MEETINGS AND CONFERENCES

CONFERENCE ON PHYSICAL AND MEASUREMENT ACOUSTICS

An expanded conference on questions of measurement and physical acoustics, convened by the Acoustics Commission of the Division of Physical and Mathematical Sciences of the Academy of Sciences of the USSR jointly with the Committee on Measures and Measuring Instruments under the Council of Ministers of the USSR, was held in Moscow. The development of acoustics in recent years on the basis of improved electronic equipment has led to the achievement of significant successes in increasing the accuracy of measurement methods, to the wider application of these methods in various fields of scientific research and industry, and to the appearance of a number of new research methods that make it possible to obtain very precise data with simple electroacoustic apparatus. Acoustic methods of measurement, Corresponding Member of the Academy of Sciences of the USSR N. N. Andreev noted in his introductory remarks, make it possible in a number of cases to obtain such information about substances and processes as is inaccessible to other physical methods of measurement. Therefore the task of standardizing the most widespread of these methods and investigating the accuracy they provide is becoming urgent. N. N. Andreev also dwelt on questions of physical acoustics, pointing out that the observed tendency for acoustics to merge with other branches of physics is very fruitful for its further development. The development of boundary regions makes it possible not only to discover facts that radically enrich our knowledge. Theoretical investigations in statistical acoustics continue the line of development of Soviet acoustics in this field.

The conference heard 10 reports on questions of measurement acoustics and 4 reports on questions of physical acoustics.

I. G. Rusakov, in his report “On Units and Instruments for Sound Measurements,” noted that the choice and definition of units of measurement, as well as the establishment of the procedure for comparing and verifying standard measures and measuring instruments, are of essential importance for ensuring the uniformity of sound measures and measurements in the Soviet Union. The speaker reported that the acoustic laboratory of the D. I. Mendeleev All-Union Scientific Research Institute of Metrology (VNIIM), under his direction and with the participation of the Metrological Bureau of VNIIM, had developed drafts of a new “Regulation on Sound Units” and a verification scheme for state verifications of sound measuring instruments. I. G. Rusakov said that the definitions of the fundamental acoustic quantities—sound pressure, sound energy density, mechanical resistance, sound power, difference of sound-power levels, elasticity and flexibility—given in the current GOST VKS 7242 do not fully enough reflect the specific features of these quantities and do not satisfy a number of metrological requirements. For example, the unit of sound pressure—the bar—is defined by ...

B. D. TARTAKOVSKII

as a static quantity, and exact conditions are not given for its reproduction in a dynamic regime (type of sound field, ratio of receiver dimensions to wavelength, etc.). In addition, in some definitions different systems of units are mixed (“watt per sq. centimeter”). The main task in revising the GOST was to bring its content closer to the practical problems of sound reproduction and the maintenance of correct sound units. To coordinate acoustic measurements with electrical, thermal, and other measurements, it is proposed to move entirely to the MKS system established in the USSR for mechanical and electrical measurements. The speaker gave a number of definitions of acoustic quantities in the new version, noting in this connection that instead of “mechanical resistance” the “acoustic resistance,” frequently measured in practice, is introduced. The quantities “elasticity” and “compliance,” as referring to mechanical oscillations and not specifically to acoustics, are excluded from the GOST.

In the second part of the report a verification scheme was described for state verifications of acoustic measuring instruments. Since the unit of sound pressure cannot be preserved in the form of a material standard, the basic scheme will be the following standard method for reproducing the unit of sound pressure. Comparing the method of absolute measurement of sound pressure by means of an acoustic disk with the method of self-calibration, the speaker came to the conclusion that the former has the advantage. This method makes it possible, with the aid of installations of the acoustic laboratory of VNIIM, to reproduce the unit of sound pressure in the frequency range 20—12,000 cps with an error not exceeding 1.0—1.5%.

The sound pressure measured in this way will serve for calibrating first-grade standard measuring microphones, whose error is not more than 1.5—4%, depending on frequency. Second-grade standard instruments are calibrated by comparison with first-grade instruments, and they are stored not only at VNIIM but also in large departmental laboratories. It is intended to carry out verifications of ordinary microphones, “artificial ear” instruments (used for verifying telephones), and “artificial voice” instruments.

In conclusion, the speaker noted that the introduction of a unified scheme for state verifications of acoustic instruments does not exclude the use of other, simpler methods of microphone calibration, in particular the reciprocity method. However, in all cases where measurement results may have legal or economic significance, strict observance of the verification procedure established by the proposed scheme is necessary.

In the report by N. A. Kaluzhinova, results were presented from the “Investigation of the method of resonant standing waves with an acoustic disk for reproducing the unit of sound pressure.”

The speaker noted a number of advantages of this method: reliability and stability of results; simplicity of measurements and good sensitivity; the simplest kind of sound field (this makes it possible to determine the magnitude of the sound pressure most accurately); independence of the measurements from the accuracy of setting the frequency (measurements are made at resonant frequencies, which can be determined from the dimensions of the tube) and from the frequency characteristic of the emitter; and a wide amplitude and frequency range (90—20,000 cps). For the measurements, tubes from 86 to 432 cm long and with an internal diameter from 5.3 to 1.6 cm were used. At one end of each tube an electromagnetic telephone is mounted, serving as the emitter; at the other end there is a calibrated microphone, the membrane of which forms part of the solid end wall. The disk of the acoustic meter is fastened in a special branch made in the middle of the tube. An optical device for reading the angle of rotation of the acoustic disk is arranged outside the tube. As acoustic disks, glass-

disks 5.5 · 10⁻³ cm thick; disk diameter 4–6 mm. The suspension threads of the disks are quartz.

Analyzing the possible errors of the method of measurement, taking into account the attenuation of sound in air, N. A. Kaluzhinova showed that, in precise measurements, one may neglect the error in determining the density of the air, as well as the error of the correction for the motion of the disk in air. The error in the deviation of the disk may be not only random, owing to inaccuracy of reading, but also systematic, owing to the influence of extraneous air currents on the sound-measuring disk and to imperfection of the form of the sound field. Systematic errors may also be affected by the elasticity of the suspension thread and by the speed of sound in the tube, which differs from the speed of sound in unbounded space. Check investigations established good reproducibility of the results and good agreement of the measured speed of sound (from the resonance frequencies) with the values expected from the literature. The width of the resonance curve was used to determine the attenuation of sound in air. Measurements carried out in a tube with one open end made it possible to find experimentally the correction for the open end, \(\Delta l = 0.69\), which agrees with the theoretical value \(\Delta l = 0.613\) with an accuracy determined by the error of measurement. Comparison of microphone calibration in an open and a closed tube showed good agreement of the results. The report gave an estimate of the total relative probable error of microphone sensitivity, determined according to the law of accumulation of the mean errors of the individual terms of the formula: the total error is about 1%. The speaker noted that such a magnitude of the error should be considered quite satisfactory, since the sensitivity of the MIK and MD-30 microphones changes over a year by more than ±10%.

A. N. Krishtalevich described a method for checking “artificial ear” instruments, developed for the purpose of obtaining uniform results in measuring the sensitivity of telephones carried out with the aid of these instruments. As the author’s investigation showed, these results depend strongly on the magnitude of the input acoustic impedance of the “artificial ear.” The measured sensitivity of a telephone is the higher, the greater the impedance.

In view of the normal conditions of sound emission by a telephone, one should strive for the impedance of these instruments to correspond accurately to the input acoustic impedance of the natural ear. However, the magnitude of this impedance varies greatly among different persons. Therefore, for the purpose of uniform testing of telephones, a purely reactive impedance has been adopted for “artificial ear” instruments, approximately equal to the reactive impedance of the average natural ear. This is achieved by applying, in the instrument, a standard air cavity of definite form having a volume of 6 cm³. The author related that, in a systematic investigation of “artificial ear” instruments with the aid of a standard telephone, he discovered a change in the volume of the cavity owing to unequal compression of the rubber ring against which the test object is pressed (in this case, the standard telephone). Because of this, the magnitude of the input impedance changed, in individual cases, by 40% over the entire frequency range of the measurements. A formula was obtained which makes it possible to convert the sensitivity of a telephone measured with a given “artificial ear” instrument to the average sensitivity of the telephone tested with an ear having a standard impedance. The speaker pointed out, however, that it is desirable to standardize the characteristic of the input acoustic impedance of the “artificial ear” and to regard as unsuitable those instruments whose input acoustic impedance differs from the standard by more than 10%. Therefore, serious attention should be paid to the standard nature of rubber rings and other details of the acoustic part of “artificial ear” instruments.

L. A. Varshavsky and G. V. Glekin’s report concerned the features of calibrating dynamic telephones on the natural and the “artificial ear.” Depending on what exactly is meant by the sound pressure developed by the telephone, several definitions can be given of the “sensitivity” of a telephone, i.e., of the ratio of the magnitude of the sound pressure it develops to the voltage applied at its clamps. Correspondingly, there are several calibration methods: on the artificial ear; on the natural ear by sound pressure at the entrance to the auditory canal; on the natural ear by sound pressure at the eardrum; and by the equivalence of the loudness of the telephone and the loudness in a free sound field of a certain intensity (field calibration). The latter method is of considerable interest in cases where the telephone is evaluated according to its ability to reproduce the effect on the ear of an external source, which is important, in particular, when studying auditory processes in the presence of acoustic interference created in the external sound field. The speakers developed a simple method for measuring telephones by the equivalence of their sound field and found that the results of telephone calibration obtained by this method differ substantially from the calibration of the same telephones (dynamic telephones TD-6) on the artificial ear. Over the entire range of audio frequencies the sensitivity is reduced, and a large unevenness of the frequency characteristic is observed, as well as large individual differences in sensitivity for the subjects tested.

These results were obtained both with the standard ear tips used for TA-4 telephones and with special attachments that reproduced, on the same telephone (without disassembling it), the shape of the shell ordinarily used on subscriber telephones.

The calibration of telephones on the natural ear by sound pressure at the entrance to the auditory canal, carried out by the authors for comparison, showed that, both in absolute values and in the form of the frequency characteristic, such calibration does not differ substantially from calibration on the artificial ear, except in the region of low frequencies, where the sensitivity is reduced (in comparison with the artificial ear) because of the not entirely tight fit of the telephone to the ear. The individual scatter in such calibration is considerably smaller than in field calibration, reaching values close to the latter only at low frequencies.

In the opinion of the speakers, the difference between the sensitivity of the telephone measured in field calibration and the sensitivity of the telephone obtained with calibrations on the artificial and the natural ear that nearly coincide with one another (by pressure at the entrance to the ear) indicates that the main cause of the difference is not the individual features of the input acoustic impedance of the natural ear.

The speakers indicated that among the factors capable of causing the observed difference between field calibration and sound-pressure calibration, the following can be referred to first of all: a) the frequency dependence of the ratio between the sound pressure in the auditory canal at the same loudness in the case of the action on the ear of a telephone and of a free sound field; b) the frequency dependence of the ratio between the sound pressure at the entrance to the ear and in the free sound field.

Since measurements of the sensitivity of telephones by the sound pressure at the entrance to the ear show that the individual features of the input acoustic impedance of the natural ear cannot explain such large magnitudes of individual differences as were observed in field calibration, these differences, in the speakers’ opinion, should be attributed to large individual deviations in the relations indicated above.

I. M. Litvak, in the report “A New Set of Acoustic Measuring Apparatus,” presented some data on modernized instruments: a measuring microphone, an acoustic probe, and an artificial ear.

The measuring microphone is intended for measuring sound pressure in an open sound field. The acoustic probe, which consists of a microphone with a sound-conducting tube, serves for measuring sound pressure in those cases when the point of the field at which the measurements are made must be precisely fixed, and also when the sound pressure must be measured in small chambers or tubes where a measuring microphone cannot be placed. Finally, the artificial ear is intended for measuring the sound pressure developed by a telephone in a chamber imitating the properties of the ear as an acoustic load. The basic common element of the above-mentioned instruments is the capsule of a condenser microphone. The capsule has a rectilinear frequency characteristic over a wide range of frequencies.

In the modernized apparatus the low-frequency circuit for connecting the condenser microphone has been retained as simpler and more stable. The use of a cathode-follower circuit made it possible to obtain a more uniform characteristic in the low-frequency region. All the instruments consist of two parts: a sound receiver and an amplifying-and-feeding device; the latter contains an additional amplifier and a rectifier, providing full power supply for each of the instruments from the alternating-current mains. The measuring microphone makes it possible to carry out measurements over a wide frequency range. The body of the microphone has a bottle-like shape, which makes it possible to move the capsule away from the wider part of the body, in which the tube of the first stage is located, to such a distance that the reflected wave practically does not affect the magnitude of the pressure at the capsule. Thus, the effective size of the microphone is equal to the size of the capsule. The microphone is placed on a stand, which makes it possible to set the microphone in the required position. The acoustic probe is a microphone provided with a metallic sound-conducting tube. To ensure uniformity of the frequency characteristic, the metallic sound-conducting tube passes into a rubber one and has damping sufficient for complete absorption of the sound wave. The capsule of the condenser microphone is connected with the sound-conducting tube through a slit in its side surface. Such a system makes it possible to ensure a uniform frequency characteristic in the range up to 6000 cps.

The artificial ear is a closed chamber, at the bottom of which the microphone membrane is located. The telephone under test is placed on the chamber and pressed against it by a load provided for in the design of the instrument. The sound pressure developed in the chamber by the telephone when an alternating voltage is applied to it is measured by the microphone.

In conclusion the speaker expressed some considerations on the further improvement of acoustic measuring instruments.

I. G. Rusakov reported on “the thermodynamic correction in the pump method.”

The speaker recalled that at very low frequencies the calculation of sound pressure from the deformation of the gas volume in the “pistonphone” pump requires a significant correction, since, owing to the cooling effect of the walls, a violation of the adiabatic law of gas deformation is possible. The expressions known in the literature for the correction for heat removal into the walls of the pump are derived under the assumption of uniformity of sound pressure inside the pump. However, the author noted, this assumption is artificial, and consequently the results of the calculation are doubtful.

I. G. Rusakov considered a rigorous solution of the problem and showed that in the pump there are an acoustic wave and a thermal diffusion, decaying over a distance of the order of one wavelength. The sound pressure in the acoustic-wave part is proportional to the temperature.

The speaker calculated the integration constants for the case when only the receiving part of the calibrated microphone has thermal conductivity, while the pump walls and piston do not possess thermal conductivity and their cooling influence may be neglected. He also found an expression for the correction in the case of a pump whose length is small in comparison with the wavelength. In the report there was also presented the result of calculating the correction for the case when both ends of the pump possess thermal conductivity, which, however, differs little from the one considered earlier. A substantial simplification of the calculations is achieved as a result of neglecting the diffusion terms in the expression for the sound pressure. This approximate method is applicable only in the case of small cavities (although of varied form), when the sound pressure inside the cavity may be considered equal to the pressure on the walls. In all other cases, when the constancy of the sound pressure at all points of the cavity is doubtful (for example, waves in a narrow tube), it is necessary to use the general solution given by the author.

“Some remarks on the calibration of microphones by the reciprocity method in a free field at short distances” were made by A. V. Rimsky-Korsakov and A. N. Krishtalevich. The authors indicated that the determination of the sensitivity of electroacoustic transducers by the reciprocity method is based on the application of the reciprocity theorem extended to the case of pressures and velocities averaged over the surfaces of the sound-source elements. Although it is assumed that the distances between the individual surface elements of the radiators are equal, i.e. that the dimensions of the radiators themselves are small in comparison with the distance between them, it is nevertheless unclear between which elements of the transducers this distance should be determined. One of the methods for determining the effective distance consists in first, before making sensitivity measurements, finding the dependence of the amplitude of the sound pressure \(p\) as a function of an arbitrarily chosen distance between the transducers \(r\), and determining the product \(pr\). From the deviation of this quantity from a constant value a correction to the adopted distance is found. At first glance it seemed that, because of interference phenomena and the nonplanar surface of the radiator, large errors could arise only for wavelengths of the order of or smaller than the linear dimensions of the radiators. However, the authors found that the greatest deviations from the ideal horizontal straight line \((pr=\mathrm{const})\) occur at low frequencies: ordinary diffusor loudspeakers behave at these frequencies as dipole radiators, for which the law of decrease with distance at small distances depends on the ratio between the wavelength and the distance. By increasing the distance one can make the error negligibly small, but this is disadvantageous, since interference from reflected waves increases. The error can be reduced by arranging the reverse side of the diffusor. But since a radiator with a closed rear surface is rather a radiator of order \(0+1\) than of zero order, in this case too the error will still be present. The authors adopted the approximately applicable law \(pr=\mathrm{const}\), and from the slope of the \(pr=f(r)\) curve determined the “error” \(\Delta\), which they then took into account in the calculation formula by replacing \(r\) by \(r+\Delta\).

This method enabled them to obtain, at low and medium frequencies, good agreement between the results of calibration by the reciprocity method and calibration in a tube with a sound-measuring disk. At frequencies of \(\sim 100\) cycles/s it was possible to eliminate a systematic error reaching up to 4 dB. The report also noted that, when calibration is carried out by the reciprocity method, considerable errors are obtained because of the sharp decrease in mechanical resistance in the region of the mechano-acoustic resonance of auxiliary diffusor transducers and, at high frequencies, because of diffraction.

In the report by M. V. Kazantseva, questions of the “calibration of electroacoustic transducers by the reciprocity method” were considered. The essence of the method, as is known, consists in the fact that, by using an auxiliary electroacoustic transducer (in the case of calibration on stationary sinusoidal oscillations) or the calibrated transducer itself (in the case of self-calibration on pulses), it is possible to avoid the need for direct measurement of acoustic quantities and to reduce all measurements to purely electrical ones.

M. V. Kazantseva gave expressions for the reciprocity parameter in the general form and, using the equations of electroacoustic four-terminal networks and the reciprocity relations for them, showed how in individual special cases one must choose the experimental conditions so that the parameters of the transducer under study are excluded from the calibration results. As examples, values of the reciprocity parameter were given for particular cases: for a chamber small in comparison with the wavelength, for standing waves in a tube, and for calibration in a free field in a plane and spherical wave. The speaker also determined those corrections which have to be introduced if the “pure conditions” of calibration by the reciprocity method are not observed. The author described a method she had developed for calibrating microphones on standing waves in a tube in the audible frequency range. In another method of self-calibration of a transducer by the field in a plane traveling wave, the transducer was attached to the lower end of a vertical tube with rigid walls; the tube was filled with water, and its upper end was open. The transducer was supplied with current from a pulse generator and sent a consecutive series of rectangular packets of sinusoidal oscillations, whose duration was sufficiently small so that standing waves did not arise along the length of the tube, while the intervals between neighboring transmissions were sufficiently large for the last signal to have time to decay before the sending of the next packet and not be superposed on it. In this case the self-calibration of the transducer was reduced to the measurement of the e.m.f. developed by the transducer when receiving a signal after its first reflection from the upper boundary of the water and to the measurement of the current feeding the transducer during radiation. In conclusion, the speaker gave some numerical values of the results of calibration carried out by this method.

The report by B. D. Tartakovsky and M. M. Efrussi, “On the measurement of sound-absorbing materials and of a reverberation chamber,” contained the results of experimental studies of a method of such measurements carried out by the authors in the reverberation chamber of the Acoustics Laboratory of the P. N. Lebedev Physical Institute.

Giving a review of the literature data characterizing modern reverberation chambers, the authors noted the good acoustic quality of the chamber they described: a uniform diffuse sound field in the center of the chamber, a “smooth” decrease of sound intensity with time (according to an exponential law), and a uniform frequency characteristic used in measurements of continuous noise filtered by an octave filter. At the same time, they emphasized the necessity of a more refined analysis of the quality of reverberation chambers than is customary in the literature. For example, because of the different frequency characteristics of loudspeakers, displacement of the maxima of sound pressures in individual noise octaves relative to their midpoints is possible; this causes an error in determining the “mean” frequencies of the individual octaves.

In determining the dependence of the obtained results of the sound-absorption coefficients on the area of the material, the authors found that the measurement results become stable beginning with an area of 15 m² (about 7% of all surfaces of the chamber).

The sound-absorbing capacity of material placed in parts on different surfaces of a chamber was investigated, as well as of the same material placed at the vertex of the trihedral angle formed by these surfaces. Although, according to wave theory, one might have expected an increase in sound absorption in the second case, the experiment showed a decrease in sound absorption at all frequencies by 20–30%. To determine whether this was the result of the manifestation of an “edge effect,” caused by a reduction in the length of the boundaries of the material, a control experiment was carried out, during which the boundary of the material was changed several times while the area remained constant. It turned out that the sound-absorption coefficient changed by no more than 5%.

According to another assumption, the “angular effect” was explained by a decrease in the “effective area” of the material due to a change in the conditions of incidence of sound rays, or else by a decrease in absorption associated with the angular characteristic of sound absorption. However, testing established the untenability of this hypothesis as well: material moved closer to the edges of different angles did not give a decrease in sound absorption. The authors explain the “angular effect” by the fact that a portion of the material placed in a corner is used with little efficiency, since sound rays that have just been reflected from the sound-absorbing material fall on the material within a considerable part of the solid angle. The calculations carried out qualitatively confirm this assumption.

V. P. Kislov reported “On a simple ultrasonic interferometer” for measuring the velocity of sound in a liquid, differing from those already known in that, for recording the interference maxima, it uses a fountain arising on the surface of a liquid under the influence of ultrasound. For this purpose the liquid to be measured is placed between a plane piezoelectric radiator and a sound-hard plane spherical lens, over which an indicator liquid is poured. When an integral number of half-waves is accommodated in the layer of the liquid being tested, a fountain appears on the surface of the indicator liquid, the height of which can be regulated by changing the voltage on the radiator. Owing to the nonlinear dependence between the height of the fountain and the voltage on the radiator, which is approximately quadratic in character, the moments of appearance of the fountains can be noted rather accurately. The liquid layer, with the aid of micrometer screws, can be varied within limits that ensure observation of up to 100 maxima in low-viscosity liquids and about 20 maxima in liquids with considerable viscosity. Since the error in measuring adjacent maxima is of the order of 3%, the average error of the result, according to the speaker’s estimate, is no more than 0.05%. The accuracy of the result depends substantially on the degree of stability of the generator feeding the piezoelectric transducer. With good quartz stabilization, it was possible to obtain a total error of no more than 0.1%. The author made a number of measurements with the aid of the interferometer he had developed and in several cases obtained good agreement with the experimental data of other authors. V. P. Kislov reported that he had clearly registered the maximum velocity of sound in distilled water lying in the temperature interval 70–75°, equal to 1554 m/sec. Comparing the dependence he obtained of the velocity of ultrasound in glycerin on temperature with data obtained earlier by P. A. Bazhulin, the speaker noted the identical course of the curves, but a difference in their slopes, explained, in the author’s opinion, by differences in the viscosities and densities of the glycerins investigated.

V. P. Kislov believes that the simplicity and reliability of the data obtained on the magnitude of the velocity make possible the wide use of the method he developed for semindustrial purposes.

G. N. Kubanskii spoke “On the influence of acoustic oscillations of large amplitude on convective heat exchange.” The author studied the character

…flows arising near the wall of a heated solid body in a standing acoustic wave of large amplitude, and also the influence of these flows on convective heat exchange both in free and in forced motion.

In the experiments, a gas-jet acoustic vibrator placed in a parabolic reflector was used. To retard the air streams issuing from the vibrator, a partition of thin paper was installed in front of it. At a distance of about 40 cm from the vibrator, a wall was placed to form a standing wave; between it and the vibrator there was a calorimetric tube supplied with an electric heater and a thermocouple for measuring the temperature of the wall. The pattern of acoustic flows near the tube was made visible by using the shadow method. Simultaneously with the optical observations, all quantities necessary for determining the coefficient of heat transfer from the wall of the tube to the surrounding medium or to the flow were measured. In addition, the behavior of resonant systems in the field of acoustic waves was investigated in order to determine the character of the flows arising at the resonators and their influence on convective heat exchange. Numerous cylindrical or conical recesses drilled in the walls of calorimetric tubes served as resonators. The intensity of the vibrations emitted by the vibrator in the central part of the beam reached tens of watts/cm².

On the basis of his experiments the author drew the following conclusions: 1. In a standing acoustic wave, near the surface of a solid body located in an unbounded space, peculiar flows arise. The presence of higher harmonics produces additional flows due to these harmonics. 2. In a standing acoustic wave, flows may also arise near the walls of a solid body when the body is washed by a stream. The direction of the acoustic flows at the walls of the body depends on the arrangement of nodes and antinodes relative to the place of separation of the boundary layer. By producing flows of the desired direction, one can control the boundary layer. 3. Acoustic flows markedly increase heat transfer from the wall of a heated body to the surrounding medium both under conditions of free and of forced motion. 4. When resonant systems are excited by external oscillations of large amplitude, powerful flows arise at the mouths of the resonators. This also occurs when the resonant system is washed by a stream. 5. The presence of a resonant system on a heated body increases heat transfer in forced motion, manifesting itself like roughness. 6. Excitation of resonators by external oscillations of large amplitude significantly increases heat transfer both in free motion and under forced oscillations and creates a fundamental possibility of controlling the boundary layer by means of powerful acoustic flows directed normally to the boundary layer.

In the report by I. G. Shaposhnikov and Z. A. Goldberg, “On sound absorption in a binary mixture,” it was stated that, when sound propagates in a gaseous or liquid mixture, the temperature, pressure, and concentration of the components at any instant in different points are different; therefore the propagation of sound is accompanied by irreversible diffusion processes. Kohler, using the methods of kinetic theory, determined the influence exerted by these diffusion phenomena on sound absorption in a binary mixture of ideal gases, noting at the same time that a phenomenological treatment of the question under consideration is impossible. The speakers showed, however, the possibility and relevance of such a way of considering the question, which makes it possible to obtain a result suitable for any mixture, gaseous or liquid. Using the equations of hydrodynamics for a binary mixture of nonreacting components and the general expressions for the heat flux and the diffusion mass flux of each of the components of the mixture, they obtained the acoustic equations. Then restricting themselves to the approximation of linear acoustics

B. D. TARTAKOVSKY

and, using thermodynamic relations, they found the basic equations connecting the “acoustic parts” of the corresponding quantities with the quantities characterizing the equilibrium state of the medium without sound.

Having considered, as particular cases of the general solution found, a flat monochromatic sound wave and having used the method of successive approximations, the speakers found that in the first approximation there is no dispersion of the speed of sound, while the absorption coefficient is the sum of the absorption coefficient due only to viscosity and thermal conductivity and the absorption coefficient connected with the influence of diffusion phenomena. For binary mixtures of ideal gases the speakers found an expression coinciding with that obtained by Kogler, and also specialized the general result for the case when the concentration is so small that one may use an approximate expression for the thermodynamic potential of a dilute solution.

The report noted that, in order to compare the results obtained with experiment, in the general case one must have sufficient information about the thermodynamic potential of the mixture. However, for the case of small concentration and for the case of a mixture of ideal gases at any concentration this difficulty disappears.

In conclusion, the authors pointed out that their results can possibly be used for the experimental determination of the coefficient of thermodiffusion.

M. A. Isakovich delivered the report “On the Scattering of Waves by a Statistically Rough Surface.”

Methods developed in the works of Rayleigh, L. I. Mandelstam, A. A. Andronov, M. A. Leontovich, and others, which considered scattering by roughnesses small in comparison with the wavelength, are not applicable in the case when the roughnesses are large in comparison with the wavelength. This latter problem has to be solved by approximate methods. Recently L. M. Brekhovskikh solved such a problem for a surface with periodic roughness. In M. A. Isakovich’s work, roughnesses are considered that are also large in comparison with the wavelength and that have a statistical character.

The author solved the problem using Kirchhoff’s principle, i.e. assuming that the field on the rough surface is entirely determined by the laws of geometrical optics. The acoustic case was examined in detail, and the applicability of the formulas obtained, with minor changes, to the calculation of the scattering of electromagnetic waves was shown. The speaker obtained general formulas for the mean quantities characterizing the field: the mean field intensity, the mean field fluctuation, and the connection between these quantities and the correlation properties of the rough surface was characterized.

M. A. Isakovich calculated the field scattering for a normal distribution of displacements of points of the surface from the mean plane, presenting the results of the calculation for one type of correlation coefficient in the form of scattering directivity characteristics for various values of the initial parameters.

L. A. Chernov considered in his report “The Propagation of Sound in a Statistically Inhomogeneous Medium.”

Assuming that “macroscopically” the medium is considered homogeneous and isotropic, while irregular, “microscopic” changes in the properties of the medium from point to point and with the passage of time are sufficiently small and slow, the speaker solved the problem of sound propagation in such a medium in the ray approximation. Specifying the “microscopic” characteristic of the medium by a correlation function connecting small deviations of the speed of sound from the mean value at two points of the medium, L. A. Chernov calculated the mean square deviation of the ray from its initial direction as it travels a given path. In doing so he chose the length of the path to be large in comparison with the correlation radius, but such that the deviation of the ray along this path would still be small.

As a result of taking into account the statistical independence of the deviations of the velocities at the ends of the ray, a constant characteristic of the medium is obtained, determined through the correlation function and playing the role of a diffusion coefficient.

Using this quantity, one can determine the probability of the direction that a ray will have after having traversed a certain path. The distribution function of the ray directions satisfies the Einstein–Fokker–Kolmogorov equation. L. A. Chernov obtained a visual representation of the propagation of a ray by calculating the mean value of the cosine of the angle of deviation of the ray from its initial value and expressing this value in terms of the constant of the medium that had been found. It turned out that, for small angles of deviation, the angular distribution corresponds to the Gaussian distribution law.

Having determined the mean square of the distance along a straight line from the point of emergence of the ray to the point it reaches after traversing a complicated path in the medium, the speaker found that, in the particular case of small deviations, his result coincides with the formula obtained by Smoluchowski for the mean square displacement of a heavy molecule that has traversed a complicated path in a light gas. The speaker further showed that the mean squares of the displacements of a ray from its initial direction grow in proportion to the cube of the path traversed.

The conference adopted a resolution on questions of standardizing acoustic measurements, approving in general the draft proposed by the Committee of Metrology, but introducing certain amendments concerning terminology and the definition of certain acoustic quantities. In another resolution of the conference, the necessity was indicated of more rapid development of industrial production of various acoustic measuring instruments, and corresponding practical measures were outlined.

The fruitfulness of the present conference was also noted, since it made possible an exchange of views on questions of acoustic measurements, physical acoustics, and the propagation of sound waves.

It was decided henceforth to convene thematic conferences on questions of acoustics 2–3 times a year.

B. D. Tartakovsky