Mechanical vibrations propagating in the medium. Types of vibrations
The process of propagation of vibrations in an elastic medium is called a wave. The distance the wave travels in a time equal to the oscillation period is called the wavelength. The wavelength is related to the oscillation period of the particles T and wave propagation speed υ ratio
λ = υT or λ = υ /ν,
where ν = 1 / T Is the vibration frequency of the particles of the medium.
If two waves of the same frequency and amplitude propagate towards each other, then as a result of their superposition, under certain conditions, a standing wave may arise. In a medium where standing waves are established, particle oscillations occur with different amplitudes. At certain points in the medium, the amplitude of the oscillation is zero, these points are called nodes; at other points the amplitude is equal to the sum of the amplitudes of the added oscillations, such points are called antinodes. The distance between two neighboring nodes (or antinodes) is equal to l / 2, where l is the length of the traveling wave (Fig. 1).
A standing wave can form when the incident and reflected waves overlap. Moreover, if the reflection occurs from a medium many times denser than the medium in which the wave propagates, then in the place
Rice. 1 reflection, the displacement of particles is zero, that is, the image
there is a node. If the wave is reflected from a less dense medium, then due to the weak retarding effect of the particles of the second medium, oscillations with a double amplitude arise at the boundary, that is, an antinode is formed. In the case when the densities of the media differ little from each other, partial reflection of waves from the interface between the two media is observed.
Consider standing waves that form in a pipe with air of length l closed on both sides (Fig. 1, a). Through a small hole in one end of the pipe, using a speaker, we excite the oscillations of the audio frequency. Then a sound wave will propagate in the air inside the pipe, which will be reflected from the other closed end and run back. It would seem that a standing wave should arise at any oscillation frequency. However, in a pipe closed on both sides, knots should form at the ends. This condition is fulfilled if half the length of the traveling wave fits in the pipe: l= l / 2 (Fig. 1, b). Here, the amplitudes of the displacement of air particles are plotted vertically. The solid line represents the traveling wave, the dotted line - the reflected one. Such a standing wave is also possible in the pipe, where there is also one more node, while two halves of the wavelength are stacked: l= 2l / 2 (Fig. 1, v). The next standing wave occurs when the length of the traveling wave satisfies the condition l= 3λ / 2 (Fig. 1, G). Thus, in a pipe closed on both sides, a standing wave is formed when an integer number of half the wavelengths fits along the pipe length:
where m= 1, 2, 3. Expressing l from (1) and substituting into the formula ν = υ /λ,
The resulting formula expresses the natural frequencies of oscillations of the air column in a pipe with a length l, where m= 1 corresponds to the main tone, m= 2, 3 - overtones. In the general case, the oscillation of the air column can be represented as the superposition of natural oscillations.
Chapter 2. WAVES
Wave process. Types of waves
Solid, liquid and gaseous bodies can be considered as media consisting of individual particles interacting with each other. If we excite vibrations of particles in a local area of the medium, then due to the forces of interaction, forced vibrations of neighboring particles will arise, which, in turn, will cause vibrations of the particles associated with them, etc. Thus, vibrations excited at any point in the medium will propagate in it at a certain speed, depending on the properties of the medium. How further down the particle from the source of vibration, the later she will start oscillating... In other words, the phase of oscillations of the particles of the medium depends on the distance to the source.
The process of propagation of oscillations in a certain medium is called a wave process or wave.
The particles of the medium in which the wave propagates, make an oscillatory motion about their equilibrium positions. When distributing waves of a particle of a medium are not carried by a wave. Together with the wave vibrational motion and its energy are transmitted from particle to particle of the medium. Thus, the main property of waves, regardless of their nature, is the transfer of energy without transfer of matter.
The following types of waves are found in nature and technology: gravitational capillary waves(waves on the surface of the liquid), elastic waves(propagation of mechanical disturbances in an elastic medium) and electromagnetic(propagation in the environment of electromagnetic disturbances).
Elastic waves are longitudinal and transverse... In longitudinal waves particles of the medium vibrate in the direction of wave propagation, in transverse - in planes perpendicular to the direction of wave propagation(Fig. 2.1.1, a; b).
· Free vibrations are performed under the action of the internal forces of the system after the system has been brought out of the equilibrium position. For free oscillations to be harmonic, it is necessary that the oscillatory system be linear (described linear equations motion), and there was no energy dissipation (the latter would cause damping).
· Forced vibrations are committed under the influence of an external periodic force. For them to be harmonic, it is sufficient that the oscillatory system is linear (described by linear equations of motion), and the external force itself changes over time as a harmonic oscillation (that is, the time dependence of this force is sinusoidal).
A special role in oscillatory processes has simplest view hesitation - harmonic vibrations. Harmonic vibrations underlie a unified approach to the study of vibrations of various natures, since vibrations found in nature and technology are often close to harmonic, and periodic processes of a different form can be represented as the superposition of harmonic vibrations.
Harmonic vibrations
such oscillations are called in which the oscillating quantity changes from time to time according to the lawsinus
orcosine
.
Harmonic Equation looks like:
,
where A - vibration amplitude
(the value of the greatest deviation of the system from the equilibrium position); -circular (cyclic) frequency.
Periodically changing cosine argument - called phase of oscillation
... The oscillation phase determines the displacement of the oscillating quantity from the equilibrium position at a given time t. The constant φ is the phase value at time t = 0 and is called the initial phase of the oscillation
... The value of the initial phase is determined by the choice of the reference point. The value of x can take on values ranging from -A to + A.
The time interval T through which certain states of the oscillatory system are repeated, called the oscillation period
... The cosine is a periodic function with a period of 2π, therefore, for a time interval T, after which the phase of the oscillations will gain an increment equal to 2π, the state of the system performing harmonic oscillations will be repeated. This period of time T is called the period of harmonic oscillations.
The period of harmonic oscillations is
: T = 2π /.
The number of vibrations per unit of time is called vibration frequency
ν.
Harmonic frequency
is equal to: ν = 1 / T. Frequency unit hertz(Hz) - one oscillation per second.
Circular frequency = 2π / T = 2πν gives the number of oscillations in 2π seconds.
Graphically, harmonic oscillations can be depicted as a dependence of x on t (Fig. 1.1.A), and rotating amplitude method (vector diagram method)(Figure 1.1.B) .
The rotating amplitude method allows you to visualize all the parameters included in the equation of harmonic oscillations. Indeed, if the amplitude vector A is located at an angle φ to the x-axis (see Figure 1.1. B), then its projection on the x-axis will be: x = Acos (φ). The angle φ is the initial phase. If the vector A put into rotation with an angular velocity equal to the circular frequency of oscillation, then the projection of the end of the vector will move along the x-axis and take values ranging from -A to + A, and the coordinate of this projection will change with time according to the law:
.
Thus, the length of the vector is equal to the amplitude of the harmonic oscillation, the direction of the vector at the initial moment forms an angle with the x-axis equal to the initial phase of oscillations φ, and the change in the angle of direction with time is equal to the phase of harmonic oscillations. The time during which the amplitude vector makes one complete revolution is equal to the period T of harmonic oscillations. The number of revolutions of the vector per second is equal to the oscillation frequency ν.
- Propagation of vibrations in biological media. Shear and longitudinal waves
If in some place of a solid, liquid or gaseous medium vibrations of particles are excited, then due to the interaction of atoms and molecules of the medium, vibrations begin to be transmitted from one point to another at a finite speed. The process of propagation of vibrations in a medium is called a wave.
Mechanical waves are different types... If in a wave the particles of the medium experience a displacement in the direction perpendicular to the direction of propagation, then the wave is called transverse. An example of a wave of this kind is waves traveling along a stretched rubber band (Fig. 2.6.1) or along a string.
If the displacement of the particles of the medium occurs in the direction of wave propagation, then the wave is called longitudinal. Waves in an elastic bar (Figure 2.6.2) or sound waves in a gas are examples of such waves.
Waves on the surface of a liquid have both transverse and longitudinal components.
In both transverse and longitudinal waves, the transfer of matter in the direction of wave propagation does not occur. In the process of propagation, the particles of the medium only oscillate around the equilibrium positions. However, waves transfer vibration energy from one point of the medium to another.
Characteristic feature mechanical waves is that they propagate in material environments(solid, liquid or gaseous). There are waves that can propagate in emptiness (for example, light waves). For mechanical waves, a medium is required that has the ability to store kinetic and potential energy. Consequently, the medium must have inert and elastic properties. In real environments, these properties are distributed throughout the volume. So, for example, any small element of a rigid body has mass and elasticity. In the simplest one-dimensional model solid can be represented as a collection of balls and springs (Fig. 2.6.3).
If in any place of an elastic medium (solid, liquid or gaseous) vibrations of its particles are excited, then due to the interaction between particles, this vibration will begin to propagate in the medium from particle to particle at a certain speed v.
For example, if an oscillating body is placed in a liquid or gaseous medium, then the oscillatory motion of the body will be transmitted to the adjacent particles of the medium. They, in turn, involve neighboring particles in oscillatory motion, and so on. In this case, all points of the medium vibrate with the same frequency, equal to the frequency of vibration of the body. This frequency is called the frequency of the wave.
Wave is the process of propagation mechanical vibrations in an elastic medium.
The frequency of the wave is the frequency of oscillations of the points of the medium in which the wave propagates.
The wave is associated with the transfer of vibration energy from the vibration source to the peripheral regions of the medium. In this case, in the environment there are
periodic deformations, which are transferred by a wave from one point of the medium to another. The particles of the medium themselves do not move with the wave, but oscillate around their equilibrium positions. Therefore, wave propagation is not accompanied by the transfer of matter.
In accordance with the frequency, mechanical waves are divided into different ranges, which are indicated in table. 2.1.
Table 2.1. Mechanical wave scale
Depending on the direction of vibration of the particles in relation to the direction of wave propagation, longitudinal and transverse waves are distinguished.
Longitudinal waves are waves during the propagation of which the particles of the medium vibrate along the same straight line along which the wave propagates. In this case, the areas of compression and discharge alternate in the medium.
Longitudinal mechanical waves can occur in all environments (solid, liquid and gaseous).
Transverse waves are waves during the propagation of which the particles vibrate perpendicular to the direction of propagation of the wave. In this case, periodic shear deformations occur in the medium.
In liquids and gases, elastic forces arise only during compression and do not arise during shear; therefore, transverse waves in these media are not formed. The exception is waves on the surface of the liquid.
VIBRATIONS, WAVES, SOUND
Harmonic sin or cos.
1. Displacement (s)
2. Amplitude (A) is the maximum displacement.
3. Period (T)
4. Linear frequency (v) ... v = 1 / T.
ω = 2πv .
6. Oscillation phase (φ) φ = ωt + φ 0
1. Free
2. Damped
3. Forced
4. Self-oscillations
s = Asin ωt
Then the total energy is:
longitudinal.
: λ = υT, λ = υv
: S = A sinωt
s = Asin (ωt-2πх / λ) 2πх / λ = φ 0
W = (mω 2 A 2) / 2
ε = W 0 / V
where W o = εV
ε = n 0 W = n 0 mω 2 A 2/2 , but n o m = p , then ε = (pω 2 A 2) / 2
Ps = W 0 / t (W)
J = Ps / s = W 0 / st (W)
J = Ps / s (W / m2)
logarithmic. J (c) = LgJ / J 0 (W / m 2)
sound pressure.
objective subjective.
Pitch
timbre
Volume Weber-Fechner:
E = kLg J / J 0
1. Audiometry
2. Auscultation
3. Percussion
Reflection laws
A medium, at all points of which the speed of light propagation is the same, is called an optically homogeneous medium. The boundary of two media is the surface that separates two optically inhomogeneous media. The angle α between the incident ray and the perpendicular restored to the boundary of the two media at the point of incidence is called the angle of incidence. The angle β between the reflected ray and the perpendicular to the interface between the two media at the point of incidence is called the angle of reflection.
I law: An incident ray, a perpendicular restored to the interface between two media at the point of incidence, and the reflected ray lie in the same plane.
II law: angle of incidence equal to the angle reflection: α = β
Law I: An incident ray, a perpendicular restored to the interface between two media at the point of incidence, and the refracted ray lie in the same plane.
I I law: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant value for these two media and is called the refractive index of the second medium relative to the first:
sinα / sinγ = const = n 21
Lenses
A lens is a transparent body bounded by two spherical surfaces, and in terms of refractive index differs from environment.
The straight line passing through the centers of the spherical surfaces bounding the lens (SS ") is called the main optical axis.
The point of intersection of the main optical axis with the refractive plane is called the optical center of the lens (O). Any straight line passing through the optical center of the lens is called the optical axis (AA). Beams parallel to the main optical axis, after refraction in the lens, are collected at one point, called the main focus of the lens (F). The point of intersection of the optical axis with the focal plane is called a side focus (F ").
Such lenses are called collecting. A parallel beam of rays after refraction in the lens can be scattered, then at one point, called imaginary focus, the extensions of these rays will gather. Such lenses are called scattering.
The plane perpendicular to the main optical axis and passing through the main focus of the lens is called the focal plane.
In collecting lenses, the image depends on the position of the object. If the subject is between the optical center of the lens and the main focus, then the image will be imaginary, direct and magnified.
If the subject is between focus and dual focus, the image is real, reverse, magnified.
If the subject is between double and triple focus and further, the image is real, reverse, reduced.
Diffusion lenses always give a ghost, direct and reduced image.
The distance from the optical center of the lens to the main focus is called focal length F... The reciprocal of the focal length is called optical power lenses: D = 1 / F
The optical power of the lens is measured in diopters (diopters). One diopter is the optical power of such a lens, the focal length of which is 1 m . For collecting lenses it is positive, for scattering lenses it is negative. In practice, the thin lens formula is used to determine the focal length and optical power of a lens: D = 1 / F = 1 / d + 1 / f ,
where d is the distance from the object to the lens, f is the distance from the lens to the image.
Images taken with a single lens tend to differ from the subject itself. In this case, they talk about image distortion. Spherical aberration arises because the edges of the lens deflect the rays more than the central part.
As a result, the image of the luminous point on the screen is obtained in the form of a blurry spot, and the image of an extended object becomes not sharp, blurred. To eliminate spherical aberration, centered optical systems are used, consisting of converging and diffusing lenses. Centered is a system of lenses that have a common main optical axis. .
Chromatic aberration caused by light dispersion, since the lens can be thought of as a prism. In this case, the focal length for beams of different wavelengths is not the same.
Therefore, when illuminating an object with a complex, for example, white light, a point on the screen will be visible as a colored spot, and the image of an extended object will also be colored and unsharp. Chromatic aberration can be eliminated by combining collecting and diffusing lenses made from different types of glass having different relative dispersions. These lens systems are called achromats... The reason astigmatism is the unequal refraction of rays in different meridional planes of the lens. There are two types of astigmatism. The first, the so-called astigmatism of oblique rays, occurs in lenses that have a spherical surface, but the rays fall on the lens at a significant angle to the main optical axis. In this case, the rays in mutually perpendicular planes are refracted unevenly and a point on the screen will be visible as a line, and the shape of an extended object is distorted, for example, a square will be visible as a rectangle.
The second type of astigmatism, correct, arises when the lens surface deviates from the spherical one, when there is an unequal radius of curvature along different meridional planes, i.e. the shape of the surface in this plane is not spherical. Astigmatism of oblique beams is eliminated by turning the lens towards the imaged object. Correct astigmatism is eliminated by adjusting the radii of curvature and optical powers of the refracting surfaces. These are most often cylindrical lenses. An optical system corrected for astigmatism in addition to spherical and chromatic aberrations is called anastigmatome.
Optical system of the eye
The human eye is a kind of optical device that occupies a special place in optics. This is explained, firstly, by the fact that many optical instruments are designed for visual perception, and secondly, the human eye is an animal), as improved in the process of evolution biological system, brings some ideas for the design and improvement of optical systems. The eye can be represented as a centered optical system formed by the cornea (P), fluid by the anterior chamber (K) and the lens (X), bounded in front by the air environment, and behind by the vitreous body. The main optical axis (MA) passes through the optical centers of the cornea and lens. In addition, the visual axis of the eye is also distinguished (30), which determines the direction of the highest photosensitivity and passes through the centers of the lens and the macula (G). The angle between the main optical and visual axes is about 5 ". The main refraction of light occurs at the outer border of the cornea, the optical power of which is about 40 diopters, the lens is about 20 diopters, and the entire eye is about 60 diopters. The adaptation of the eye to a clear vision of variously distant objects is called accommodation. In an adult healthy person when an object approaches the eye up to a distance of 25 cm, accommodation is performed without tension, and thanks to the habit of looking at objects in the hands, the eye most often accommodates exactly this distance, called the distance of the best vision. To characterize the resolving power of the eye, the smallest angle of view is used, at which the human eye still distinguishes two points of the object. In medicine, the resolution of the eye is assessed by visual acuity. One is taken as the norm of visual acuity, in this case the smallest angle of view is 1 ".
VIBRATIONS, WAVES, SOUND
Any deviations physical body or the parameter of its state, now in one direction or in the other direction from the equilibrium position, is called oscillatory motion or simply oscillation.
Oscillatory motion is called periodic if the values physical quantities, changing in the process of oscillations, are repeated at regular intervals.
Harmonic are called vibrations that occur according to the law sin or cos.
s = Asin (ωt + φ 0), s = Acos (ωt + φ 0)
They are performed under the action of quasi-elastic forces, i.e. forces proportional to displacement
The main characteristics of vibrations are:
1. Displacement (s)- This is the distance by which the oscillating system deviates at a given time, from the equilibrium position.
2. Amplitude (A) is the maximum displacement.
3. Period (T)- the time of one complete oscillation.
4. Linear frequency (v)- this is the number of oscillations per unit of time, measured in Hz - this is one oscillation per second ... v = 1 / T.
5. Cyclic or circular frequency (ω). It is related to the linear frequency by the following relationship: ω = 2πv .
6. Oscillation phase (φ) characterizes the state of the oscillating system at any time: φ = ωt + φ 0 , φ 0 - the initial phase of the oscillation.
The oscillatory process can be represented graphically in the form of an expanded or vector diagram.
An expanded diagram is a graph of a sinusoid or cosine wave, from which you can determine the displacement of an oscillating system at any time.
However, any complex vibration can be represented as a sum of harmonic ones. This provision defines a special diagnostic method - spectral analysis.
The set of harmonic components into which a complex vibration is decomposed is called the harmonic spectrum of this vibration.
Fluctuations are divided into the following main types:
1. Free- these are ideal vibrations that do not exist in nature, but help to understand the essence of other modes of vibrations and determine the properties of a real vibrational system. They occur with a natural frequency, which depends only on the properties of the oscillating system itself. The natural frequency and period will be denoted by v 0 and T about.
2. Damped- these are oscillations, the amplitude of which decreases over time, and the frequency does not change and is close to its own. Energy is supplied to the system once. The decrease in the amplitude per unit time is characterized by the damping coefficient β = r / 2m, where r is the friction coefficient, m is the mass of the oscillating system. The decrease in the amplitude over the period is characterized by a logarithmic damping decrement δ = βТ. The logarithmic damping decrement is the logarithm of the ratio of two adjacent amplitudes: δ = log (At / A t + T).
3. Forced- these are vibrations that occur under the influence of a periodically changing external force. They are performed with the frequency of the compelling force. The phenomenon of a sharp increase in the amplitude of oscillations when the frequency of the driving force approaches the natural frequency of the system is called resonance. This increase will depend on the amplitude of the driving force, the mass of the system, and the damping factor.
4. Self-oscillations are called continuous oscillations that exist in any system in the absence of variable external influences, and the systems themselves are called self-oscillatory. The amplitude and frequency of self-oscillations depend on the properties of the self-oscillating system itself. The self-oscillating system consists of three main elements: 1) the oscillating system itself; 2) energy source; 3) feedback mechanism. A striking example of such a system in biology is the heart.
Let us determine the energy of a body of mass m performing free harmonic oscillations with amplitude A and cyclic frequency ω.
s = Asin ωt
The total energy is the sum of the potential and kinetic energy:
Wn = ks 2/2 = (kA 2/2) sin 2 ωt, where k = mω
W = mυ 2/2, taking into account that υ = ds / dt = Aωcosωt
we get Wk = (mω 2 A2 / 2) * cos 2 ωt
Then the total energy is:
W = (mω 2 A 2/2) (sin 2 ωt + cos 2 ωt) = (mω 2 A 2) / 2
The process of propagation of vibrations in space is called wave motion or simply wave.
There are two types of waves: mechanical and electromagnetic. Mechanical waves propagate only in elastic media. Mechanical waves are divided into two types: transverse and longitudinal.
If the vibrations of the particles are perpendicular to the direction of propagation of the wave, then it is called transverse.
If the vibrations of the particles coincide with the direction of propagation of the wave, then it is called longitudinal.
Consider the main characteristics of wave motion. These include:
1. All parameters of the oscillatory process (s, A, v, ω, T, φ).
2. Additional parameters that characterize only wave motion:
a) Phase velocity (υ) is the speed with which oscillations propagate in space.
b) Wavelength (λ) is the smallest distance between two particles of wave space, oscillating in the same phases, or the distance over which the wave propagates during one period. Characteristics are related : λ = υT, λ = υv
The oscillatory motion of any particle in wave space is determined by the wave equation. Let at point O oscillations occur according to the law : S = A sinωt
Then, at an arbitrary point C, the oscillation law is: s c = sinω (t-∆t), where ∆t = x / υ = x / λv, xc = Asin (2πv t- (2πvx / λx))
s = Asin (ωt-2πх / λ) is the equation of the wave. It determines the law of oscillation at any point in wave space 2πх / λ = φ 0 is called the initial phase of the oscillation at an arbitrary point in space.
3. Energy characteristics of the wave:
a. Vibration energy of one particle: W = (mω 2 A 2) / 2
b. The vibration energy of all particles contained in a unit volume of wave space is called volumetric energy density: ε = W 0 / V
where W o = εV is the total energy of all vibrating particles in any volume.
If n 0 is the concentration of particles, then ε = n 0 W = n 0 mω 2 A 2/2 , but n o m = p , then ε = (pω 2 A 2) / 2
The vibration energy is constantly transferred to other particles in the direction of wave propagation.
The quantity numerically equal to the average value of the energy carried by the wave per unit time through a certain surface perpendicular to the direction of wave propagation is called the energy flux through this surface.
Ps = W 0 / t (W)
The energy flux per unit surface is called the energy flux density or wave intensity.
J = Ps / s = W 0 / st (W)
Sound waves are a special case of mechanical waves:
Sound waves are vibrations of particles that propagate in elastic media in the form of longitudinal waves with a frequency of 16 to 20,000 Hz.
For sound waves, the same characteristics are valid as for any wave process, however, there are some specific features.
1. The intensity of a sound wave is called sound power. J = Ps / s (W / m2)
For this value, special units of measurement are adopted - Bela (B) and decibels (dtsB). The scale of sound intensity, expressed in B or dcB, is called logarithmic. To convert from SI to a logarithmic scale, the following formula is used: J (c) = LgJ / J 0 (W / m 2)
where J o = 10 -12 W / m 2 - some threshold intensity.
2. To describe sound waves, a quantity is used, which is called sound pressure.
Sound or acoustic pressure is called the additional pressure (excess over the average pressure of the environment) in places of the greatest concentration of particles in sound wave.
In the SI system, it is measured in Pa, and the off-system unit is 1 acoustic bar = 10 -1 Pa.
3. The form of vibrations of particles in a sound wave, which is determined by the harmonic spectrum of sound vibrations (∆v), is also important.
All listed physical characteristics sound are called objective, i.e. independent of our perception. They are determined using physical instruments. Our hearing aids are able to differentiate (distinguish) sounds by pitch, timbre and volume. These characteristics of the auditory experience are called subjective. A change in the perception of sound by ear is always associated with a change in the physical parameters of the sound wave.
Pitch is determined mainly by the frequency of vibrations in a sound wave and slightly depends on the strength of sound. The higher the frequency, the higher the pitch of the sound. In this respect, the range of sounds perceived by the hearing aid is divided into octaves: 1- (16-32) Hz; 2 - (32-64) Hz; 3- (64-128) Hz; etc., 10 octaves in total.
If the vibrations of particles in a sound wave are harmonic, then such a tone of sound is called simple or pure. Such sounds are produced by a tuning fork and a sound generator.
If the vibrations are not harmonic, but periodic, then such a tone of sound is called complex. ...
If complex sound vibrations do not periodically change their intensity, frequency and phase, then such a sound is usually called noise.
Complex tones of the same pitch, in which the vibration mode is different, are perceived differently by a person (for example, the same note on different musical instruments). This difference in perception is called timbre sound. It is determined by the spectrum of frequencies of harmonic vibrations that make up a complex sound.
Volume The perception of sound depends mainly on the strength of the sound, as well as on the frequency. This dependence is determined by the psychophysical law Weber-Fechner:
As the sound intensity increases exponentially (J, J 2, J 3, ...), the sensation of loudness at the same frequency increases by arithmetic progression(E, 2E, ZE, ...).
E = kLg J / J 0
where k is a coefficient depending on the sound frequency. Loudness is measured in the same way as the strength of sound in Belah (B) and decibels (dcB). The dB of loudness is called the background (F) in contrast to the dB of the sound power. It is conventionally believed that for a frequency of 1000 Hz, the scales of loudness and sound intensity completely coincide, i.e. k = 1.
Using sound methods in diagnostics
1. Audiometry- a method for measuring hearing acuity by the perception of sounds standardized in frequency and intensity.
2. Auscultation- listening to sounds arising from the work of various organs (heart, lungs, blood vessels, etc.)
3. Percussion- listening to the sound of individual parts of the body when tapping them.
Ultrasound is a process of propagation of vibrations in a compact medium in the form of longitudinal waves with a frequency of over 20 kHz.
Ultrasound is obtained using special devices based on the phenomena of magnetostriction - at low frequencies and the inverse piezoelectric effect - at high frequencies.
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