cause undesirable effects of a chemical nature.

6. Features of blood flow through large vessels, medium and small vessels, capillaries;
blood flow during vasoconstriction, sound effects.

The blood flow rate in different vessels is different. Approximate values \u200b\u200bof this speed are presented in table. 2.1.

Table 2.1. Blood speed and pressure in various vessels

At first glance, it seems that the given values \u200b\u200bcontradict the continuity equation - in thin capillaries, the blood flow velocity is less than in arteries. However, this discrepancy is apparent. The fact is that in table. 2.1 shows the diameter of one vessel, but as the vessels branch out, the area of \u200b\u200beach of them decreases, and the total branching area increases. Thus, the total area of \u200b\u200ball capillaries (about 2000 cm 2) is hundreds of times larger than the area of \u200b\u200bthe aorta - this explains such a low blood velocity in the capillaries (500 - 600 times less than in the aorta).

Later, when the capillaries merge into the venules, into the veins, up to the vena cava, the total vascular lumen decreases again and the blood flow rate increases again. However, for a number of reasons, the blood flow velocity at the confluence of the vena cava into the heart does not increase to the initial value, but to approximately ½ of it (Fig. 2.7).

Aorta arteries arterioles capillaries venules veins vena cava

Figure: 2.7. Distribution of blood flow velocities in different departments

of cardio-vascular system

In the capillaries and veins, the blood flow is constant, in other parts of the cardiovascular system, pulse waves.

A wave of increased pressure propagating through the aorta and arteries, caused by the release of blood from the left ventricle of the heart during systole, is called a pulse wave.

When the heart muscle contracts (systole), blood is expelled from the heart into the aorta and arteries extending from it. If the walls of these vessels were rigid, then the pressure that occurs in the blood at the exit from the heart would be transmitted to the periphery at the speed of sound. However, the elasticity of the vessel walls leads to the fact that during systole, the blood pushed out by the heart stretches the aorta, arteries and arterioles. During systole, large vessels perceive more blood than it flows to the periphery. A person's systolic pressure (PC) is normally approximately 16 kPa. During relaxation of the heart (diastole), the stretched blood vessels collapse and the potential energy transmitted to them by the heart through the blood is converted into kinetic energy of blood flow, while the diastolic pressure (P D) is maintained at approximately 11 kPa.

P, Pa P, Pa

1 - in the aorta 2 - in the arterioles

Figure: 2.8. Pressure fluctuations in the vessels during the passage of pulse waves

The amplitude of the pulse wave P 0 (x) (pulse pressure) is the difference between the maximum and minimum pressure values \u200b\u200bat a given point of the vessel (x). At the beginning of the aorta, the amplitude of the P 0, max wave is equal to the difference between the systolic (P C) and diastolic (P D) pressures: P 0, max \u003d P C - P D. The attenuation of the amplitude of the pulse wave during its propagation along the vessels can be represented by the dependence:

where β is the damping coefficient, which increases with decreasing vessel radius.

The speed of propagation of the pulse wave, measured experimentally, is 6 - 8 m / s, which is 20 - 30 times greater than the speed of movement of blood particles \u003d 0.3 - 0.5 m / s. During the expulsion of blood from the ventricles (systole time) t s \u003d 0.3 s, the pulse wave has time to spread over a distance

L p \u003d · t s »2m,

that is, to cover all large vessels - the aorta and arteries. This means that the front of the pulse wave will reach the extremities before the pressure in the aorta begins to decline.

Experimental determination of the pulse wave velocity underlies the diagnosis of the state of the vessels. With age, the elasticity of blood vessels increases 2 - 3 times, and, consequently, the speed of the pulse wave also increases.

As is clear from experiments and from general ideas about the work of the heart, the pulse wave is not sinusoidal.

(harmonic) (Fig. 2.9).

1 - artery after passing 2 - passes through the artery

pulse wave pulse wave front

3 - pulse wave in the artery 4 - decrease in high blood pressure

Figure: 2.9. Artery profile during the passage of the pulse wave.

The speed of the pulse wave in large vessels as follows depends on their parameters (the Moens-Korteweg formula):

, where E is the elastic modulus (Young's modulus); ρ is the density of the vessel substance; h is the thickness of the vessel wall; d is the diameter of the vessel.

It is interesting to compare this formula with the expression for the speed of sound propagation in a thin rod:

, E - Young's modulus; ρ is the density of the rod substance

In humans, with age, the modulus of vascular elasticity increases, therefore, the speed of the pulse wave also becomes greater.

Along with the pulse wave, sound waves can also propagate in the “vessel-blood” system, the speed of which is very high in comparison with the speed of movement of blood particles and the speed of the pulse wave. Thus, in the vessel-blood system, three main processes of movement can be distinguished:

1) movement of blood particles (\u003d 0.5 m / s);

2) pulse wave propagation (~ 10 m / s);

3) propagation of sound waves (~ 1500 m / s).

The flow of blood in the arteries is normally laminar, with slight turbulence occurring near the valves. In pathology, when the viscosity is less than normal, the Reynolds number may exceed the critical value and the movement will become turbulent. Turbulent flow is associated with additional energy consumption during fluid movement, which in the case of blood leads to additional work of the heart.

The noise generated by turbulent blood flow can be used to diagnose diseases. This noise is heard on the brachial artery when measuring blood pressure using the Korotkoff sound method.

The air flow in the nasal cavity is normally laminar. However, with inflammation or any other abnormalities, it can become turbulent, which will entail additional work of the respiratory muscles.

The transition from a laminar flow to a turbulent one occurs not only when flowing in a pipe (channel), it is typical for almost all viscous fluid flows. In particular, the flow of liquid around the profile of a ship or submarine, a body of a fish or a wing of an aircraft or bird is also characterized by a laminar-turbulent transition, while the characteristic size of the streamlined body and a constant depending on the shape of the body must be substituted into the formula.

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