1. LESSON 1 BASED OF ACOUSTICS
The chapter of physics which studies the generation, propagation and interaction of elastic waves into elastic media is called acoustics, and these waves are acoustic waves.

2. Waves in elastic media
The acoustic waves propagate only in elastic media. The particles of the medium are displaced due to the impact of external forces and return to their reference position due to elastic properties.
If the external force will influence the medium, so the first of medium layer is going to second layer and distance between this layers will be less. Then the second layer is going to third layer and first layer is coming back and distance between first layer and second layer will be widen ['waɪd(ə)n]. This process moves into medium. In the result, medium has elastic wave. Medium particles oscillate around the equilibrium [ˌiːkwɪ'lɪbrɪəm ], position. Medium particles don’t transfer into medium.

3. TYPES of GUIDED WAVES
The wave are longitudinal, if the direction of particles oscillation coincides with the direction of wave propagation.
The waves are called transverse, if the direction of particles oscillation is perpendicular to direction of wave propagation.
The compression area. The rarefaction area.
The longitudinal [ˌlɔnʤɪ'tjuːdɪn(ə)l] wave has compression and rarefaction areas .
The distance between two compression areas is the wavelength.
Schear wave (S-wave) is transverse wave.

4. TYPES of GUIDED WAVES the plate wave, which propagates in a thin plate
Thin plate flexis
A surface wave is a wave that propagates only on the surface of object

5. Waves in elastic media Antisymmetric mode
Plate waves can be symmetric mode or antisymmetric mode.
If the particles of the medium oscillate symmetrically relative to the neutral middle plate, than it is symmetric mode.
If the particles of the medium oscillate with equal phase, than it is antisymmetric mode (another name is shear wave).
Shear - сдвиг
Antisymmetric mode

6. Rayleigh waves are a type of surface acoustic wave that propagates along the surface of solids.
They are part of the seismic waves that are produced on the Earth [ɜːθ] by earthquakes.

7. CLASSIFICATION OF ELASTIC WAVES
hypersound
Infrasound
Sound
Ultrasound
hypersound
16 Hz
16 Hz
20 kHz
1 GHz
GHz
The boundaries of the ranges of acoustic waves are rather arbitrary. For example, the boundary between sound and ultrasound depends on the individual characteristics of human. Some people can't hear sounds with a frequency above 10 kHz, others can hear sounds with a frequency up to 25 kHz.
Many animals can hear sounds of much higher frequencies than people. Dogs can hear sounds with a frequency up to 44 kHz, rat is to 72 kHz, bat is up to 115 kHz. The maximum frequency of perception depends on the distance between the ears. If the distance between the ears less, than the animal can hear the higher the sound. The elephant, for example, can hear sounds above to 12 kHz.
The maximum frequency of elastic waves is determined the mean free path of molecules into gases or intermolecular (interatomic) distances in liquids and solids. So the maximum frequency of elastic waves in gases is about 1 GHz, and solids – about GHz.

8. WAVE VELOCITY INTO LIQUID
ρ- the density of the liquid (kilogram over stere)
β- the coefficient of adiabatic compressibility
The wave velocity into liquid depends on the coefficient of compressibility of fluids and density.
The wave velocity into liquid equals the square root of 1 over ρ multiply β
ρ- the density of the liquid (kilogram over stere)
β equals minus 1 over delta P multiply delta V over V
The wave velocity into air is 333 meter per second if temperature is 25°C .
The wave velocity into water and soft biological tissues is about 1500 m/s if temperature is 25°C
-change of the volume
- change of the pressure

9. WAVE VELOCITY INTO SOLID
E is Young modulus
P is the pressure
λ =c/f
Wavelength:
Propagation velocity equals Young modulus over pressure
young's modulus characterizes the elastic properties of the solid.
The wave velocity into bone is 3500 m/s if temperature is 25°C .
The wave velocity is independent of frequency.
wavelength λ equals the wave velocity over frequency.
For example, wavelength into water is 1,5 mm if frequency is 1 MHz.
f is frequency

10. Ultrasonic attenuation
The attenuation due to absorption of elastic wave by environment, i.e. transformation of acoustic energy into other forms of energy (heat energy).
The absorption coefficient in liquid is proportional to the square of the frequency and viscosity
the ultrasonic wave attenuates in the medium, and their intensity and the amplitude of oscillation of the particles of the medium decrease with increasing distance from the source.
Elastic wave energy absorptions by the medium, i.e. [id est;] elastic wave energy transfers into other forms of energy, particularly in thermal, scattering of wave by irregularity of the medium, therefore the wave energy reduces (decreases) in the wave propagation direction.
The amplitude and intensity of ultrasound wave decreases if distance increase.

11. REFRACTION and REFLECTION of the longitudinal wave
longitudinal [ˌlɔnʤɪ'tjuːdɪn(ə)l]
Acoustic wave propagates into the medium in accordance with the laws of geometrical acoustics: in a straight line in a homogeneous medium, reflected and refracted at boundaries of media with different acoustic properties. It can be focusing, using lenses and spherical mirrors.
Ultrasonic wave has REFRACTION and REFLECTION at the interface between two media with different acoustic properties. The proportion of wave energy depends on acoustic impedance of mediums.
The refraction angle can be calculated using Snell's law.
The sine of the incidence angle over the sine of the refraction angle equals to the elastic wave velocity into the first medium ( V sub A) over the elastic wave velocity into the second medium ( V sub b) .
If the elastic wave velocity into the first medium is more of the elastic wave velocity into the second medium, so alpha angle is more betta angle.
angle of incidence equals angle of reflection

12. FIRST CRITICAL ANGLE
If the elastic wave velocity into the first medium is less than the elastic wave velocity into the second medium, so the incidence angle is less to the refract angle.
If the refract angle equals 90 degree, the incidence angle names first critical angle.
the sine of the incidence angle equals to the elastic wave velocity into the first medium over the elastic wave velocity into the second medium

13. REFLECTION and TRANSMISSION COEFFICIENTS
The reflection coefficient of acoustic waves from the interface of two media equals to the ratio of the intensities of the reflected and incident waves. If the wave incidents on a surface by perpendicular thereto, the reflection coefficient can be calculated using the Rayleigh formula:
Z sub 2 minus Z sub 1 over Z sub 2 plus Z sub 1
Z is the density multiplied by the velocity
the more difference between the acoustic impedance, the lower the proportion of energy carried by the wave through the interface.
If Z sub 2 a lot more Z sub 1, than R is about 1.
For example, the intensity of the ultrasonic waves propagate from water to air is only 0.1% of the intensity of a wave incident on the surface of the water, and 99.9% is reflected into water.
Therefore, the use of ultrasound in the diagnosis needs to be good contact between the ultrasound emitter and the surface of the body.
For this purpose, liquid – gel, water, glycerin, mineral oil, solution of medications.
For this it uses a special gel.
If the ultrasonic wave is reflected from the surface perpendicular to the direction of its propagation, the incident and reflected waves are superimposed on each other. In cases where between the emitter and the reflective surface is placed an integer number of half waves in the medium, it has a so-called standing wave.

14. absorption factor, db/sm,
IMPEDANCE
Z=ρc
ρ – density of medium
c – velocity of elastic wave into medium
Acoustic properties of some mediums
Meduim
velocity, m/s
impedance, кg/(s m²)
absorption factor, db/sm,
for f = 1 МHz
Blood
1570
1,61
0,13
Adipose
1450
1,38
0,63
Kidney
1561
1,62
1,0
Liver
1549
1,65
0,94
bone
4080
7,80 13
water
1480
1,48
0,0022
Symbol ['sɪmb(ə)l]
Blood - кровь
Bone [bəun] - кость
Adipose ['ædɪpəus] – жировая ткань
Kidney ['kɪdnɪ] - почка
Liver - печень

15. ACOUSTIC FIELD Acoustic pressure P= ρcAω =ZVm
V sub m is the maximum amplitude of the particle velocity, ω - circular frequency, A - the maximum amplitude of displacement of particles, z is impedance.
Intensity of acoustic wave
W – energy of acoustic wave, S – surface square exposed to acoustic wave, t – time.
Acoustic wave:
ω – cyclic frequency of oscillations; х – the position of a particle in the direction of wave propagation; k– wave number; φ0 - the epoch angle or the initial phase.
k = 2π/λ
Medium part, in which propagates acoustic wave, called an acoustic field.
The acoustic field is characterized by a variable acoustic pressure in each point and the intensity of propagating waves.
Acoustic wave transfers energy.
Acoustic pressure equals acoustic impedance multiply the maximum amplitude of displacement of particles and the circular frequency
Intensity of acoustic wave equals energy of acoustic wave over surface square exposed to acoustic wave and time
Unit of measurement Watt over square meter.
the mathematical formula of Acoustic wave.
Acoustic wave is the harmonic oscillation.
A is the maximum displacement of the particle relative to the equilibrium position (the amplitude);
ω = 2πf; f= 1/Т
T is the period of oscillation.
φ0 (φ sub 0) - the epoch ['iːpɔk ] angle
if you know the intensity I of a wave, its frequency ω and the acoustic impedance z of the medium, we can calculate the displacement amplitude of particles A, their oscillation, velocity V sub m, the oscillating acceleration and variable pressure of elastic wave.
For example, if the wave frequency is 1 MHz, it propagates in water and the intensity of 10,000 Watt per meter square (1 Watt per centimetre square) the particles have amplitude oscillate A=20 nanometers, the amplitude of vibrational velocity equals 0.1 m/s, and acceleration 700 meter per second square. It is more approximately 70 times than the free fall acceleration. The amplitude of the acoustic pressure in an ultrasonic wave under these conditions is equal to pascal or 1.8 atmosphere.

16. ACOUSTIC FIELD The amplitude of vibrational velocity: Vm = ωA,
Vm is the maximum amplitude of vibrational velocity:
Vm = ωA,
A - the maximum displacement of the particle relative to the equilibrium position (the amplitude); ω – cyclic frequency of oscillations;
The acceleration amplitude:
V of t equals differential of A by differential of t
It equals A sub zero multiply omega cosine ['kəusaɪn] of omega t
And it equals V sub m multiply cosine ['kəusaɪn] of omega t
B equals d two A by t squared. It equals d V sub m by d t and it equals minus A sub zero multiply omega squared sine ['saɪn] of omega t
Example.

17. DESIGN OF ULTRASONIC SENSOR
The design of the acoustic sensor
1 – piezo ceramics;
2 - damper (to reduce the duration of the vibrations on impact (shot)), (material with high absorption);
3 - protector (to protect the piezoelectric element), (epoxy resin);
4 - contact lubricant layer;
5 - testing object;
6 - transducer body
7 – input cable
this substance consists of a mixture of zirconium, titanium and plumbum
Ceramic [sə'ræmɪk]
Точка соединения - junction point
d – the thickness of the piezoelectric ceramic

18. ACOUSTIC FIELD OF ULTRASONIC SENSOR
For a circular plate A = 1,22
for a square plate A = 1,
Z0 = d²/4λ
In medicine, veterinary and experimental biology are used planar high-frequency emitter.
For practical purposes you can assume that the amplitude at the surface is constant, and the diameter D is much greater than the length of the ultrasonic waves.
An idealized form of the acoustic field of this radiator is shown in Fig
ultrasonic field near of the emitter has a cylindrical shape of diameter D and length Z sub zero.
The interval from the emitter to Zsub zero is called the near zone or Fresnel zone.
The distance, where Z > (more ) Z0, is called the far zone or Fraunhofer zone.
In this zone, the pressur amplitude decreases proportionally to the distance from the emitter and a acoustic field has cone-shaped.
The angle α between the direction of propagation of ultrasonic waves and beam forming is determined by the condition
For a circular plate A = 1,22
D – diameter of a circle;
for a square plate A = 1,
D is the length of one side of the square.
Fresnel zone
Fraunhofer zone
The interval from the radiator to Z0 called the near area, or Fresnel zone. The area where Z> Z0, called the far zone, or Fraunhofer zone.
Z0=d²/4λ

19. ACOUSTIC FIELD OF ULTRASONIC SENSOR
the intensity of the ultrasound in the near field has periodically shape and it can has several peaks.
In the far zone the intensity of a single peak and monotonically decreases Z0

20. DIRECTIONAL CHARACTERISTIC of single probe
The pattern is the dependence of the intensity of the ultrasonic wave in the far zone from the viewing angles in the space
The radiation pattern of the emitter (NAM) is the dependence of the intensity of the ultrasonic wave in the far zone from the viewing angles in the space.
The main maximum is called the main lobe coincides to the direction of main radiation (or reception). Accordingly, the first minimum, or (rarely) zero values around the main lobe determine its boundary. All other maximums of the field are called side lobes.
the radiation pattern can be represented in Cartesian or polar coordinates.
One of the most important parameters is the width of the main lobe at zero radiation θ sub 0 and the width of the main lobe at the half power level θ sub 0,5.
Half power corresponds to the level of 3 dB, or the level of 0,707 of the voltage.
Another important parameter is the level of side lobes.
The side lobe amplitude is measured in dB.
Side lobes would affect the accuracy of detection, if the ratio of the amplitude of the main lobe to the side lobe is not high enough, then there are artifacts

21. Thank you