MEETINGS AND CONFERENCES

SCIENTIFIC CONFERENCE ON PHYSICAL ACOUSTICS AND ULTRASOUND

1. SECTION ON PHYSICAL ACOUSTICS

On March 3–7, 1955, in Moscow, on the premises of the Physics Faculty of Moscow State University, a scientific conference on physical acoustics and ultrasound was held, convened by the Commission on Acoustics, the Acoustics Institute of the Academy of Sciences of the USSR, Moscow Order of Lenin State University named after M. V. Lomonosov, and the Leningrad Electrotechnical Institute named after V. I. Ulyanov (Lenin). Thirty-three reports were heard, including two reports at the plenary session (N. N. Andreev and V. L. Ginzburg), 15 reports in the section on physical acoustics, and 16 reports in the section on ultrasound.

In the section on physical acoustics, reports were heard on the propagation and radiation of sound waves, on reflection, focusing, and the passage of sound waves through various systems, and also on certain problems of acoustic measurements and effects arising during the propagation of sound waves in special media.

In the report “On quantities of second order in acoustics,” N. N. Andreev set forth questions concerning the density and flux of sound energy, the momentum and pressure of sound radiation. Initially these questions had been discussed in the author’s published work; subsequently they were discussed in a number of works by other authors. Corrections of the second approximation to the equations of hydrodynamics were calculated. The author believes that the discrepancy between the calculation made by him and the usual formulas for the density and flux of energy is insignificant, although in principle the solution in the first approximation is insufficient for calculating acoustic energy.

The speaker noted that the idea of dividing the energy of vibration into two parts—“essential” and “inessential,” indicated by Schöch, should be supplemented by the formulation of initial and boundary conditions that define the conditions of an acoustic experiment. This point was illustrated in the report by the case of radiation from a transmitter into a medium with reflecting boundaries. It was further noted that the radiation pressure cannot be considered to be determined by the total energy. In reality it depends on the mean density of potential energy, which, generally speaking, is not equal to the mean density of kinetic energy.

The speaker described the phenomenon of propagation of a packet of traveling waves bounded in front by a weak discontinuity. The nonlinearity in the system, necessary for the equalization process, is due in this case to the nonlinearity of the equations themselves and to the nonlinearity of the equation of state.

The author indicated that the question of the possibility of the existence of acoustic wind, not due to the viscosity of the medium, remains open. In conclusion it was noted that a theory including the second approximation cannot encompass many interesting phenomena without taking viscosity and thermal conductivity into account.

V. L. Ginzburg’s report, “On the general connection between the absorption and dispersion of sound waves,” consisted of two parts. In the first part the author noted that, when considering the question of the absorption and dispersion of electromagnetic and sound waves in various media on the basis of definite model representations or phenomenological equations, it always turns out that dispersion and absorption are connected with one another. This circumstance is not accidental, but reflects the fact of the existence of a quite general connection between dispersion and absorption, independent of any particular model representations. The question was clarified of the connection between the dispersion and absorption of electromagnetic waves, which, although established long ago, is not sufficiently well known. In the second part of the report the question of the universal connection between the dispersion and absorption of sound waves was considered.

The report discussed the conditions for obtaining and applying integral relations between the real speeds of sound at frequencies \(\omega_1\), \(\omega_2\) and the amplitude coefficients of sound absorption at these frequencies. The integrals are taken within the limits from zero to \(\omega_0\), where \(\omega_0\) is the maximum frequency at which the acoustic approximation is still applicable. The expressions given make it possible to estimate absorption from known dispersion and to determine dispersion from known absorption.

In conclusion, the speaker indicated that the question of the accuracy and significance of such estimates is determined by the completeness and accuracy of the available data on the dispersion and absorption of sound in the medium under consideration.

G. S. Gorelik, in the report “On the measurement of very small amplitudes of acoustic oscillations,” gave a brief review of work relating to the measurement of small acoustic oscillations by means of the optical modulation-interference method proposed by the speaker and subsequently improved by I. L. Bernstein. This method is analogous in many respects to the microbarometric method previously considered by I. L. Bernstein for certain radiophysical problems.

The method under consideration is based on the detection and measurement of very small periodic changes in the optical path difference of two light rays, using periodic changes of current in a photoelectric receiver, which can be singled out against the background of noise by a narrow-band filter. The sensitivity limit is determined by fluctuations in the apparatus and can be lowered arbitrarily at the cost of increasing the time constant of the apparatus. Calculations and experiments have shown that in this way periodic path differences of two light rays of the order of \(10^{-2}\) and even \(10^{-3}\) angstroms can be detected rather simply.

Measurements are made with the aid of a two-beam optical interferometer, in one of whose arms the optical path length is periodically changed. Such a change may occur, for example, as a result of mechanical oscillations of one of the interferometer mirrors, or as a result of a periodic change in the refractive index of an optically transparent medium due to the propagation in it of an acoustic wave.

The recording device consists of a slit parallel to the interference fringes, a photomultiplier, and a narrow-band electric filter tuned to the frequency of the path-difference variation. The current at the filter output is measured by a pointer instrument.

This device makes it possible to measure very small amplitudes of mirror displacement, or very small periodic changes in the refractive index and, consequently, in the density of the medium. The author indicated that the method developed also makes it possible to measure comparatively large acoustic oscillations with great absolute accuracy.

L. M. Brekhovskikh reported on “Some questions concerning the propagation of waves in layers.” Determining the characteristics of normal waves propagating in layers—phase and group velocities, attenuation, and others—presents great mathematical difficulties, since it is connected with the study of integral expressions for fields in the complex plane. The author proposed a simpler and more elementary method for determining the characteristics of normal waves, one that also permits certain qualitative conclusions to be drawn about the degree of excitation of various normal waves.

Considering the field at comparatively large distances from the radiator, where the waves may be represented as plane waves, the speaker expressed the boundary conditions in terms of the reflection coefficients at the boundaries. As a result he found a relation between the reflection coefficients, the thickness of the layer, and the angles of inclination of the plane waves, making it possible to determine the desired characteristics of the normal waves. Waves were considered in liquid layers and in layers in which the medium has a density contrast. Analysis of the limiting form of the relation found in the case of an infinitely thick layer and the presence of small attenuation makes it possible to find the conditions for the formation of surface waves (analogous to a Rayleigh wave) propagating along the upper and lower boundaries of the layer.

In the particular case of a liquid layer bounded by an elastic medium and a free surface, one obtains the dispersion equation known from the literature for a liquid layer lying on an elastic half-space. Cases can be studied in an analogous manner, for example, of a three-layer liquid half-space. For this it is only necessary to take into account the reflection coefficient from the layer separating the two different media.

Yu. P. Lysanov presented a calculation of the “scattering of sound from an inhomogeneous surface with periodically varying normal impedance.”

The solution of the problem for a plane periodically inhomogeneous surface, characterized by a normal impedance or acoustic admittance independent of the angle of incidence of the sound wave, is presented in the form of a series, for the \(n\)-th term of which a recurrence formula is obtained. Numerical calculation shows that the scattering is very significant at small angles of incidence and decreases as the angle of incidence increases. The method is applicable for any ratios between the wavelength of sound and the spatial period of the inhomogeneity. Comparison of the results obtained with an approximate solution derived under the assumption that the properties of the inhomogeneous surface change little over distances of the order of a wavelength makes it possible to give a quantitative estimate of the limits of applicability of the approximate solution.

Calculation of the absorption coefficient of a periodically inhomogeneous surface showed that, at small angles of incidence, its values are somewhat smaller than the values of the absorption coefficient for a homogeneous surface with acoustic admittance equal to the mean value of the acoustic admittance of the inhomogeneous surface. The problem considered is of interest for certain questions of architectural acoustics, in particular for the reflection of sound from coffered ceilings and from surfaces with alternating bands of reflecting and sound-absorbing materials, and others.

L. A. Chernov spoke “On the correlation of amplitude and phase fluctuations in the propagation of waves in a statistically inhomogeneous medium.”

Theoretical study of the most general statistical characteristics of a field in a medium with random inhomogeneities of correlation functions for amplitude and so forth shows that fluctuations of amplitude and phase at the receiving point are, generally speaking, correlated. However, the correlation weakens with distance. The correlation coefficient between fluctuations of amplitude and phase falls from a value of 0.6 at small distances to zero at large distances. The autocorrelation of amplitudes (or phases) in space depends substantially on the arrangement of the receivers. When the receivers are arranged in a plane perpendicular to the direction of propagation, the autocorrelation extends over a distance of the order of the correlation radius of the refractive index in the medium. The speaker noted that this opens up new possibilities for studying the properties of the medium. By experimentally determining the radius of transverse autocorrelation of the wave field, one can thereby find the characteristic scale of inhomogeneities in the medium. Longitudinal autocorrelation between fluctuations of amplitude (or phase) extends over a considerably greater distance than transverse autocorrelation: over a distance within which the ray approximation is applicable. In practice, the weakening of statistical dependence is determined by the transverse displacement of the receivers. The correlation of amplitude over time was studied for the case in which the variation of the inhomogeneities is caused by their motion relative to the observer or, equivalently, by the motion of the observer relative to the inhomogeneities. This made it possible to explain the form of the temporal correlation function obtained as a result of Shuleikin’s observations on a moving ship.

The report by S. N. Rzhevkin concerned the theory and certain results of an experimental investigation of “sound emitters with a traveling wave.”

When, on the surface of a sphere, a wave of the type
$u = u_m \sin^n \vartheta e^{i(\omega t - m\psi)}$
runs in the azimuthal direction, where $u_m$ is the amplitude of the velocity at the equator, $\vartheta$ is the polar angle, $\psi$ is the azimuth, and $m, n$ are integers, then in the field surrounding the sphere there arise waves also traveling in the azimuthal direction. The author found expressions for the potential of the velocity, for the sound field, expressions for the Umov vector in the radial and azimuthal directions, and calculated the amplitudes of the sound pressure, the values of the added mass, the radiation power, and certain other quantities.

For large $n$, the radiation is concentrated in a circular equatorial belt in directions close to
$\vartheta = \dfrac{\pi}{2}$. The sound intensity does not depend on $\psi$ and, for $r = \text{const}$, is everywhere the same in the azimuthal direction, which is a characteristic feature of an emitter with a traveling wave. For an emitter with a traveling wave there exist both a radial and an azimuthal energy flux. The azimuthal flux decreases sharply with distance; moreover, it closes into a ring around the sphere and has a reactive character.

An emitter of sectorial type with standing waves on the surface, for which the radial velocity on the surface is given by the expression
$u = u_m \sin^n \vartheta \cos m\psi e^{i\omega t}$,
may be regarded as a superposition of two emitters with a traveling wave, having equal amplitudes but opposite directions of the traveling waves.

An analogy has been established between the emitter under consideration and a rotating emitter—a rapidly rotating rigid sphere with sinusoidal grooves. The efficiency of radiation increases sharply as the ratio of the circumferential velocity of the wave $v$ to the sound speed $c$ grows. If the circumferential

speed much greater than the speed of sound, the radiation tends to a maximum value independent of the ratio \(\frac{v}{c}\).

The theory developed, being limited to a linear approximation, is not applicable to rotating radiators because at large circumferential velocities it neglects viscous effects and the occurrence of shock waves.

For the experimental investigation a steel cylindrical cup was used, on the circumference of which, on the outside, two electromagnetic exciters were placed at a distance of a quarter (or three quarters) of a wavelength; between them a phase shift of

\[ \frac{\lambda}{4}. \]

was established. By creating with each of the exciters equal excitation amplitudes of standing waves (which corresponded to the excitation of resonant oscillations of the sectorial type), it was possible, when the exciters operated jointly, to produce a traveling wave.

The distribution of sound pressure around the radiator when excited by traveling waves was uniform, whereas excitation by standing waves showed a series of minima and maxima as a function of the azimuth.

A report by G. D. Malyuzhinets, “On the edge effect of large radiators,” was presented to the conference. The author noted that the energy radiated by a piston oscillating in an infinite rigid screen differs from the energy radiated by an equal-area part of an infinite piston by active and reactive additions. If the dimensions of the piston are increased, then the share of the active addition assigned to a unit of circumferential length of the piston tends to zero, while the reactive one tends to a certain value. The latter is equivalent to the effect of an added mass per unit of edge, equal to

\[ m_1=\frac{\rho \lambda^2}{4\pi^3}, \]

where \(\lambda\) is the wavelength, \(\rho\) the density. The fact that the share of the active addition of energy per unit length of the edge tends to zero is of great interest for estimating the role of the edge effect.

Next, the magnitude of the energy falling on the edge of a two-sided oscillating wedge with different velocities on the faces was considered. Using the exact solution, found by him, for the sound field in a wedge-shaped region, the author calculated the edge correction for a wedge with infinite faces and found that, independently of the ratio of the velocities, on the faces it is purely reactive. The presence of the edge does not affect the mean radiated power, independently of the opening angle of the wedge.

To make the effect under consideration more graphic, the speaker gives as an example the case of equal normal velocities on both faces of the wedge, treating the wedge in this case as the result of bending an infinite plane radiating plate. The theory shows that in this case the active power remains constant, independently of the bending angle. There appears only an additional reactive power \(P_r\), whose magnitude and sign depend on the angle \(\alpha\) of the wedge. At \(\alpha=180^\circ\) (a plane plate) \(P_r=0\); at \(\alpha=90^\circ\), \(P_r=-0.5\) (the radiation resistance inside the wedge has an elastic character); at \(\alpha=0^\circ\), \(P_r=-\infty\); at \(\alpha=360^\circ\), \(P_r=+0.16\) (the radiation resistance outward has an inertial character).

G. I. Makarov and N. N. Shaposhnikov reported on the results of a calculation of “the nonstationary radiation of a sphere and a spherical segment.”

The authors investigated the sound field of a sphere set into oscillation, described by a rapidly varying or discontinuous function. Integration of the wave equation for the velocity potential with zero initial-

...with given initial and boundary data prescribed on the surface of the sphere was carried out by the method of incomplete separation of variables. The wave equation was subjected to a Laplace transform, and the eigenfunctions of the problem were found; after this the boundary conditions were expanded in series in the eigenfunctions thus found, and the general solution of the problem was represented in the form of analogous series, whose coefficients were determined. As a result, the solution of the problem was represented by an infinite sum of contour integrals.

The solution was investigated by the method of asymptotic estimates proposed by G. I. Petrashen. The field in the neighborhood of the wave fronts is described by a rapidly varying, or discontinuous, function. Since each term of the series representing the solution is a continuous function, in the formation of the fronts the last terms of the series play a principal role. This makes it possible to compute the contour integrals by asymptotic methods, for example by the method of stationary phase, to sum the infinite series, to construct the wave fronts, and to find simple formulas describing the field in their neighborhood. In the region of the field far from the fronts, where a stationary diffraction pattern is established, the series describing the solution converge exponentially, and it suffices to compute several of the first terms of the series with sufficient accuracy. In the case of excitation of the segment by harmonic oscillation, characteristic resonance terms are singled out in this region; moreover, the resonance frequencies and damping coefficients are connected with the dimensions of the spherical segment.

The report by L. M. Lyamshev, “Reflection of Sound by Thin Plates in Water,” was devoted to the description of a new effect of strong non-specular reflection by a thin plate when plane sound waves from a liquid are incident on it. This effect is due to the propagation in the plate, along its surface, of longitudinal waves excited by the incident sound wave through transverse compressions of the plate. The new effect is similar to the effect of specular reflection, noted earlier by Fynn, which is due to flexural vibrations of the plate. A theory is given for the reflection and transmission of sound by a thin plate of finite dimensions, taking into account longitudinal and flexural waves in the plate. The theory is in good agreement with experimental data. It has been established that, when sound is scattered by a thin bounded plate, a complex resonance trace is observed: a resonance in frequency, when the natural frequency of one of the modes of vibration of the plate coincides with the frequency of the incident sound, and a spatial resonance, when the distribution of pressure along the plate in the incident wave coincides with one of the natural modes of vibration of the plate. To clarify the conditions for the stationarity of the plate vibrations, along with the time of establishment of the vibrations it is necessary to use the concept of the length of spatial establishment. The fine structure of non-specular reflection was investigated experimentally. It is shown theoretically that the fine structure of non-specular reflection is due to the phenomenon of spatial-frequency resonance in the plate.

The report by A. N. Barkhatov was devoted to the description of a laboratory installation for studying the propagation of sound in a layered-inhomogeneous medium. In a laboratory installation it is easier to separate the influence of some factors on sound propagation from the influence of others and to identify the most essential of them. Therefore such a method, without replacing the study of phenomena under natural conditions, can help in understanding them. With the aid of thermal action and the use of solutions of common salt of various concentrations, two cases of wave propagation were created and investigated: 1) in a medium with a constant negative vertical gradient of the speed of sound, 2) in a surface isothermal layer with, below it, a medium with a constant negative vertical gradient of the speed of sound.

The experimental setup consisted of a tank with a surface heater and a bottom cooler, movable thermometers, a coordinate-measuring device, a sound emitter with a generator, a receiver with an amplifier, and a sound-recording device. The surface of the water poured into the tank was uniformly heated by a flat electric furnace placed at some distance from the surface of the water. Along with this, bottom cooling of the water was carried out by means of a battery of narrow tubes laid along the bottom of the tank, through which water at a temperature of 2–4° C flowed. A steady constant gradient throughout the entire depth of the tank was formed after 30–40 hours of the combined action of the heater and cooler under a definite operating regime found experimentally.

To obtain above the medium a constant negative gradient of the sound velocity of the surface isothermal layer, sharp cooling of the water surface was employed by rapidly lowering the air temperature in the laboratory and creating wind with the aid of a fan.

The region of the sound shadow formed in the sound field under a constant vertical temperature gradient was studied in detail. The measurement results are basically in agreement with Pekeris’ theory. The sound field of an emitter located inside the surface isothermal layer, with an underlying medium having a constant negative sound-velocity gradient, was studied. It was found that the magnitude of sound attenuation in the surface layer at a certain distance from the emitter is characterized by the parameter \(s\), introduced by L. M. Brekhovskikh; moreover, for the same value of \(s\), the sound field closer to the emitter depends on the thickness of the surface field and on the magnitude of the velocity gradient. The attenuation, other conditions being equal, is smaller the deeper within the isothermal layer the measurement level passes. Study of the vertical pattern of the sound distribution showed that the greater the thickness of the isothermal layer, the more indented the vertical pattern of the sound field becomes, and the more so the closer the plane of observation is to the emitter; at considerable distances from the emitter, the interference maxima and minima are weakly expressed, with a general increase of sound intensity with depth.

The report by Yu. M. Sukharevsky and A. G. Sokolinsky, “Study of a Quartz Vibrator into a Solid Medium,” was devoted mainly to clarifying the role of the contact layer of liquid between the vibrator and the solid medium in the frequency characteristics of sound radiation.

It is known from practice that the influence of this layer on radiation is very great and, in particular, an increase in the layer thickness narrows the radiation frequency band. The speakers investigated, theoretically and experimentally, the operation of a quartz vibrator loaded onto an infinite solid medium through a contact layer that is thin compared with the wavelength. They found that the frequency of maximum radiation coincides with the resonance frequency only under ideally acoustic contact with the solid medium and under very weak contact. In the intermediate (real) case, the resonance frequency of the system in the presence of a transition layer shifts upward, and consequently the frequency of maximum sensitivity does not coincide with the resonance frequency of the quartz. The maximum shift of the frequency may reach several tens of percent. With liquid contact layers, even with very small thickness, the relative frequency band does not exceed 0.2–0.3; with solid contact layers the frequency band broadens, but for transverse waves and solid layers, obtaining a broad frequency band presents difficulty. The calculated results agree well with the experimental data.

L. D. Rozenberg reported on the methodology and results of calculating “sound-focusing cylindrical systems.” Pointing out the convenience of applying

...of such systems for irradiating not very large objects continuously moving along a conveyor, for example in ultrasonic cleaning, the speaker noted that, up to now, no calculation of their focusing action has been carried out.

The speaker obtained integral formulas for calculating the sound pressure and vibrational velocity of infinitely long systems with an arbitrary distribution of potential along the arc of a cylinder, under the assumption that the wavelength is small in comparison with the dimensions of the radiator. Analysis of these formulas made it possible to establish that the optimal functions of the potential distribution (for which the pressure and velocity along the axis of the system will be greatest for a given energy flux of the converging wave front) are the same as for axisymmetric systems. For example, for a maximum of sound pressure there must be a uniform distribution of the potential.

The speaker calculated focusing factors, i.e. the ratios of the actual amplification provided by a given system to the greatest amplification that can be obtained, using the available energy flux (per unit axial length of the front), for various special cases of the distribution of the potential over the surface of the cylinder, including cylindrical parabolic mirrors.

B. D. Tartakovskii reported on “Ultrasonic filters.” Using the previously developed general method for calculating the passage of plane sound waves through an arbitrary collection of homogeneous plane layers, the author found the conditions for selecting such collections of layers as make it possible to pass or stop ultrasonic waves of a specified frequency band, or of a specified direction. Methods were developed for calculating such ultrasonic frequency filters and direction filters.

An elementary filter is already a half-wave plate made of a material whose impedance differs from the impedance of the surrounding medium. The use of three or more layers, of which one or two may vary in thickness, makes it possible to obtain a frequency filter and a direction filter with a variable frequency. It is shown that the action of an ultrasonic filter isolating a specified frequency band is equivalent to the action of two sets of transition layers matching the impedance of the outer media with the impedance of the middle layer. In particular, the possibility is shown of a sharp broadening of the frequency characteristics and of an overall increase in sound transparency, for example, of steel plates placed in water.

The calculated and experimentally realized direction filters with variable frequency make it possible to filter out oblique beams of ultrasonic waves arising from the inhomogeneity of the ultrasonic field of the radiator, and thereby sharply improve the accuracy of operation of ultrasonic interferometers and the quality of the ultrasonic images obtained. The use of these filters makes it possible to obtain a sufficiently good sound field even with ordinary technical piezoelectric plates. Along with this, broadband frequency filters were experimentally realized, which made it possible to obtain a sound-transmission coefficient through a steel plate in water of the order of 90–95% in the frequency band 0.3–0.4 of the nominal.

L. L. Myasnikov and G. K. Ul’yanov reported on “Investigation of the magneto-acoustic effect in dia- and paramagnetic metals.”

For the first time an experimental investigation was carried out of the magneto-acoustic effect in dia- and paramagnetic metal plates, which is expressed in the dispersion of sound and in the formation of a secondary alternating electromagnetic field of eddy currents.

Magnetic dispersion for longitudinal sound waves in plates and rods made of dia- and paramagnetic metals is due to the occurrence of eddy currents in a conductor oscillating perpendicular to a magnetic field. The active resistance, equivalent to the resistance of losses in the metal due to eddy currents, produces additional sound attenuation, while the additional equivalent elasticity caused by electromechanical forces opposing the motion of the conductor increases the phase velocity; the dispersion is determined mainly by the skin effect. Experimentally, the change in the frequencies of natural oscillations and in the logarithmic decrement of damping was determined as a function of the magnetic induction of the transverse field, and the secondary alternating field was studied by means of a miniature induction coil. The investigations were carried out in the frequency range 2–20 kcps and in the range of magnetic inductions 0–1.4·10⁴ gauss, and Seignette-salt piezoelectric elements of a 45% X-cut were used to excite the natural oscillations of the plate. A change in the phase velocity in an aluminum plate by 0.02% and an increase in the logarithmic damping decrement by 30% were observed.

Roby’s theoretical investigation of the magnetic dispersion of longitudinal sound waves in a nonferromagnetic metallic thin unbounded layer, published after part of the work had already been carried out, gives an expression for the phase velocity of sound which leads to a value of the dispersion one to two orders of magnitude greater than the value established experimentally. On the other hand, the theory agrees with the experimental data concerning the dependence of the change in phase velocity on magnetic induction, frequency, and plate thickness.

Magnetic dispersion was also found for transverse and torsional waves in magnesium, aluminum, and copper plates containing impurities. With the corresponding replacement of the phase velocity of longitudinal waves in the absence of a magnetic field by the phase velocity of torsional waves, the dependences obtained for the relative change in phase velocity and the change in damping on frequency, magnetic induction, plate thickness, and the constants of the metal prove to be in satisfactory qualitative agreement with Roby’s theory. For a magnesium plate, at a magnetic induction of 3500 gauss and a frequency of 7 kcps, the increase in phase velocity reaches 1.3%, while the logarithmic damping decrement increases 20-fold. The dispersion increases with increasing magnetic induction and conductivity of the metal, and decreases with increasing frequency and plate thickness, which is determined by the skin effect.

In the report “Some New Methods for Investigating the Sound Field,” read by V. A. Zverev, a method was discussed for the absolute calibration of sound receivers and emitters based on the radiation pressure of sound, as well as methods for detecting and measuring the sound field on the basis of changes in the properties of a medium (density, dielectric permeability) caused by the sound field.

For the absolute calibration of sound receivers, two experiments are performed. In the first, the calibrated receiver receives a high-frequency wave \(\omega\), modulated by a lower frequency \(\Omega\). In this case the radiation pressure changes as a consequence of the modulation of the incident wave, and the receiver receives the sum of oscillations of frequencies \(\omega\) and \(\Omega\).

The magnitude of the sound pressure on the receiver is determined from the ratio of the voltages at the receiver output at frequencies \(\omega\) and \(\Omega\) and from the ratio of its sensitivities. In the case where the ratio of sensitivities is unknown, it is determined from the second experiment. A wave of frequency \(\omega^*\), higher than \(\omega\) and \(\Omega\), modulated by the frequencies \(\omega\) and \(\Omega\) with a known ratio of modulation depths, is sent to the receiver. From the ratio of the voltages of frequencies \(\omega\) and \(\Omega\) at the receiver output (arising as a result of radiation pressure), the required ratio of sensitivities is determined.

tions. By an analogous method a sound emitter can also be calibrated.

In the second part of the report, examples were given of the author’s application, together with collaborators, of the microphasometry methods set forth in the report by G. S. Gorelik in the field of acoustics. There were measurements of the change in the dielectric permittivity of water for a frequency of 5 MHz under the action of a sound field of frequency 78 kHz. In this experiment the sound field was excited inside a capacitor that was part of an oscillatory circuit tuned to 5 MHz. The change in the dielectric permittivity of water under the action of sound led to detuning of the oscillatory circuit and to small changes in the oscillation phase at its output. This phase change was measured by the microphasometry method developed by I. L. Bershtein. Microphasometry methods were also applied to measure the interaction of sound waves in water. A sound wave of frequency \(\Omega\) passed through a column of water tuned in resonance to frequency \(\omega\). In this case, a detuning of the column was observed, leading to a small phase modulation of the oscillations in the column. All the phenomena observed in this case are readily explained if one assumes that the wave of frequency \(\Omega\) changes the propagation velocity of the wave of frequency \(\omega\). This phenomenon can be used for detecting and measuring sound fields and for studying the properties of various media.

In the report by L. D. Rosenberg, “A Survey and Comparative Evaluation of Methods for Converting a Sound Image into a Visible One,” it was noted that the visualization of sound fields and, in particular, the production of sound images have recently acquired great importance in various areas of technical and physical acoustics—for example, in defectoscopy for determining the shape and dimensions of a defect; for vision in optically opaque media; and in medical diagnostics for determining the location and shape of internal organs, tumors, and foreign bodies. The speaker divided the various methods of visualizing ultrasonic fields, according to the nature of the effect acting on the converter of the sound field into a visible image, into three groups: methods based on the action of the principal (linear) quantities characterizing the sound field; methods based on the use of ponderomotive (quadratic) effects; and methods based on the use of various secondary effects caused by ultrasonic oscillations.

Visualization methods may also be divided into reversible, in which the image disappears when the external action ceases, and irreversible, in which it remains afterward. An important characteristic of visualization methods is also the degree of distortion of the sound field by the receiver (the formation of “halos”).

The first group includes methods in which a piezoelectric receiver is used in combination with mechanical or electronic scanning (Sokolov, Schreiber, Barbé, and others). In schemes with electronic scanning, the change in secondary-electron emission is used, caused by the incidence of the scanning electron beam on the surface of a quartz plate as a function of the additional charge produced by the relief of the sound pressure. This group also includes known optical methods (the shadow method and the method of diffraction of light by ultrasound), which use the change in the refractive index of optical waves associated with a change in the density of the medium, as well as their various improvements for increasing sensitivity.

Quadratic effects include the surface-relief method proposed and used by Sokolov and then by Sette, Schuster, Rust, and Drubba. In this method, by means of various optical methods, the deformation of the interface between liquid and gas is observed under

...of the sound incident upon it. This also includes the suspension method (Pohlman), which uses the phenomenon of orientation, under the influence of ultrasound, of solid particles suspended in a liquid.

Among the secondary effects are various modifications of the chemical action of ultrasound, the thermal action on heat-sensitive paints and on luminescence phenomena, as well as the direct action of ultrasound on a photographic layer.

The speaker noted that the scarcity of published quantitative data does not make it possible to judge the sensitivity of most methods. It may be supposed, however, that methods based on the use of piezoelectric transducers should have the greatest sensitivity, since electronic amplification of the signal is possible here. But, in comparison with other methods, they are relatively complex and have lower resolving power. Visualization of sound fields is a promising direction both for the study of physical processes and for various technical applications of ultrasound.

V. V. Tyotekin spoke on “the measurement of the shear modulus and loss coefficient of rubber-like materials by means of a solid acoustic long line at sonic and ultrasonic frequencies.” The developed method makes it possible to measure these quantities in a continuous frequency range from 4 to 50 kHz over a fairly wide temperature range. The method is based on measuring the reflection coefficient of the specimen under study, which is glued to one end of a duralumin tube excited at the other end by a bundle of longitudinal waves transformed into shear vibrations of the specimen. For this purpose the amplitudes and phases of the reflected pulses are compared in one case with the specimen glued on, and in the other case with the line free. This makes it possible to determine the load impedance, and from it the required impedance of the specimen, and then to calculate special nomograms. The frequency characteristics of several rubber specimens were investigated experimentally. Comparison of these characteristics with results obtained by other authors gave good agreement. Measurements of temperature dependence were also carried out by comparing a loaded and an unloaded line; but, in order to exclude the dependence of the sound-propagation velocity along the line on temperature change, pulses were sent simultaneously along both lines, which were under identical temperature conditions.

E. N. Plotnikova gave a report on the results of investigations of the “modulation method for measuring small stresses in the audio-frequency range,” carried out by D. K. Balabukha, L. L. Myasnikov, and the author.

Amplification of very weak signals over a broad band of audio frequencies is limited by the noise of the amplifying device, which cannot be reduced below the limit determined by the shot effect of the tube and by the noise of the input resistances. By applying the modulation method it was possible to detect signals whose intensity is an order of magnitude lower than the intensity of the apparatus’s own noise for a frequency band of (0.2–20 kHz) and a large input resistance (more than 100 MΩ).

In the modulation microvoltmeter developed, the signal under investigation first enters a capacitive modulator operating at a frequency of 24 Hz, and then the amplifier input, at whose output the modulated signal is detected and the modulation envelope frequency (24 Hz) is selected by an analyzer. The output signal is fed to a thermocouple with a galvanometer, whose readings correspond to the level of the signal entering the input. The filter plug included in the amplifier circuit does not pass directly the frequency 24 Hz, which arises as a result of the transformation of the contact-potential difference of the capacitive modulator into an alternating voltage at the modulation frequency.

The stability and sensitivity of the device are improved when, instead of a thermocouple synchronous detector, a synchronous capacitive modulator is used, to which a “reference” voltage is simultaneously applied from another synchronous capacitive modulator, powered by a constant voltage and converting it to a frequency of 24 cps.

The method developed made it possible to increase the sensitivity of measurements by an entire order of magnitude. Thus, for example, with a bandwidth of 0.2–20 kcps and an amplifier intrinsic-noise level of about 5–7 μV, it was possible to measure sinusoidal and noise signals of about 0.7 μV (with an input resistance greater than 100 MΩ). With the aid of the new method, the noises of capacitors and Seignette-salt piezoelectrics were measured.

Measurement of the noise of capacitors in the audio range gave satisfactory agreement with the theoretical values obtained on the basis of the thermal character of this noise.

B. D. Tartakovskii