ULTRASONIC VIBRATIONS

N. N. Malov, Moscow

Ultrasonic vibrations, i.e., vibrations having frequencies on the order of tens of thousands of hertz and higher, obtained chiefly by electromechanical means (usually with the aid of piezoelectric quartz), have in recent years attracted the attention of a number of investigators; as a result of their work, varied and very interesting material has accumulated, to a survey of which the present article is devoted1.

1. Methods of obtaining ultrasonic vibrations

Instead of purely mechanical methods (excitation of a rod by impact, Galton’s whistle, etc.), which make it possible to obtain only ultrasonic vibrations of negligible power and with a rapidly decreasing amplitude, electromechanical methods are used for obtaining sustained vibrations; these may be divided into three principal groups:

a) Piezoelectric oscillators. When an alternating electric field is created in a piezoelectric plate (quartz, tourmaline, Rochelle salt), it enters into mechanical vibrations with a frequency corresponding to the frequency of the field. At electromechanical resonance the amplitude of the vibrations increases sharply. This phenomenon, discovered quite long ago, proved very valuable for radio engineering, since it was found that a piezoelectric crystal oscillating in the circuit of a tube generator tends to stabilize its frequency, maintaining it equal to the crystal’s own frequency with very high accuracy. Recently this quartz stabilization has become extremely widespread.*

Quartz oscillators are used predominantly, being sufficiently strong and inexpensive. The natural frequencies of quartz plates lie in the range from hundreds of thousands to a few million hertz. For lower frequencies excessively thick plates are needed, which are difficult to make from the quartz crystals obtained; as the frequency is raised the plates become too thin and fragile. Without special difficulties it is possible to obtain less intense vibrations by exciting quartz

not at the fundamental tone, but at one of its overtones. For example, Bergmann⁵ succeeded in proving the presence of all odd overtones of a quartz plate up to and including the 69th.

Rochelle-salt crystals are more fragile than quartz crystals; they have not become widely used. Recently, tourmaline plates have appeared which are also suitable for producing ultrasonic vibrations. According to the investigations of Gerald, Fuchs, and Underwood⁶, the resonance frequency of a tourmaline plate of thickness \(l\) mm, vibrating in thickness, is

\[ f_t=\frac{3.77\cdot 10^6}{l}\ \text{cycles}, \]

i.e., it exceeds the corresponding frequency for quartz

\[ f_q=\frac{2.73\cdot 10^6}{l}\ \text{cycles}. \]

In addition, when working with tourmaline one can use lower anode voltages, which reduces the possibility of breakdown of the plate. The authors believe that tourmaline plates can be used for stabilizing short-wave transmitters. The temperature coefficient (i.e., the change of the natural frequency with temperature) for tourmaline is determined by the relation

\[ \frac{\Delta f}{f^t}=3.6\cdot 10^{-5}, \]

i.e., it is close to the temperature coefficient of quartz \((2—5\cdot 10^{-5})\).

To obtain powerful ultrasonic vibrations, which give rise to a whole series of very interesting effects, it is necessary to increase considerably the voltage applied to the oscillator. To avoid flashover along its surface, the oscillator is placed in transformer oil or another liquid. This also improves the emission of ultrasonic energy, since the acoustic resistances of quartz and liquid are considerably closer to each other than those of quartz and air.

The intensity of the vibrations emitted by quartz depends strongly on the method of attaching the electrode to the quartz surface⁷. Apparently, the most reliable method is to coat the surface of the quartz with a metallic layer (for example, by cathode sputtering). Under powerful vibrations the electrode surface is gradually destroyed. Intense vibrations can be obtained only from single-crystal plates. Since these plates usually have small dimensions, while the radiated power increases with the surface of the oscillator, it is necessary to resort to mosaic radiators, first used by Langevin⁸ for underwater signaling.

Wood and Loomis⁹, using voltages up to 50 kV, were the first to investigate the phenomena occurring in the field of powerful ultrasonic vibrations; we shall return to these phenomena at the end of the review.

b) Magnetostrictive oscillators. Magnetostrictive vibrations of ferromagnetic rods are easily obtained by placing the rod in the coil of the oscillatory circuit of an undamped-oscillation generator,^10 or in a coil inductively coupled to the circuit. If the frequency of the circuit is varied, then when it coincides with the natural frequency of the rod the amplitude of its vibrations increases sharply. This increase in amplitude is clearly seen in Fig. 1, which presents an oscillogram of vibrations obtained with the aid of a mirror fastened to an axle clamped between the vibrating rod and an elastic roller. The vibrations of the mirror caused the light spot to be displaced in the vertical direction. The oscillographic film moved in the horizontal direction, its displacement being connected with the change in the generator frequency;

Fig. 1. Increase in the amplitude of vibrations of a magnetostricting rod at resonance.

The rod can be excited both at the fundamental tone and at overtones.^11 Since the natural frequency of a ferromagnetic rod of length \(l\) cm, fixed at the middle, is approximately

\[ f=\frac{2.5\cdot 10^{5}}{l}\ \text{hertz}, \]

it is evident that this method is quite suitable for obtaining vibrations with frequencies of the order of thousands and tens of thousands of hertz.

Studying magnetostrictive vibrations, Pierce^12 found that a magnetostricting rod, when properly placed in the coil of an undamped-oscillation generator, is capable of stabilizing the frequency of the generator. One of the possible circuits is shown in Fig. 2. The coils \(L_1\) and \(L_2\) create fields of the same direction. Vibrations arise only when the periods of the circuit and of the rod nearly coincide, and they acquire a frequency equal to the natural frequency of the rod. This frequency remains stable under small changes in the capacitance of the circuit; with strong detuning, however, the vibrations break off. A theoretical treatment of the conditions of magnetostrictive stabilization was made by Black^13 and Freeman.^14 In addition, Kopylovich^15 studied magnetostrictive vibrations.

By selecting appropriate materials, Pierce succeeded in obtaining a magnetostrictive oscillator with a temperature coefficient equal to \(2\cdot 10^{-5}\), i.e. close to the coefficient of quartz.

and tourmaline. By making the form of the oscillator somewhat more complicated, Pierce was able to obtain a natural frequency \(f = 1\,000\) hertz with a rod length of only 94 cm. Thus acoustic frequencies can be obtained with rods of acceptable length.

To obtain ultrasonic vibrations one can use straight rods. With \(l = 2\) cm about 125 thousand hertz is obtained. Further shortening of the rod (and with it the coils) is difficult. Here too, however, Pierce succeeded in going further. With the aid of an oscillator with a periodically varying cross-section, several centimeters in length, Pierce obtained a frequency \(f = 295\) thousand hertz. For obtaining powerful ultrasonic vibrations, nickel rods are most suitable, since in nickel the coefficient of relative magnetostriction is large. Newton Gaines\(^{16}\), exciting a nickel rod with a powerful generator

Fig. 2. Diagram of a magnetostrictive generator with stabilized frequency.

Fig. 3. Production of high-frequency mechanical vibrations by means of the interaction of Foucault currents with a constant magnetic field.

(500 W), obtained vibrations so intense that the rod broke. The rod was placed in a liquid in which powerful ultrasonic waves were produced; moreover, effects were observed analogous to the effects caused by powerful ultrasonic vibrations of quartz (see below).*

c) Oscillators using Foucault currents. Finally, electromechanical vibrations can be obtained in the following way. If a copper tube \(T\), the end of which is in a constant magnetic field directed along the radii of the tube cross-section (Fig. 3), is placed in the coil of an oscillatory circuit, then, owing to the interaction of the Foucault currents developing in the tube with the magnetic field, the tube begins to vibrate, the amplitude of these vibrations increasing sharply at resonance, which is readily observed from the sound emitted by the rod at the moment of resonance (of course, if

* Danilenko\(^{29}\) also worked with nickel tubes.

the natural frequency of the rod lies in the range of sonic frequencies). An attempt to use these oscillations for stabilizing a tube generator did not give positive results (it is possible that the magnetic field available was not sufficiently strong). Similar oscillations were used by Tomilina for studying the elastic properties of the material of a tube, and quite satisfactory results were obtained.

By using sufficiently short tubes, ultrasonic oscillations can be obtained in this way. The possibility of producing powerful ultrasonic oscillations appears, however, rather doubtful.

2. Study of the propagation of ultrasonic waves

a) Gases.

For investigating the propagation of ultrasonic waves in gaseous media, one usually uses the Pierce interferometer (Fig. 4), consisting of a polished plate placed parallel to the vibrating quartz and moved by means of a micrometer screw along a straight line perpendicular to its plane\(^18\). The plate reflects the ultrasonic waves back to the surface of the quartz; when an integral number of half-waves fits between the plate and the quartz, a maximum reaction of the sound field on the vibrating quartz is produced, the generation regime is disturbed, and the grid current changes sharply (one may also follow the changes in the anode current). In more exact measurements with the Pierce interferometer, Pan-Cheng Kao\(^19\) established that the measured wavelength near the quartz turns out to be greater than in measurements at considerable distances. In addition, it was possible to observe double maxima of the anode current\(^20\), and the determination of the velocity from one or another maximum gives results differing by approximately \(0.5\%\). Pilmeyer sees the cause of these distortions in measurements in the influence of multiple reflections. Reid\(^21\), who also found an increase of the velocity near the quartz, made measurements at distances up to \(1\ \text{m}\); he found that the increase of the velocity near the quartz grows with frequency; at large distances the velocity proved independent of frequency. Hubbard\(^22\), who considered that the accuracy of the interference method is very high (up to \(0.05\%\)) and is limited only by the accuracy of manufacture of the micrometer screw, denied a decrease in the propagation velocity with increasing distance from the quartz.

Fig. 4. Diagram of the Pierce interferometer.

A cruder method is the use of the cooling effect of ultrasonic waves. In the region of sonic frequencies, Krenke\(^23\) used a heated wire stretched along the tube

Kundt. In the formation of standing air waves, the wire was cooled at the loops and remained incandescent at the nodes, thanks to which the distribution of the standing waves could be demonstrated to an entire audience. This method proved inapplicable at frequencies greater than 25 kilohertz, since the cooled and heated regions came too close to one another.

Büch and Müller \(^{24}\) used, for investigating the ultrasonic field in air, an incandescent Wollaston filament, the temperature of which changed at the loops of the ultrasonic waves; the filament was connected into one arm of a Wheatstone bridge, the disturbance of whose equilibrium made it possible to monitor changes in temperature. They succeeded in investigating the distribution of field energy at the surface of quartz, which has a rather complex character (it is possible that the distortions in the speed of sound near the quartz are due precisely to the complexity of the field near it), and in measuring the length of standing waves in air.

Johnson \(^{92}\) theoretically developed the question of the absolute measurement of energy in an ultrasonic field (in air) by means of a thermoelement. On the basis of his theory he constructed a special thermoelement from bismuth and antimony, deposited on a cellulose film by cathode sputtering.

Testing this thermoelement at low frequencies (up to 5 kilohertz) gave favorable results. In Johnson’s opinion, his thermoelement will be applicable up to 300 kilohertz.

Taviy \(^{25}\) used the following ingenious Toepler method for detecting ultrasonic waves. An optical system gives an image of a slit, which is hidden from the observer by a wire of suitable thickness. When standing ultrasonic waves are created in the path of the light beam, the image of the slit becomes visible, since the resulting changes in the density of the air change its refractive index and the path of the rays.

Petržílka and Zachoval \(^{26}\) used an analogous method to study the optical properties of oscillating quartz. For this purpose they passed a beam of light through a lens and the quartz, and then, with the aid of another lens, projected the image onto a screen. At the point where the rays collected by the first lens converged, they placed a thin wire that concealed the image of the quartz in the absence of oscillations. When the quartz, driven by a tube generator, was excited, a pattern was obtained on the screen that made it possible to judge the distribution of amplitudes in the oscillating quartz. The patterns obtained by the authors make it possible to conclude that changes in the optical properties of the oscillating quartz are proportional to even powers of the components of the electrical or mechanical stresses produced in the crystal.

Krenke \(^{23}\) investigated the field of ultrasonic oscillations of rather low frequency (20.5 kilohertz) by means of a narrow, thin-walled glass tube containing sand. The ends of the tube were drawn out, and one of them was fixed. Under the action of ultrasonic oscill...

the tube begins to vibrate in a manner resembling the vibrations of a bell (four nodal lines are formed, parallel to the axis of the tube). The excitation sometimes proves so strong that the tube breaks. By this method Kröncke observed standing waves, interference, and diffraction of ultrasonic waves. Of course, for very rapid vibrations this method is inapplicable, since the dimensions of the tube would have to be made too small.

Yagi and Matumoto\(^ {27}\) obtained ultrasonic vibrations with a frequency of the order of \(10^4\) hertz by means of two slightly detuned magnetostrictive generators. The resulting difference tone of sound frequency excited a glass tube with a drawn-out end. Its wide end was placed near a microphone connected through a suitable amplifier to a loudspeaker. It turned out that, when the drawn-out end of the tube was additionally blown with a jet of air, the tube acted as a detector of sound vibrations. This ingenious method made it possible to detect the ultrasonic field at a distance of two hundred meters (!) from the sources of vibration.

Abello\(^ {28}\) placed peculiar torsion balances with a light vane in an ultrasonic field. The angle of torsion of the thread under the action of ultrasonic waves served as a relative measure of the intensity of the ultrasound. This method proved very valuable for investigating the absorption of ultrasonic energy.

In a number of investigations he\(^ {29}\), and also Grossmann\(^ {30}\), used as a receiver of ultrasonic energy a second quartz, tuned to resonance with the first. Such a receiver does not respond to side frequencies or to constant pressure, which gives certain advantages. The method proposed by Hubbard and Loomis\(^ {31}\) also proved very precise. Near the quartz generator serving for the investigation, another stabilized generator operates, tuned to a nearby frequency (for example, 500 and 501 kilohertz). The resulting beat note is compared with the note of a tuning fork excited electrically. When the reflector of the interferometer is displaced, owing to the influence of the sound field on one of the quartz crystals, slight changes in frequency occur; these are compensated by an auxiliary condenser and controlled by the coincidence of the pitch of the beat note and the tuning fork.

Also worthy of mention is the observation of the Doppler effect described by Möller and Kräft\(^ {91}\). They placed opposite one another two quartz crystals whose frequencies differed slightly; at frequencies close to 100 kilohertz, a difference tone of sound frequency (800 hertz) was obtained. One of the quartz crystals was immobile, while the other was attached to a seconds pendulum. When the pendulum was set into oscillation, the second quartz crystal alternately approached the first and moved away from it. As a result, two difference tones arose, with frequencies \(800 \pm 24\) hertz, easily distinguishable from the difference tone with the quartz crystals at rest.

Sacerdote\(^ {96}\) succeeded in constructing a condenser microphone with a membrane of thin (from 2 to 5 microns) aluminum, prov…

...proved suitable for recording ultrasonic vibrations with a frequency of up to 90 kilohertz. The sensitivity of the microphone began to fall off at 20,000 hertz. With the aid of this microphone it was possible to observe standing ultrasonic waves in air and to carry out a number of other interesting observations.

b) Liquids and solids. In investigating the propagation of ultrasonic waves in a liquid, in addition to the methods indicated above, several others were also used. In studying the distribution of the ultrasonic field in a liquid it is convenient to use a resistance thermometer, through which as small a current as possible is passed, so that the thermometer remains cold and does not create heating of the liquid[^35]. Owing to the ultrasonic energy absorbed by it, it is heated; to increase the sensitivity it is useful to surround it with an auxiliary half-cylinder reflecting the ultrasonic waves onto the wire of the thermometer. In this way it is possible to investigate the reflection, refraction, and diffraction of ultrasonic vibrations and to determine the length of standing waves in a liquid.

Fig. 5. Reflection of ultrasonic waves in a liquid.

In Fig. 5 is shown the arrangement of the quartz \(Q\), the mirror \(S\), and the resistance thermometer \(T\), and the polar diagrams of the heating of the thermometer during gradual rotation of the mirror; these curves prove that ultrasonic waves are reflected according to the ordinary laws.

Fig. 6. Measurements of standing ultrasonic waves in a liquid by means of a resistance thermometer.

In Fig. 6 are shown examples in standing waves (curves \(a\) and \(b\)). When the reflector \(S\) is removed, curves \((c, d)\) are obtained, which have no heating maxima. Instead of the resistance thermometer, one may also use a thermoelement.

Similar to Kundt’s dust figures in standing waves in a gas, the same figures can be obtained in a liquid; thus, in water excellent figures are obtained with the aid of fine coke powder[^36]. Boyle and Lehmann[^37] were the first to notice that gas bubbles released from a liquid penetrated by a beam of ultrasonic waves collect in standing waves at the nodal surfaces,

thereby making possible direct measurement of the wavelength. This method, however, is rather crude.

In measurements that do not claim exceptional accuracy, it is convenient to measure the energy (in relative units) by means of a vane deflected under the action of sound pressure and shown in Fig. 7^38. Richards^39 investigated the distribution of the intensity of ultrasonic waves in a liquid by observing the oscillations of the meniscus in a capillary attached to a small funnel placed in the liquid. He found that this method is very convenient at the most varied intensities. In studying the propagation of ultracoustic waves in solids, it is also possible to observe standing waves from the motion of light particles placed on the surface of the body. Thus, Sokolov^40, transmitting ultracoustic vibrations along a metal bar,

Fig. 7. Vane for measuring the energy of ultrasonic oscillations in a liquid.

Fig. 8. Observation of light diffraction in an ultrasonic grating.

observed the oscillations of droplets of water placed on the surface of the bar.

To determine the absorption of ultrasonic energy by solids, one may also use the vane shown in Fig. 7, measuring its deflection with a plate of the material under investigation \(P\) placed in the path of the ultrasonic beam and without it. Instead of the vane, one may also use a thermoelement^41.

Klein and Herzberger^42 determined the velocity of ultrasonic waves in solids by placing them in the liquid of an interferometer and observing the displacement necessary to restore the standing wave.

c) Optical methods of measurement. Lucas and Biquard^43 and, independently of them, Debye and Sears^44 established that when a beam of light propagating perpendicular to the ultrasonic waves is passed through a liquid or a solid penetrated by ultrasonic waves (Fig. 8), diffraction phenomena are observed and, instead of a single image of the slit, several are obtained, their number increasing with the intensity of the ultrasonic oscillations. From the theoretical point of view, this phenomenon, closely connected with the concept of “thermal waves,”

penetrating the body in all directions, is of considerable interest. A detailed theory of it was developed by Brillouin^45 and Debye^46.

In Fig. 9 are shown the diffraction patterns observed when light is passed through an ultrasonic grating in water (A), ether (B), and quartz (C).

Since the constant of the ultrasonic diffraction grating is determined by the velocity of propagation of the ultrasonic vibrations, and the number of spectra obtained characterizes the intensity of the ultrasonic waves, this method is very valuable in studying the propagation of ultrasonic waves in various media (transparent to light).

Biquard^47 proposed a highly original method for determining the absorption coefficient. By moving the vessel shown in Fig. 8, he makes the light beam penetrate the ultrasonic field at a greater or lesser distance from the quartz. The image of the central slit is projected onto a photocell, whose current serves as a measure of the intensity of light scattering in the ultrasonic grating, which in turn depends on the intensity of the ultrasonic vibrations.

Bergmann^48 used this phenomenon for calibrating a wavemeter. If the fundamental frequency of the quartz is known, then the frequency of overtones, easily excited up to very high orders, is simply determined from the relative position of the diffraction images of the slit, whereby a large number of reference points, determined without any difficulty, is obtained for the calibration.

A

B

C

Fig. 9. Diffraction phenomena when light passes through an ultrasonic grating in various substances.

Baer and Meyer[^49] replaced one slit of the blende with a large number of small holes, the image of which was projected by a lens onto a screen. In this way they succeeded in obtaining a visual picture of the distribution of intensity over a considerable region of the ultrasonic field, since the rays issuing from each hole gave their own characteristic pattern on the screen. This method was used by Hiedemann and Asbach[^50] to study the passage of ultrasonic vibrations through a solid body. A wedge-shaped piece of brass was placed in the liquid, and the blende with holes was set so that some of the holes lay before the wedge and some after it.

Fig. 10. Observation of diffraction according to Baer—Meyer.

In the latter case, different holes corresponded to different wedge thicknesses. In Fig. 10 the left part represents the pattern obtained before the wedge (the greatest intensity, everywhere the same), while the right part represents the pattern obtained after the wedge. The figure clearly shows that, as the thickness of the wedge increases, the amount of energy passing through it changes periodically, reaching maxima at a thickness equal to an integral number of half-waves (see below § 4). Recently the Baer and Meyer method has repeatedly been used for research and demonstration purposes.

If not one but several ultrasonic beams are passed through a liquid, one can obtain a diffraction pattern corresponding to the case of crossed gratings.

Owing to the scattering of light by the ultrasonic grating, the intensity of the light in a plane parallel to the plane of the light wave,

entering the liquid becomes nonuniform. By sending a light wave into the liquid and examining one of these planes under a microscope, one can observe directly the structure of the ultrasonic grating, if standing ultrasonic waves have been created in the liquid[^51] (in the case of traveling ultrasonic waves one has to use a stroboscope). The brightness of the image obtained is very great, and the division of the field of view into light and dark bands is quite distinct. In Fig. 11, borrowed from the article by Hiedemann, Asbach, and Bachem[^52], there are shown microphotographs of a standing wave and of interfering incident and reflected waves formed in a vessel filled with xylene.

Fig. 11. Observation of standing ultrasonic waves by the Hiedemann—Asbach method.

Schaefer and Bergmann[^89] produced in a liquid three mutually perpendicular beams of ultrasonic vibrations and observed the diffraction of light in such a spatial grating. They also excited a quartz plate of cubic shape and observed interference patterns obtained when beams of light of various orientations were passed through it.

In this way interference patterns were obtained possessing the same symmetry as the corresponding Laue diagrams. Hiedemann studied the ultrasonic grating in quartz vibrating in overtones of high orders (up to the 51st), and found that the number of bands obtained in the quartz is equal to the number of the excited overtone[^53]. Schaefer and Bergmann[^89] also used the optical method to study the distribution of the intensity of vibrations in quartz. Wyss[^90] combined the method of diffraction spectra with the method of the acoustic interferometer. He placed the reflector of the interferometer opposite the quartz and observed the diffraction of a light beam perpendicular to the ultrasonic one, while displacing...

of the reflector. The intensity of the diffraction pattern served as an indicator of the formation of standing ultrasonic waves. The accuracy of setting the reflector reached \(0.2^\circ/00\). Wiss’s results proved unexpected: comparing the values of the ultrasonic wavelength calculated from the displacement of the interferometer reflector with the values calculated from the diffraction pattern (evidently, Wiss’s method makes it possible to carry out both observations simultaneously), Wiss found a considerable discrepancy in the results obtained, far exceeding the limits of observational error. Wiss’s work, published recently and in a little-circulated journal, has not yet elicited responses, so that the question of the reality and the causes of this discrepancy remains open to the present time.

Of great interest also is the study of the distribution of the amplitudes of oscillations on the surface of oscillating quartz. The simplest method is the observation of nodal lines by means of some powder (for example, lycopodium) sprinkled over the surface of the quartz. However, this method is rather crude, and at strong oscillations becomes quite inapplicable, owing to the formation of the “sound wind” noted by Meissner \(^{32}\) as early as 1926. This “wind,” so strong that it can deflect the flame of a candle, is produced by periodic changes in the dimensions of the plate. The resulting air currents, of course, distort the distribution of lycopodium on the surface of the quartz.

A more reliable method appears to be that proposed by Osterberg \(^{33}\) and Straubel \(^{34}\). They use quartz as one of the mirrors of a Michelson interferometer and observe changes in its illumination during oscillations. Straubel found that the nodal lines obtained on a rectangular quartz plate are straight in the middle of the plate and curve toward its edges. In circular plates a complex pattern of lines is obtained. With an increase in the amplitude of oscillations the distribution of the lines changes somewhat. Straubel further indicates that the amplitude of the quartz oscillations increases not in proportion to the voltage, but somewhat more slowly.

Hiedemann and Zeifen \(^{95}\) developed an elegant method for a visual optical proof of the excitation of quartz at overtones, as well as for demonstrating the broadening of the resonance curve of quartz owing to considerable damping caused by the liquid surrounding the quartz. The quartz was placed on the bottom of a vessel with parallel walls, filled with xylol; perpendicular to the direction of propagation of the ultrasonic waves a parallel beam of light rays was passed, and the resulting pattern of the ultrasonic diffraction grating was projected onto a screen by means of an optical system that gave only an image of a small region, on which it was easy to count the number of bright and dark bands. At the fundamental frequency of the quartz (697.6 kilohertz) 8 bands were obtained. By decreasing the excitation frequency, it was possible to bring the number

bands to 7, while with increasing frequency it grew to 9. These changes in the number of bands clearly prove that the resonance curve of quartz is broadened owing to the damping produced by the liquid. The experiment showed that excitation of the fundamental tone of quartz occurred in the frequency interval from 560 to 935 kilocycles. In an analogous way one can also observe the excitation of quartz at overtones, with the number of visible bands correspondingly increasing. Owing to damping, the range of frequencies at which the overtones are excited also proves to be rather broad; thus, the third harmonic was excited in the interval from 1,421 to 2,143 kilocycles, the fifth—from 3,140 to 3,700 kilocycles, etc.

The possibility of obtaining such a picture on the screen of a large lecture hall, where the distance between the bands can be brought up to 10 cm, so that the change in the picture with variation of the frequency of excitation of the quartz becomes readily observable, makes this method very valuable from the pedagogical point of view.

3. Velocity of propagation and absorption of ultrasonic vibrations in various media

a) Solids

The velocity of propagation of ultrasonic vibrations in solids of limited dimensions (rods, plates) obviously depends on the kind of vibrations that are excited in the body. The following types of vibrations may arise: 1) tensile (ordinary longitudinal), whose velocity of propagation is determined at acoustic frequencies by the modulus of elasticity and the density, and at very high frequencies decreases somewhat; 2) flexural vibrations (transverse), whose velocity of propagation is small and varies in proportion to the square root of the frequency; 3) radial and 4) torsional. The last two kinds of vibrations are excited relatively rarely.

Measurements of the velocity of ultrasonic vibrations in solids are rather few in number. Boyle ⁵⁴, determining by the standing-wave method the velocity of longitudinal ultrasonic vibrations in duralumin rods of length \(l\) from 4 to 60 cm and radius \(R = 0.6\text{--}2.5\) cm, found that for small values of \(R/l\) the velocity of propagation is \(v = \sqrt{\frac{E}{\rho}}\), where \(E\) is the modulus of elasticity, \(\rho\) the density; for larger values of the ratio \(R/l\) this relation loses its force, and none of the known correction terms gives results coinciding with experiment. Derfler ⁵⁵, working with quartz plates, found that at low frequencies the velocity of propagation of flexural vibrations corresponds to the theoretical value, while at high frequencies it tends toward the velocity of propagation of transverse vibrations in an unbounded medium.

Roerich ⁵⁶, who set metallic rods into longitudinal vibration by placing between them and the vibrating quartz a layer of oil, found that at certain values of the exciting frequency there arose

formation of standing waves is hindered by the appearance of torsional oscillations. The velocity of propagation of longitudinal oscillations at frequencies exceeding 100–150 kilohertz decreased and at 500–600 kilohertz coincided with the velocity obtained by Derflinger.

A number of works by Canadian investigators were devoted to the study of the propagation of ultrasonic oscillations in tubes filled with various liquids. Summarizing them, Field^57 finds that at a certain frequency, coinciding with the natural frequency of radial oscillations of the tube, dispersion of the velocity of longitudinal oscillations occurs, accompanied by intense absorption of them, since the radial oscillations are maintained at the expense of the energy of the longitudinal ones.

Fig. 12. Interference pattern of ultrasonic waves on the surface of a metal blank (after Sokolov).

Measurements of the absorption of ultra-acoustic energy in solids are complicated by the fact that, when studying the passage of oscillations through a partition placed in a liquid containing an oscillating quartz, one must take into account not only absorption but also reflection of ultrasonic energy (see below). In metals the absorption of ultrasonic energy is very small, so that Sokolov^40 was able to investigate the passage of ultrasonic oscillations through a metal blank several tens of centimeters long. He placed the blank on a mercury electrode, through which a high voltage was supplied to the quartz (the transfer of energy from mercury into the metal takes place with relatively small reflection), and poured a layer of molten paraffin onto the upper base of the blank. The ultrasonic oscillations that passed through had so considerable an amplitude that, in the solidifying paraffin, a distinct interference pattern was obtained, usually possessing a certain symmetry (Fig. 12). If cavities or other defects were present inside the blank, the symmetry was sharply disturbed. In Sokolov’s opinion, such “ultrasonic defectoscopy” may play an important role in the metal industry. In viscous media (resins, pitch), as well as in ebonite and Bakelite, the absorption of ultrasonic energy is very great.

When ultrasonic energy passes from one medium into another, the phenomenon of reflection comes to the fore. The fraction of reflected energy (if the incident energy is taken as unity) is determined by the reflection coefficient:

\[ R=\left(\frac{\rho_1 v_1-\rho_2 v_2}{\rho_1 v_1+\rho_2 v_2}\right)^2, \tag{1} \]

where \(\rho_i v_i\) is the product of the density of the medium by the velocity of propaga-

ULTRA-ACOUSTIC OSCILLATIONS

of the oscillations. This formula, theoretically obtained for infinitely extended media, is well justified in those cases where the extent of the medium considerably exceeds the wavelength. At the boundary between a solid body and air the reflection is very great, as a result of which all ultrasonic investigations requiring appreciable power must be carried out in a liquid. Let us give several values of the reflection coefficient:

Water—steel \(R=0.85\)
Water—granite \(R=0.6\)
Water—ice \(R<0.13\) (depending on pressure)
Mercury—steel \(R=0.10\)

An interesting confirmation of the correctness of these values was obtained in echo-sounder investigations off the shores of Canada. With the aid of one and the same instrument, the presence of a coastal rock was detected at a distance four times greater than the distance at which floating ice was observed.

If, however, one investigates the sound permeability of a thin partition (in comparison with the wavelength), then the reflection coefficient, as Rayleigh showed, is determined by the expression:

\[ R=\frac{(r_{21}-r_{12})^2}{(r_{21}+r_{12})^2+4\operatorname{ctg}^2\frac{2\pi d}{\lambda_2}};\qquad r_{ik}=\frac{\rho_k v_k}{\rho_i v_i}, \tag{2} \]

where \(\rho_1 v_1\) is the acoustic resistance of the medium surrounding the partition, \(\rho_2 v_2\) is the acoustic resistance of the material of the partition, \(d\) is its thickness, and \(\lambda_2\) is the wavelength in the material from which the partition is made.

It is easy to see that in this case, as the thickness of the partition increases, the reflection must vary periodically, vanishing at thicknesses satisfying the condition

\[ d=n\frac{\lambda_2}{2}\;(n=1,2,3\ldots). \tag{3} \]

Boyle and his collaborators devoted much attention to the experimental verification of this formula.^58 The results of their investigations with lead partitions placed in water are shown in Fig. 13, where the dashed curve represents the theoretical values and the solid curve the measured values of the reflection coefficient. The qualitative agreement is quite satisfactory; the quantitative discrepancies may be explained partly by absorption in the wall and, chiefly, by the imperfection of the energy meter (torsion pendulum). Richards,^41 measuring the energy of ultrasound that had passed through a partition by means of a thermocouple, likewise observed periodic changes in the amount of transmitted energy as the thickness of the partition was increased.

In architectural acoustics an attempt is made to relate sound insulation, i.e. the logarithm of the ratio of incident energy to transmitted energy, to the weight of \(1\ \mathrm{cm}^2\) of the wall surface. This dependence may be ob-

...obtained under certain conditions from Rayleigh’s formula; moreover, one should expect that the sound insulation will be proportional to the square of the weight and will increase with increasing frequency of the vibrations incident on the wall. However, experimental data on the sound insulation of building materials at audio frequencies give other values for the exponent of the wall weight (from 1.4 to 2.5).

Analogous investigations at an ultrasonic frequency[^38] showed that, within known limits, sound insulation is proportional to the weight to the power 1.4. Its absolute values, as was to be expected, proved to be considerably higher than at audio frequencies. The investigations were carried out by placing the partitions under study in transformer oil. It is also interesting to note that the sound insulation of partitions made of cardboard or wood, when first immersed in oil, proved to be very great; however, after the partitions had been impregnated with oil it dropped sharply. Evidently the high initial value is explained by the presence of air bubbles in the pores of these partitions.

Fig. 13. Dependence of the reflection coefficient of ultrasonic waves on partition thickness (according to Boyle). Solid curve — experimental data. Dashed curve — theoretical.

b) Liquids. The first measurements of the velocity of propagation of ultrasonic waves in liquids were made by Boyle and his collaborators[^59]. The velocity was determined from standing waves, observed by the accumulation of gas bubbles on nodal surfaces. For water, various alcohols and aqueous solutions of NaCl and KCl, as well as for transformer oil and an oil of high viscosity (50 times greater than the viscosity of water), the velocity proved to be independent of frequency in the frequency interval from 45 to 570 kilocycles. In addition, these authors studied the temperature dependence of the velocity; with increasing temperature the velocity increased. The numerical values of the velocity did not differ from the velocity of propagation of audible frequencies, or from the values calculated by the usual formula:

\[ v=\sqrt{\frac{\gamma}{\rho\chi}} \tag{4} \]

where \(\rho\) is the density, \(\gamma=c_p/c_v\) is the ratio of specific heats, and \(\chi\) is the compressibility coefficient of the liquid.

A number of determinations of the velocity, giving analogous results, were carried out by Hubbard and Loomis[^31] and by Malov[^35], who determined...

speed by measuring the length of standing waves and the refractive index with the aid of a resistance thermometer. Taylor and Sproul \(^{60}\) found that, after two days of continuous passage of intense ultrasonic vibrations through tap water, the velocity of the ultrasonic waves changed from 1,480 to 1,520 m/sec (at constant temperature). They attribute this change in velocity to the removal of absorbed gas released, as indicated above, under the action of ultrasonic vibrations. Randall \(^{61}\) determines the compressibility coefficients of liquids from the length of standing ultrasonic waves.

Table 1 gives the velocities of propagation of ultrasonic vibrations in various liquids.

TABLE 1

Velocity of propagation of ultrasonic vibrations
(in m/sec)

After the discovery of the diffraction action of ultrasonic vibrations on light rays, Biquard \(^{47,62}\) carried out a series of measurements

propagation velocity and absorption coefficients of ultrasonic vibrations in liquids. Biquard’s measurements were carried out at a frequency of about 8 megahertz and gave (for the absorption coefficient) a considerable discrepancy from the values calculated on the basis of ordinary conceptions (Table 2); no explanation has yet been given for this discrepancy.

TABLE 2

Absorption coefficients of ultrasonic vibrations

Measurements of the propagation velocity of ultrasonic vibrations were also made by other authors \(^{44,48,49}\), and the velocity values obtained by them proved to be in good agreement with the results obtained by other methods. Apart from Biquard’s results given in Table 2, the data of the other works allow one to think that the propagation of ultrasonic frequencies in liquids obeys the ordinary laws derived for audible frequencies. Starting from the exponential law of decrease of the amplitude in the propagation of vibrations in an absorbing medium

\[ A = A_0 e^{-\alpha_1 x} = A_0 e^{-\alpha_1 n\lambda} \]

(the distance \(x\) is here expressed in wavelengths) and assuming that the absorption is due chiefly to the internal friction of the medium conducting the vibrations, for the damping factor \(\alpha_1\) we obtain the following expression, given by Stokes:

\[ \alpha_1 = \frac{16\pi^2 f\eta}{3\rho v^2}, \tag{5} \]

where \(\rho\) and \(v\) are the density and the propagation velocity, \(\eta\) is the coefficient of internal friction, and \(f\) is the frequency. Using (5), it is easy to calculate that a decrease of the amplitude to \(1/e\) of its initial value will occur (at \(f = 100\) kilohertz) in water at \(x = 3.6\) km. Hence the convenience of using ultrasonic vibrations for underwater telegraphy becomes clear. The impossibility of appli-

replace, for this purpose, oscillations of audible frequency is explained by the necessity of using a directed (slightly divergent) beam, the production of which at low frequencies requires a very large radiating surface or the use of nonportable large mirrors. At ultrasonic frequencies, however, the area of a radiator giving a sufficiently powerful, weakly divergent beam of rays proves not to be too large. Indeed, from the theory of oscillations of circular piston membranes it is known that the directivity of the beam increases with an increase in the ratio of the radius \(R\) of the membrane to the wavelength \(\lambda\) of the emitted beam of oscillations. In Fig. 14 the radiation characteristic of membranes is given for \(R/\lambda = 0.48;\ 0.80\) and \(1.75\). Already in the last case the directivity of the beam is expressed very sharply.

In the practically used quartz echo sounder the radius of the radiator was equal to \(10\ \mathrm{cm}\), the frequency was \(37.5\) kilohertz (the wavelength in water about \(4\ \mathrm{cm}\)); here \(R/\lambda = 2.5\), and the directivity of the beam is still greater than in the last case of Fig. 14. The angle of aperture was only \(14^\circ\).

Measurements of the velocity of ultrasonic oscillations in a number of liquids at frequencies of 243 and 940 kilohertz were made by Shpakovsky \(^{97}\); at both frequencies the velocity proved to be constant.

Assuming the possibility of dispersion at a high frequency of ultrasound owing to the falling out of part of the heat capacity (see dispersion in polyatomic gases, § 3.b), the author finds that the ratio of the velocities \(v_1\) and \(v_2\) at frequencies \(f_1\) and \(f_2\) must be determined by the equation:

\[ \frac{v_1}{v_2}=\sqrt{k-\frac{c_p'}{c_p''}(k-1)}, \]

where \(k=\dfrac{c_p'}{c_v'}\), \(c_p'\) is the heat capacity at constant pressure, determining the velocity of propagation of low-frequency oscillations, \(c_p''\) is the heat capacity existing at high frequencies, with \(c_p' > c_p''\). The author estimates the magnitude of the possible dispersion at \(10\%\).

Fig. 14. Radiation characteristic of piston membranes as a function of the ratio between the wavelength and the radius of the membrane.

In addition to the insignificant absorption of ultrasonic oscillations in liquids, the conditions for the transfer of energy from the radiator into the liquid are also very favorable (see above); in the case of propagation of ultrasonic waves in gases their absorption increases, while the conditions of their radiation, owing to strong reflection, sharply deteriorate; therefore aerial signaling by ultrasonics is not

is of practical significance. However, the study of the propagation of ultrasonic waves in gases (especially polyatomic ones), to which we now turn, is of considerable interest from the theoretical point of view.

b) Gases. The study of the propagation of ultrasonic vibrations in gases attracted the attention of investigators because of the occurrence of anomalous dispersion of ultrasonic vibrations in polyatomic gases; this dispersion is absent in the region of audible frequencies and appears only at frequencies of the order of hundreds of thousands of hertz. From the theoretical point of view it is of considerable interest, and a large number of works have been devoted to its study.

When the discussion concerns monatomic gases, the velocity of propagation of ultrasonic vibrations is determined by the usual equation:

\[ v = \sqrt{\frac{p}{\rho}\,\gamma}, \]

where \(p\) is the pressure of the gas, \(\rho\) its density, and \(\gamma\) the ratio of the specific heats \(c_p\) and \(c_v\). In studying the absorption of ultrasonic vibrations in gases, in addition to the absorption due to internal friction \(\alpha_1\) (see § 3, b), one must also take into account other factors that increase absorption. Owing to the instantaneous heating of compressions, there is a certain heat transfer from these regions to the cooled regions where rarefaction predominates. This heat transfer occurs at the expense of the energy of the propagating vibrations and is characterized by the coefficient \(\alpha_2\), which for air amounts to about \(0.3\,\alpha_1\). For water and other liquids \(\alpha_2\) is much smaller than \(\alpha_1\).

Furthermore, when vibrations propagate in a mixture of several gases whose constituent parts do not enter into chemical reactions with one another, one must take into account an additional scattering of energy caused by a relative increase in the concentration of the heavier constituents in compressions and of the lighter ones in rarefactions[^63]; these changes in concentration require an additional expenditure of the vibrational energy, characterized by the coefficient \(\alpha_3\), which for air reaches approximately one tenth of \(\alpha_1\).

All the coefficients \(\alpha_1\), \(\alpha_2\), \(\alpha_3\) increase in proportion to the frequency. The absorption of ultrasonic energy in monatomic gases is relatively small; the increase in velocity caused by the increase in absorption lies beyond the limits of measurability throughout the entire range of ultrasonic frequencies. Much more complex phenomena are observed in polyatomic gases, where absorption may become very considerable and the dispersion of ultrasonic vibrations proves easily measurable.

The reason for this phenomenon is that, at sufficiently high frequencies, part of the heat capacity of the gas ceases to influence the process of propagation. Indeed, in a polyatomic gas the total

the energy of a molecule is made up of the energy of translational motion (this energy also exists in monatomic gases) and the energy of rotational or vibrational motions that the component parts of a polyatomic molecule can perform (internal energy). The number of molecules possessing rotational or vibrational energy is a function of temperature. In some cases the establishment of equilibrium between internal and external energy when the temperature changes takes place over intervals of time comparable with the period of the adiabatic temperature changes in an ultrasonic wave, if its frequency is sufficiently high.

With a further increase in frequency it will turn out that one or another vibrational or rotational state will in general be unable to become established, since the temperature changes in the wave occur too rapidly; owing to this the heat capacity of the gas will correspondingly decrease, and the velocity of propagation of ultrasonic waves should increase.

Fig. 15. Dispersion and absorption of ultrasonic waves in a polyatomic gas.

If we suppose that among the possible states of the molecule there is only one requiring a considerable time for its establishment, i.e. that only molecules of two kinds can exist—with an excited state and without it—then, as shown by Kneser’s calculation^64 and, in a somewhat different form, by Herzfeld and Rice^65, the dependence of the velocity \(v\) on the frequency of oscillations \(f\) is determined by the curve shown at the top of Fig. 15. The velocity \(V_1\) corresponds to infinitely slow changes of temperature (and, consequently, to infinitely long periods of ultrasonic oscillations), in which all the molecules enter the excited state; the velocity \(V_2\) corresponds to very short periods of oscillation, in which not a single molecule has time to follow the changes of temperature, so that the share of the heat capacity of the molecule corresponding to the excited state drops out of the total heat capacity of the gas.

Obviously, if several vibrational or rotational states of molecules are possible, requiring different intervals of time for their establishment, the spectrum of the propagation velocity of ultrasonic oscillations will have several rises, similar to that shown in Fig. 15.

In the region of dispersion frequencies an additional ...

absorption of ultrasonic energy. Indeed, since a fraction of the molecules, on being excited, absorbs the corresponding amount of energy, while another fraction, leaving the state of rotational motion, releases the corresponding amount of energy, the equilibrium state of the gas with respect to the energy of translational motion in the ultrasonic wave is not reached immediately; consequently, the pressure, proportional to the energy of translational motion, will also not be established instantaneously, and therefore will be shifted in phase relative to the changes in density. But this means that on the diagram of the state of the gas, in each period of the ultra-acoustic wave, a certain area will be described, i.e. the energy of the ultra-acoustic oscillations will be converted into heat. At frequencies lying far from the dispersion frequencies, however, this absorption will be absent, since the equilibrium state will be established sufficiently rapidly (at low frequencies), or else the transfer of energy into the energy of rotational motion of the molecules will not occur at all (at high frequencies). The course of the absorption curve, characterized by the coefficient \(\alpha\), is shown in Fig. 15 below. With several possible states of rotational motion of the molecules, it is evident that several maxima should form on the absorption curve. Of course, in addition to the absorption considered here, one must take into account the absorption due to internal friction and heat exchange in the gas (the coefficients \(\alpha_1\) and \(\alpha_2\)).

The analytical expressions for the velocity and the absorption coefficient have the following form:

\[ v^2=\frac{p}{\rho}\left\{1+R\,\frac{c_0+c_\infty\omega^2\beta^2}{c_0^2+c_\infty^2\omega^2\beta^2}\right\} \]

\[ \alpha=4\pi \sqrt{\frac{1}{2}(1-\cos\varphi)}. \]

Here \(R\) is the gas constant, \(c_0\) and \(c_\infty\) are the heat capacities at very low and very high frequencies, \(\omega=2\pi f\) is the angular frequency of the ultra-acoustic oscillations, \(\beta=\dfrac{1}{\chi_{10}+\chi_{01}}\), and \(\chi_{10}\) and \(\chi_{01}\) determine the frequencies of transition of the molecules from the excited state to the unexcited one and conversely. These frequencies are functions of temperature, and therefore the dispersion region of ultrasonic frequencies must shift when the temperature changes.

The phase shift between density and pressure is determined by the expression:

\[ \operatorname{tg}\varphi=\frac{(V_2^2-V_1^2)\omega\omega_1}{V_1^2\omega_1^2+V_2^2\omega^2}, \]

where \(\omega_1=\dfrac{1}{\beta}\dfrac{c_0}{c_\infty}=2\pi f_1\) determines the position of the point of inflection of the dispersion curve (Fig. 15).

A more rigorous theory of anomalous dispersion in polyatomic gases was developed by Richards\(^{66}\) and Kneser\(^{64}\). An analogous dispersion should also exist in partially dissociated gases. The calculation of this phenomenon was given by Einstein\(^{67}\).

Palanolagas\(^{68}\) was one of the first to investigate the velocity of propagation of ultrasonic vibrations in air. He worked with frequencies not exceeding 207 kilocycles and did not detect any dispersion.

Measurements in monatomic gases were made by Abello\(^{29}\); he found that pure argon absorbs in the same way as air. An admixture of 1% helium to air slightly increased the absorption coefficient. In diatomic gases dispersion was first observed by Pierce\(^{18}\). He found that in \(\mathrm{CO}_2\), when the frequency was changed from 42 to 206 kilocycles, the velocity increased from \(258.8\ \mathrm{m/sec}\) to \(260.2\ \mathrm{m/sec}\). For higher frequencies \(\mathrm{CO}_2\) proved to be completely opaque (this result was not subsequently confirmed). Since small admixtures of foreign gases very strongly affect the absorption coefficient, the results of investigations of the absorption of ultrasonic vibrations in \(\mathrm{CO}_2\), carried out by various authors\(^{29,64}\), turn out not to agree completely. However, dispersion in the frequency range from \(10^5\) to \(10^6\) hertz is confirmed. Pielmeier\(^{69}\) finds a maximum of absorption at the frequency \(f = 2.17 \cdot 10^5\) hertz.

A small number of measurements were made with \(\mathrm{CS}_2\)\(^{70}\), where dispersion was found at frequencies below 500 kilocycles; with \(\mathrm{SO}_2\)\(^{30}\), where, apparently, the absorption maximum lies at very high frequencies; and with \(\mathrm{NO}_2\)\(^{29}\), where the course of the absorption curve is analogous to \(\mathrm{CO}_2\). The propagation of ultrasonic vibrations in \(\mathrm{H}_2\) was investigated by Abello\(^{29}\) and by Richards and Reid\(^{70}\); they found that the velocity increases from \(1319\ \mathrm{m/sec}\) at 94 kilocycles to \(1409\ \mathrm{m/sec}\) at 450 kilocycles; analysis of the results they obtained suggests that the dispersion is caused by the loss of that part of the heat capacity which corresponds to the rotational motion of the molecule. However, Wallmann and Becker, who have not yet published the details of their measurements, indicate\(^{1}\) that they found no dispersion in the region from 358 to 1290 kilocycles, and that the value obtained for the velocity agrees with its value for audible frequencies (in the last experiments the purity of \(\mathrm{H}_2\) reached 99.6%).

The influence of foreign gases and absorption in gas mixtures was investigated by Barnes\(^{71}\), Richards and Reid\(^{70}\), Kneser\(^{72}\), and Knudsen\(^{73}\). They all found a very sharp influence even of small admixtures, explained by the fact that collisions of different molecules prove more effective (with respect to excitation of molecules) than collisions of molecules of one and the same gas. The significance of the influence of even small admixtures can be judged from Fig. 16, taken from Kneser’s work\(^{72}\) and containing curves of absorption of audible frequencies in moist air; the corresponding measurements with very high accuracy were carried out by Knudsen\(^{73}\).

The propagation of ultrasonic vibrations in partially disso-

dissociated gases, and the dispersion associated with this partial dissociation, were studied by Richards and Taylor^74 in \(N_2O_4\) at various pressures over the frequency range from 9 to 451 kilocycles. They found dispersion at ultrasonic frequencies (earlier work, in which frequencies not exceeding 15 kilocycles were used, had given negative results); however, its precise measurement was made difficult by very large absorption.

Summing up the investigations now available on the absorption of ultrasound in gases, one may say that the experimental data give only qualitative agreement with theory; this can be explained, on the one hand, by the difficulty of making accurate measurements of this kind and, on the other hand, by certain imperfections of the theory. Further development of these investigations will undoubtedly be able to provide valuable information on the distribution of intramolecular energy in complex molecules, on the frequency of molecular excitation, and on the influence and character of collisions, etc.

Fig. 16. Absorption of sound energy in air as a function of the content of water vapor.

4. Action of Powerful Ultrasonic Vibrations

To obtain ultrasonic vibrations of high power it is necessary to excite a plate of considerable area at its natural frequency, and the excitation should, as far as possible, be amplified; the quartz oscillator has to be immersed in an insulating liquid in order to weaken the electric field at its edges, create better conditions for the transfer of ultrasonic energy to the surrounding medium, and protect the plate from fracture when the amplitude of the vibrations increases strongly.

The first investigations with powerful ultrasonic vibrations were made by Wood and Loomis^9, who raised the voltage on the quartz coatings to 50 kV. Under these conditions the power of the ultra-

of sound energy produced by quartz reaches tens of watts per cm², and the action of so powerful a flux proves very interesting. The experiments of Wood and Loomis have been described more than once (see, for example, P. Belikov, Uspekhi fiz. nauk VIII, 222, 1928); therefore we shall not dwell on them, but shall proceed to consider later work.

a) Mechanical effects. The mechanical effects of ultrasonic vibrations are manifested above all in the separation of bubbles of gas dissolved in a liquid penetrated by a beam of ultrasonic waves. The bubbles begin to be liberated⁵⁹ even at insignificant powers (of the order of hundredths of a watt per cm²) and, as was indicated above, serve as a convenient means for determining the length of standing waves. With an increase in the energy of the ultrasonic flux, the liberation of gas bubbles is intensified; but with very intense fluxes, when the amplitude of the vibrations of the bubbles increases excessively, they are again dispersed; this was demonstrated by Hopwood³. Owing to the enormous accelerations obtained at the boundary of heterogeneous media, under the action of ultrasonic vibrations it is possible to pulverize various substances and to form emulsions. The emulsions obtained are highly dispersed and very stable. Richards⁷⁵, Danilevsky⁷⁶, and others studied the emulsifying action. Danilevsky obtained an emulsion of water and kerosene at frequencies of 150, 395, and 1,160 kilocycles. He found that the amount of emulsion formed each second increases in proportion to the increase in the intensity of the ultrasonic vibrations, the coefficient of proportionality depending on the frequency of the vibrations, as does the minimum intensity at which emulsion formation begins.

Klaus⁷⁷, working at frequencies from 100 to 500 kilocycles, obtained photographic emulsions by means of ultrasonic vibrations. At sufficiently high intensity he succeeded in increasing the homogeneity and stability of the emulsions. The photosensitivity of the emulsions obtained also proved to be somewhat higher than normal. The emulsifying capacity of an ultrasonic flux of constant frequency was used by Richards⁷⁵ as a measure of the flux power.

b) Chemical effects. The study of the chemical effects of ultrasonic vibrations is complicated by the fact that, in many cases, separation of this effect from the thermal effect caused by absorption of ultrasonic energy proves difficult. In addition, it is necessary to exclude the possible influence of the electric field of the quartz oscillator. The latter is achieved by moving the vessel with the substances under investigation away from the oscillator and by metal-plating it.

Richards and Loomis⁷⁸, among the first to begin studying chemical effects, noted the influence of ultrasonic vibrations on the boiling point of certain previously degassed substances, on the recrystallization of supersaturated solutions, evap-

...heating of superheated liquids and a number of other chemical phenomena. Schmitt, Johnson, and Olson\({}^{79}\) found that under the action of ultrasonics the oxidation of various aqueous salt solutions is accelerated. They attributed this to the action of hydrogen peroxide, formed in water owing to the influence of the ultrasonic beam on the oxygen dissolved in it. Their assumption was confirmed by the work of Bete\({}^{80}\), who worked at a power of about 250 W. Bete also found that \(O_2\) and \(N_2\) dissolved in water dissociate under the action of ultrasound.

Chents-Zhorzhi\({}^{81}\) and Chalai\({}^{82}\) observed the decomposition of high-polymer molecules under the action of ultrasound, and this splitting cannot be explained by thermal action alone.

In approximate measurements of the electrical conductivity of certain solutions subjected to the action of ultrasound, the author of the present article in 1931 found changes in electrical conductivity; however, their magnitude was slight, so that it was impossible to conclude with certainty that these changes were caused by ultrasonic action and were not the result of side effects (in particular, degassing); the same applies to the change in the coefficient of internal friction of these solutions. Unfortunately, these experiments could not be continued.

c) Biological actions. The biological action of high-power ultracoustic vibrations was first observed by Wood and Loomis\({}^{9,93}\). Subsequently a whole series of works was devoted to this question.

Without dwelling on a detailed consideration of the results obtained (for a fairly detailed survey of these works, see at the end of Grossmann’s article\({}^{1}\)), we shall point out that a considerable part of them is explained by the mechanical action of ultracoustic waves, caused by the enormous accelerations produced at the boundary between two media with different acoustic densities when an ultracoustic wave passes through. A whole series of small living organisms are destroyed under the action of ultrasound. With sufficient power it is possible to cause the death of larger objects (tadpoles, young axolotls, small fish, etc.). When such objects are acted upon, one usually observes restless behavior of the objects and a tendency to move away from the walls of the vessel; subsequently, evidently, damage to the nervous system occurs, the object assumes an unusual position (for example, fish become head-down), and in the end it perishes. It is interesting to note that at powers that are small but sufficient to cause death, microscopic examination of the object’s tissues gives no results; the cause of the object’s death and the damage produced by ultracoustic waves remain unexplained\({}^{91}\).

Harvey and Loomis\({}^{83}\), who studied the action of ultracoustic vibrations under a microscope, came to the conclusion that the action of ultrasound has a purely mechanical character, even when cells are involved whose dimensions are considerably smaller than the wavelength.

Their conclusion was disputed by Johnson^84, who proved that the action of ultrasonic waves is explained by the formation of bubbles of gas dissolved in the liquid, in particular oxygen.

At very high powers, ultrasonic vibrations also have a lethal effect on larger objects; thus Hupwood^3 and Wood^9 killed frogs by ultrasonic means.

Gaines^16, who obtained powerful ultrasonic vibrations with the aid of a magnetostrictive vibrator, also observed a number of biological effects. In particular, he notes a retardation of the growth of seeds subjected to the action of an ultrasonic beam (however, in other cases seed growth was accelerated by 20–25%). In addition, ultrasonic vibrations have a bactericidal effect; in particular, milk irradiated with a sufficiently powerful beam coagulates considerably more slowly than the control milk, which had not been subjected to irradiation.

There is no doubt that powerful ultrasonic vibrations can play a certain role in the study of biological and chemical processes, since in an ultrasonic field it is possible to obtain enormous accelerations that cannot be produced in any other way. However, to obtain substantial effects, apparently, a rather large power of ultrasonic vibrations is necessary; producing it requires complicated, expensive apparatus and good single-crystal quartz plates of considerable area. These circumstances do not permit a broad development of research into the biological action of ultrasonic vibrations, in which, up to the present time, only the first, tentative steps have been taken.

In conclusion, mention should be made of the work of Freundlich, Sollner, and Rogowski^85, who proposed using ultrasonic vibrations in the therapy of diseases of the spinal cord, making use of the heat released upon absorption of ultrasonic vibrations simultaneously with heating of the organism by high-frequency currents (diathermy), and of the use of ultrasonic vibrations for the treatment of ear diseases^15,^86.

5. Some applications of piezoquartz

In addition to the production of ultrasonic vibrations and the stabilization of radio transmitters and measuring circuits, piezoquartz can be used as a pressure gauge; for this purpose, a corresponding electrical circuit with automatic recording of the voltages produced on the quartz electrodes during its deformations is connected to the quartz. Thanks to its ability to follow very rapid changes in pressure, such an instrument makes it possible to study very rapidly occurring processes, such as, for example, pressure changes in the cylinders of internal-combustion engines or the pressure in the muzzle of a gun during firing^98.

Another application is the quartz oscillograph, constructed by Filippov^87. It consists of two quartz plates $Q$

size \(70 \times 20 \times 0.7\ \mathrm{mm^3}\), stacked across their width at a certain angle. By means of a strong spring \(F\), a mirror \(S\) is pressed against the adjoining edges; the opposite edges of the plates are fixed immovably (Fig. 17). The broad surfaces of the plates are provided with electrodes \(E\), to which the measured voltage is applied. At a voltage of about 5 kV the deformation of the plates reached \(1\ \mu\) and was determined from the displacement of the light spot.

In the interval from 5 to 1,200 hertz, the sensitivity of the oscillograph proved to be completely independent of the frequency (the natural frequency of the entire oscillograph system is about 20 kilohertz) and equal to \(135\ \mathrm{V/mm}\). The power consumed is negligible—0.4 VA. In practice it proved possible to use the oscillograph for recording processes with frequencies up to 8,000 hertz, since only with a further increase of the frequency does the change in sensitivity become appreciable. The dimensions of the piezoelectric oscillograph are considerably smaller than those of a loop or cathode oscillograph.

Fig. 17. Philippov piezoelectric oscillograph.

6. Piezoelectric Clocks

Quartz clocks, used for the precise measurement of time and frequency, were constructed by Scheibe and Adelsberger[^88] at the German State Physico-Technical Institute. The quartz clock consists of a generator exciting a quartz plate (frequency—60,000 hertz) enclosed in an evacuated vessel and placed in a special double thermostat; the temperature of the inner thermostat, which contains the quartz, is kept constant with an accuracy of up to \(0.002^\circ\mathrm{C}\). The electromagnetic oscillations of the generator containing the quartz are transmitted to an amplifier, where amplification takes place, sufficient so that the withdrawal of energy from the amplifier cannot cause noticeable changes in the operating mode of the generator. The oscillations from the amplifier enter a three-stage frequency divider, which makes it possible successively to obtain frequencies of 10,000, 1,000, and 333 hertz.

The last frequency is supplied to a synchronous motor of special design, making about 5 rev/sec. On the axis of the motor rotor there is a toothed wheel which, at definite intervals of time (4.5 or 9.0 sec), closes the circuit of the recording mechanism, which writes marks on paper moving at a speed of 10 mm/sec. The position of the time marks can be read with an accuracy of up to 0.001 sec.

The clocks are powered from an alternating-current mains supply, consuming about 3 kWh per day. Frequencies of 10,000, 1,000, and 333 hertz, by means of coupling coils, can be supplied from the running clocks to various measuring apparatus, where these frequencies serve as standards.

In 1932 two specimens of the clock were in operation. An analysis of their six-month operation showed that the constancy of their operation is exceptionally great and is determined by the following quantities.

Over 24 hours the constancy of the rate is maintained to an accuracy of up to $\pm 0.001$ sec., which corresponds to constancy of frequency to $\pm 1 \cdot 10^{-8}$ of its value. Over half a year the constancy of the rate amounted to $\pm 0.002$ sec., which corresponds to constancy of frequency with an accuracy of up to $\pm 2 \cdot 10^{-8}$. A direct comparison of the two clocks showed that their rate relative to one another maintains constancy with an accuracy of up to $\pm 0.0003$ sec., which corresponds to constancy of frequency to $\pm 4 \cdot 10^{-9}$.

A detailed analysis of the possible influences causing changes in the rate of the clocks led Scheibe and Adelsberger to a new, improved design of quartz clocks, in which measures were taken to reduce the temperature coefficient of the quartz and to maintain the constancy of the supply voltages. Two more specimens of quartz clocks were built; their operation during the last 9 months has shown, in the opinion of their designers, such perfection of construction that in the coming years it is very unlikely that any substantial changes will be introduced into it. One can readily agree with this opinion after becoming acquainted (from the description of the clocks) with the remarkable thoughtfulness of the design and the foresight of its authors.

Addition

In a report at the session of the Academy of Sciences of the USSR on December 20, 1934, S. Ya. Sokolov (Leningrad) communicated a number of very interesting data on his work in the study of ultrasonic vibrations of very great power.

Using large-area radiators consisting of many quartz plates glued to one another (a mosaic), he succeeded in increasing the power of ultrasonic radiation to 150 watts. When such a beam, created by a radiator with a surface of about 1000 $\mathrm{cm}^2$, is propagated in a vessel with oil in the vertical direction, a fountain several tens of $\mathrm{cm}$ high is formed on the surface of the oil.

By directing such a powerful beam into a metal blank, it is possible to trace its propagation in a layer of metal 1 $\mathrm{m}$ thick, owing to which such “ultrasonic defectoscopy” acquires exceptional practical value.

When obtaining diffraction of light in so powerful an ultrasonic beam, Sokolov succeeded in observing spectra up to the 34th order; the change in the number of spectra when a metal blank is placed in the path of the ultrasonic beam makes it possible to judge the presence of defects inside it, and this method proves to be very convenient.

Sokolov succeeded in exciting his radiators even at a very high frequency—he succeeded in obtaining diffraction spectra

at a frequency of \(1.2 \cdot 10^8\) hertz, that is, at an electromagnetic wavelength equal to 2.5 m; up to now, attempts to obtain sufficiently powerful oscillations of so high a frequency have been unsuccessful.

Passing a powerful ultrasonic beam through molten metals, Sokolov discovered a reduction in the solidification time of the cooled metal, amounting in some cases to 30%. Since in this process the crystalline structure proved to be considerably finer than under normal solidification, this fact is of great interest for metallurgy.

Finally, mention should also be made of the results of Sokolov’s investigations on the propagation of ultrasonic oscillations along a wire. By applying ultrasonic oscillations of negligible power (only a few tenths of a watt) to a steel wire 6 mm in diameter, he succeeded in tracing their propagation along the wire over a distance of up to 500 m. To detect the oscillations, a quartz plate with two electrodes was used, from which the voltage was fed to an amplifier with a small amplification factor. Taking into account the possibility of feeding the wire with a large ultrasonic power, the use of a more powerful amplifier, and the possibility of modulating the ultrasonic oscillations, Sokolov comes to the conclusion that ultraacoustic oscillations are applicable for communication over distances on the order of hundreds of kilometers. The advantage of this kind of “ultrasonic signaling” is the impossibility of eavesdropping by an observer not directly in contact with the wire, and the elimination of difficulties with insulation that arise in electrical wire communication. A certain drawback is the requirement of uniformity of the wire along its entire length and the need to avoid sharp bends in it, since both causes impair the conditions for the propagation of ultrasonic oscillations.

LITERATURE

1. Grossmann, Ultraschall-Handb. d. Exper. Phys., B. 17, 1, 461, 1934.
2. W. Rodewald, Z. techn. Phys. 15, 192, 1934.
3. F. L. Hoopwood, Nature, 128, 748, 1931; Journ. Schient. Inst. 6, 34, 1929.
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1. See the practical use of piezoelectric vibrations in the article by P. N. Belikov, Uspekhi fizich. nauk VIII, 222, 1928. ↩