When passing through the boundaries between media, acoustic waves experience not only reflection and refraction, but also the transformation of waves of one type into another. Let us consider the simplest case of normal incidence of a wave on the boundary of two extended media (Fig. 3.1). There is no wave transformation in this case.
Let us consider the energy relations between the incident, reflected, and transmitted waves. They are characterized by the coefficients of reflection and refraction.
Amplitude reflection coefficient is the ratio of the amplitudes of the reflected and incident waves:
Amplitude transmission coefficient is the ratio of the amplitude of the transmitted and incident waves:
These coefficients can be determined knowing the acoustic characteristics of the media. When a wave is incident from medium 1 into medium 2, the reflection coefficient is determined as
, (3.3)
where , are the acoustic impedances of media 1 and 2, respectively.
When a wave is incident from medium 1 to medium 2, the transmission coefficient is denoted and defined as
. (3.4)
When a wave is incident from medium 2 into medium 1, the transmission coefficient is denoted and defined as
. (3.5)
It can be seen from formula (3.3) for the reflection coefficient that the more the acoustic impedances of the media differ, the most of energy of a sound wave will be reflected from the interface between two media. This determines both the possibility and the efficiency of detecting discontinuities in the material (inclusions of the medium with acoustic resistance that differs from the resistance of the controlled material).
It is precisely because of the differences in the values of the reflection coefficients that slag inclusions are detected much worse than defects of the same size, but with air filling. The reflection from a discontinuity filled with gas approaches 100%, and for a discontinuity filled with slag, this coefficient is much lower.
When a wave is normally incident on the boundary of two extended media, the ratio between the amplitudes of the incident, reflected, and transmitted waves is
. (3.6)
The energy of the incident wave in the case of normal incidence on the boundary of two extended media is distributed between the reflected and transmitted waves according to the conservation law.
In addition to the reflection and amplitude transmission coefficients, the intensity reflection and transmission coefficients are also used.
Intensity reflection coefficient is the ratio of the intensities of the reflected and incident waves. For normal wave incidence
, (3.7)
where is the reflection coefficient during the incidence from medium 1 to medium 2;
is the reflection coefficient when falling from medium 2 into medium 1.
Intensity Transmission Coefficient is the ratio of the intensities of the transmitted and incident waves. When the wave falls along the normal
, (3.8)
where is the transmission coefficient during the fall from medium 1 to medium 2;
is the transmission coefficient when falling from medium 2 to medium 1.
The direction of wave incidence does not affect the values of the coefficients of reflection and intensity transmission. The law of conservation of energy through the coefficients of reflection and transmission is written as follows
When a wave is obliquely incident on the interface between media, it is possible to transform a wave of one type into another. The reflection and transmission processes in this case are characterized by several reflection and transmission coefficients, depending on the type of incident, reflected, and transmitted waves. The reflection coefficient in this form has the designation ( is an index indicating the type of the incident wave, is an index indicating the type of the reflected wave). Cases are possible. The transmission coefficient is denoted by ( is an index indicating the type of the incident wave, is an index indicating the type of the transmitted wave). There are cases , and .
transmittance
reflection coefficient
And absorption coefficient
The coefficients t, r and a depend on the properties of the body itself and the wavelength of the incident radiation. Spectral dependence, i.e. the dependence of the coefficients on the wavelength determines the color of both transparent and opaque (t= 0) bodies.
According to the law of conservation of energy
Ф neg + Ф absorb + Ф pr = . (8)
Dividing both sides of the equality by , we get:
r + a + t = 1. (9)
A body for which r=0, t=0, a=1 is called absolutely black .
An absolutely black body at any temperature completely absorbs all the energy of radiation incident on it of any wavelength. All real bodies are not completely black. However, some of them in certain intervals of wavelengths are close in their properties to an absolutely black body. For example, in the region of visible light wavelengths, the absorption coefficients of soot, platinum black, and black velvet differ little from unity. The most perfect model of an absolutely black body can be a small hole in a closed cavity. It is obvious that this model is the closer in characteristics to a black body, the greater the ratio of the surface area of the cavity to the area of the hole (Fig. 1).
The spectral characteristic of the absorption of electromagnetic waves by a body is spectral absorption coefficient a l is the value determined by the ratio of the radiation flux absorbed by the body in a small spectral interval (from l to l + d l) to the flux of radiation incident on it in the same spectral interval:
.
(10)
The emissive and absorptive abilities of an opaque body are interrelated. The ratio of the spectral density of the energy luminosity of the equilibrium radiation of a body to its spectral absorption coefficient does not depend on the nature of the body; for all bodies it is a universal function of wavelength and temperature ( Kirchhoff's law ):
. (11)
For a black body, a l = 1. Therefore, it follows from Kirchhoff's law that M e,l = , i.e. the universal Kirchhoff function is the spectral density of the energy luminosity of an absolutely black body.
Thus, according to Kirchhoff's law, for all bodies the ratio of the spectral density of the energy luminosity to the spectral absorption coefficient is equal to the spectral density of the energy luminosity of an absolutely black body at the same values T and l.
It follows from Kirchhoff's law that the spectral density of the energy luminosity of any body in any region of the spectrum is always less than the spectral density of the energy luminosity of an absolutely black body (at the same wavelength and temperature). In addition, it follows from this law that if a body at a certain temperature does not absorb electromagnetic waves in the range from l to l + d l, then it does not emit them in this range of lengths at a given temperature.
Analytical form of the function for a black body
was established by Planck on the basis of quantum ideas about the nature of radiation:
(12)
The emission spectrum of a black body has a characteristic maximum (Fig. 2), which shifts to the short-wavelength part with increasing temperature (Fig. 3). The position of the maximum spectral density of energy luminosity can be determined from expression (12) in the usual way, equating the first derivative to zero:
. (13)
Denoting , we get:
X – 5 ( – 1) = 0. (14)
Rice. 2 Fig. 3
Solving this transcendental equation numerically gives
X = 4, 965.
Hence,
, (15)
= = b 1 = 2.898 m K, (16)
Thus, the function reaches its maximum at a wavelength inversely proportional to the thermodynamic temperature of a blackbody ( Wien's first law ).
It follows from Wien's law that at low temperatures, predominantly long (infrared) electromagnetic waves are emitted. As the temperature rises, the proportion of radiation in the visible region of the spectrum increases, and the body begins to glow. With a further increase in temperature, the brightness of its glow increases, and the color changes. Therefore, the color of the radiation can serve as a characteristic of the temperature of the radiation. An approximate dependence of the color of the glow of the body on its temperature is given in Table. 1.
Table 1
Wien's first law is also called displacement law , thus emphasizing that with increasing temperature, the maximum spectral density of energy luminosity shifts towards shorter wavelengths.
Substituting formula (17) into expression (12), it is easy to show that the maximum value of the function is proportional to the fifth power of the thermodynamic body temperature ( Wien's second law ):
The energy luminosity of a black body can be found from expression (12) by simple integration over the wavelength
(18)
where is the reduced Planck constant,
The energy luminosity of a black body is proportional to the fourth power of its thermodynamic temperature. This position is called Stefan-Boltzmann law , and the coefficient of proportionality s = 5.67×10 -8 – the Stefan-Boltzmann constant.
A black body is an idealization of real bodies. Real bodies emit radiation whose spectrum is not described by Planck's formula. Their energy luminosity, in addition to temperature, depends on the nature of the body and the state of its surface. These factors can be taken into account if we introduce into formula (19) the coefficient showing how many times the energy luminosity of an absolutely black body at a given temperature is greater than the energy luminosity of a real body at the same temperature
whence , or (21)
For all real bodies<1 и зависит как от природы тела и состояния его поверхности, так и от температуры. В частности, для вольфрамовых нитей электроламп накаливания зависимость от T has the form shown in Fig. 4.
The measurement of radiant energy and temperature of the electric furnace is based on seebeck effect, which consists in the occurrence of an electromotive force in an electrical circuit consisting of several dissimilar conductors, the contacts of which have different temperatures.
Two dissimilar conductors form thermocouple , and series-connected thermocouples - a thermopillar. If the contacts (usually junctions) of the conductors are at different temperatures, then in a closed circuit that includes thermocouples, a thermoEMF arises, the value of which is uniquely determined by the temperature difference between hot and cold contacts, the number of series-connected thermocouples and the nature of the conductor materials.
The value of thermoEMF that occurs in the circuit due to the energy of the radiation incident on the thermal column junctions is measured by a millivoltmeter located on the front panel of the measuring device. The scale of this device is graduated in millivolts.
The temperature of an absolutely black body (furnace) is measured using a thermoelectric thermometer, consisting of a single thermocouple. Its EMF is measured by a millivoltmeter, also located on the front panel of the measuring device and calibrated in °C.
Note. The millivoltmeter records the temperature difference between the hot and cold junctions of the thermocouple, therefore, to obtain the furnace temperature, it is necessary to add the room temperature to the instrument reading.
In this work, the thermoelectric power of a thermopillar is measured, the value of which is proportional to the energy spent on heating one of the contacts of each thermocouple of the column, and, consequently, the energy luminosity (with equal time intervals between measurements and a constant radiator area):
Where b- coefficient of proportionality.
Equating the right parts of equalities (19) and (22), we obtain:
s× T 4 =b xe,
Where With is a constant value.
Simultaneously with the measurement of the thermoelectric power of the thermopillar, the temperature difference Δ t hot and cold junctions of a thermocouple placed in an electric furnace, and determine the temperature of the furnace.
Using the experimentally obtained temperature values of a completely black body (furnace) and the corresponding values of thermoelectric power of the thermopillar, determine the value of the coefficient proportional to
sti With, which should be the same in all experiments. Then build a dependency graph c \u003d f (T), which should have the form of a straight line parallel to the temperature axis.
Thus, in the laboratory work, the nature of the dependence of the energy luminosity of a completely black body on its temperature is established, i.e. the Stefan–Boltzmann law is verified.
Low-e coating: A coating that, when applied to glass, significantly improves the thermal performance of glass (the heat transfer resistance of glazing with low-e coating increases and the heat transfer coefficient decreases).
Sun protection
Sun protection coating: A coating that, when applied to glass, improves the protection of the room from the penetration of excess solar radiation.
Emission factor
Emissivity (corrected emission factor): The ratio of the radiation power of the glass surface to the radiation power of a blackbody.
Normal emission factor
Normal emissivity (normal emissivity): The ability of glass to reflect normally incident radiation; is calculated as the difference between unity and the reflectance in the direction normal to the glass surface.
solar factor
Solar factor (total solar energy transmittance): The ratio of the total solar energy entering the room through a translucent structure to the energy of the incident solar radiation. The total solar energy entering the room through the translucent structure is the sum of the energy directly passing through the translucent structure and that part of the energy absorbed by the translucent structure, which is transmitted into the room.
Directional light transmittance
Directional light transmittance (equivalent terms: light transmittance, light transmittance), denoted as τv (LT) - the ratio of the value of the light flux that normally passed through the sample to the value of the light flux normally incident on the sample (in the range of wavelengths of visible light) .
Light reflectance
Light reflectance (an equivalent term: normal light reflection coefficient, light reflection coefficient) is denoted as ρv (LR) - the ratio of the value of the light flux normally reflected from the sample to the value of the light flux normally incident on the sample (in the range of wavelengths of visible light).
Light absorption coefficient
The light absorption coefficient (equivalent term: light absorption coefficient) is denoted as av (LA) - the ratio of the value of the light flux absorbed by the sample to the value of the light flux normally incident on the sample (in the visible wavelength range).
Solar energy transmittance
The solar energy transmittance (equivalent term: direct solar energy transmittance) is denoted as τе (DET) - the ratio of the value of the solar radiation flux normally passing through the sample to the value of the solar radiation flux normally incident on the sample.
Solar reflectance
The reflection coefficient of solar energy is denoted as ρе (ER) - the ratio of the value of the flux of solar radiation normally reflected from the sample to the value of the flux of solar radiation normally incident on the sample.
Solar absorption coefficient
The solar energy absorption coefficient (equivalent term: energy absorption coefficient) is denoted as ae (EA) - the ratio of the value of the solar radiation flux absorbed by the sample to the value of the solar radiation flux normally incident on the sample.
Shading factor
The shading coefficient is denoted as SC or G - the shading coefficient is defined as the ratio of the flux of solar radiation passing through a given glass in the wavelength range from 300 to 2500 nm (2.5 μm) to the flux of solar energy passing through glass 3 mm thick. The shading coefficient shows the share of transmission not only of the direct flow of solar energy (near infrared radiation), but also radiation due to energy absorbed in the glass (in the far infrared radiation).
Heat transfer coefficient
Heat transfer coefficient - denoted as U, characterizes the amount of heat in watts (W) that passes through 1 m2 of the structure with a temperature difference on both sides of one degree Kelvin (K), unit W / (m2 K).
Heat transfer resistance
Heat transfer resistance is denoted as R - the reciprocal of the heat transfer coefficient.
From heterogeneity in the propagation medium. Examples of inhomogeneity can be a load in a transmission line or an interface between two homogeneous media with different values of electrophysical parameters.
- the ratio of the complex voltage amplitude of the reflected wave to the complex voltage amplitude of the incident wave in a given section of the transmission line .
Current reflection coefficient- the ratio of the complex amplitude of the reflected wave current to the complex amplitude of the incident wave current in a given section of the transmission line .
Radio wave reflection coefficient- the ratio of the specified component of the electric field strength in the reflected radio wave to the same component in the incident radio wave.
Voltage reflection coefficient
Voltage reflection coefficient(in the method of complex amplitudes) - a complex value equal to the ratio of the complex amplitudes of the reflected and incident waves:
K U = U neg / U pad = |K U |e jφ Where |K U |- reflection coefficient modulus, φ - the phase of the reflection coefficient, which determines the delay of the reflected wave relative to the incident.The voltage reflection coefficient in the transmission line is uniquely related to its wave impedance ρ and load impedance Z:
K U = (Zload - ρ) / (Zload + ρ).Power reflection coefficient- a value equal to the ratio of the power (power flux, power flux density) carried by the reflected wave to the power carried by the incident wave:
K P = P neg / P pad = |K U | 2Other quantities characterizing the reflection in the transmission line
- standing wave ratio - K St = (1 + |K U |) / (1 - |K U |)
- Traveling wave ratio - K bv \u003d (1 - |K U |) / (1 + |K U |)
Metrological aspects
measurements
- To measure the reflection coefficient, measuring lines are used, impedance meters, panoramic SWR meters (they measure only the module, without phase), as well as vector network analyzers (they can measure both module and phase).
- Reflection measures are various measuring loads - active, reactive with a variable phase, etc.
Standards
- State standard of the unit of wave resistance in coaxial waveguides GET 75-2011 (unavailable link)- located in SNIIM (Novosibirsk)
- Installation of the highest accuracy for reproducing the unit of the complex reflection coefficient of electromagnetic waves in rectangular waveguide paths in the frequency range of 2.59 ... 37.5 GHz UVT 33-V-91 - located in SNIIM (Novosibirsk)
- The highest accuracy setting for reproducing the unit of the complex reflection coefficient (voltage and phase standing wave ratio) of electromagnetic waves in rectangular waveguide paths in the frequency range of 2.14 ... 37.5 GHz UVT 33-A-89 - is located in
