Advances in the Field of Acoustics over the Last 15 Years

Prof. V. D. Zernov.

Acoustics is not a branch of physics from whose development one could have expected the resolution of fundamental problems or the establishment of new points of view on the nature of phenomena. But in the science of sound there existed certain gaps that had to be filled; [[unclear: several words missing in the line]] parts of our science, its faithful servants always find new and interesting questions and apply much labor and ingenuity to the solution of the problems posed.

Surveying the literature on acoustics, we find, in every year, a large number of works that are both fundamentally important and interesting in their formulation of questions. Moreover, the study of acoustic vibrations, as more accessible to investigation, has always served and continues to serve as a good aid in the study of vibrations in general, whatever their nature may be.

Without setting myself the task of presenting readers with a complete report on work in acoustics over the past 15 years, I shall allow myself to dwell on those questions, investigated during the indicated period, which seem to me the most significant and interesting.

First of all, one should dwell on the question of sources of sound vibrations that give a small length of the sound wave, i.e., on sources of very high pitch. This question is fundamentally important because a whole series of problems in scientific acoustics requires precisely such short vibrations; or, at the very least, the experimental arrangement, under the condition of a short wave, is made less cumbersome, and the results of the investigation acquire greater reliability—not to mention that the very question of short acoustic waves is a programmatic one.

For obtaining high tones of considerable strength, during the period elapsed, use was also made of the old method of Kundt’s rods; but new methods were also proposed, which gave, to the highest degree, a successful and exhaustive solution to the problem of obtaining sound vibrations of any pitch. The first instrument of the new type was constructed

Edelmann and bears the name of the Galton whistle. This instrument consists of a cylindrical resonator of small diameter (3–5 mm), whose length can be varied by means of a movable piston. The natural tone of such a resonator is excited by a jet of air blown into the mouth of the resonator. The Galton whistle itself acts quite analogously to a steam whistle, in which the oscillations in the resonator are excited by a jet of steam. The instrument gives very high tones, lying far beyond the limits of audibility. With the aid of this instrument it is possible to obtain and record, by Kundt’s dust figures, standing oscillation wavelengths of 2 mm; that is, the number of complete oscillations still quite well recorded reaches 85,000 per second. Another, still more powerful method for obtaining short acoustic waves is found in the spark discharge, or Poulson singing arc. Electromagnetic oscillations are accompanied, as is known, by the appearance of a periodic spark in the vibrator. This periodically appearing spark heats the surrounding air each time and serves as a source of periodic elastic disturbances of the air, i.e. as a source of sound with the period of the jumping spark. The natural period of the vibrator, as is known, depends on the electrical capacitance and self-induction of the system; by decreasing these we can obtain oscillations whose frequency lies far beyond the limits of the frequency we require. The limit of the frequency of the propagating sound wave in this case is determined not by the method, but by other circumstances, of which we shall speak below.

Among the questions connected with the propagation of a sound wave in air, first of all we shall pose the question of the so-called sound pressure. This phenomenon, analogous to light pressure—the investigation of which brought fame to our unforgettable teacher Professor P. N. Lebedev—received its final experimental confirmation in his own laboratory.

The phenomenon of sound pressure was first noted as early as 1876 by Dvořák, who characterized it in the following way: “In any volume of air in which standing acoustic oscillations occur, a manometer placed at the node of the oscillation detects a small excess pressure.” Dvořák also gives a certain mechanical interpretation of the phenomenon, suggested to him by Mach. The question of sound pressure was raised anew by Rayleigh only in 1902, after the question of light pressure had already been decided by Lebedev in the positive sense. We shall hardly be mistaken if we say that the solution of the question of light pressure prompted Rayleigh to undertake the solution of the general problem of sound pressure. Rayleigh gave a complete theory of sound pressure and

to show that the pressure of a sound wave on a reflecting wall is expressed by the formula:

\[ P=\frac{1}{2}\left(\frac{c_p}{c_v}+1\right)\cdot E \]

where \(P\) is the sound pressure, \(E\) is the density of sound energy, and \(\frac{c_p}{c_v}\) is the known ratio of the heat capacities of a gas.

Experimentally, the problem of sound pressure was solved in Lebedev’s laboratory by Altberg. Strong sound oscillations, propagating from a Kundt rod, fell upon a reflecting wall that had an opening in which a piston, attached to the arm of a torsion system, moved freely. The displacement of the piston, i.e. the rotation of the torsion system, determined the force of the sound pressure. The experiments fully confirmed the result of the theoretical reasoning and showed that the pressure of propagating oscillations is a phenomenon common to all kinds of oscillations, irrespective of their nature. This latter circumstance was further confirmed by the work of Kaptsov, which lies beyond the scope of our survey; he investigated the pressure of waves propagating on a water surface. This work was also done under the direction of P. N. Lebedev.

From Rayleigh’s formula, given above, it is evident that there exists a very simple dependence between sound pressure and the density of sound energy. Thus, measurement in absolute measure of the sound pressure makes it possible to determine, likewise in absolute measure, the density of sound energy, i.e. the absolute strength of sound. But we shall return to this question somewhat later.

The question of the speed of propagation of sound attracted considerable attention, and the speed of sound in air was determined by various methods and under very varied conditions. The speed of sound was also determined in other gases, such as carbon dioxide and nitrogen, and at very varied temperatures. Thus, Bökendahl investigated the speed of sound in gases in the temperature interval from \(0^\circ\) to \(+1100^\circ\), while Cook was concerned with determining the speed of sound for low temperatures down to \(-190\).

The magnitudes of the change in the speed of sound with such a considerable change of temperature are no longer accounted for by elementary gas laws, and can be explained only by a change in the ratio of the specific heats of the gas, which, in turn, is explained by a change in the molecular structure of the gas.

The molecular structure of a gas, in the sense of the dissociation of gas molecules, is affected not only by heating but also by other agents, such as, for example, Roentgen rays. On this basis there was made

an attempt was made to establish a dependence of the velocity of sound on the action upon the gas of such agents as X-rays; but while Koepper finds such a dependence, others (Westphal, Strieder) do not find it and regard the result obtained by Koepper as an observational error.

Of particular interest is the question of the velocity of propagation of short acoustic oscillations, for if in general there exists a dependence of the velocity of propagation of sound on wavelength, i.e. a dispersion of sound oscillations, then it is easiest to notice it by investigating the velocity of propagation of short waves. In this direction, apparently, everything possible has been done. One should point to the work of Dieckmann, who used a Poulsen arc as the source and reached very short oscillations, \(\lambda = 0.59\) in illuminating gas, which corresponds to a number of oscillations \(n = 780{,}000\) per second. The number of oscillations was determined from the length of the electric wave, measured with the aid of a special apparatus used in wireless telegraphy for measuring the lengths of electric waves, while the length of the acoustic wave was determined by a reflecting diffraction grating. Another work belongs to Młodziejewski and was carried out on the suggestion and in the laboratory of P. N. Lebedev. The source of sound was a Galton whistle (\(n = 10{,}000\) to \(n = 33{,}000\)); the velocity of sound was determined by a method analogous to Fizeau’s method for determining the velocity of light. Both investigators find no change in the velocity of sound as a function of the length of the propagating wave, i.e. they establish the absence of dispersion of sound oscillations in gases.

Let us note that in a whole series of investigations on sound at the present time an arrangement of experiments is used that is analogous to optical methods. Thus, the method of determining the wavelength by means of a diffraction grating constructed from parallel wires has secured a firm place for itself, and in Młodziejewski’s experiments we see the well-known toothed wheel of Fizeau’s method.

On the question of dispersion of the sound wave we have the classical work of Professor N. P. Kasterin. He investigates the propagation of a sound wave in an inhomogeneous medium: in the tube through which the sound propagates, solid spheres are placed at a known distance from one another. Under this condition the velocity of propagation of sound depends on the wavelength, or the velocity of propagation of a given wave depends on the arrangement of the spheres. The dependence becomes still more obvious if, instead of spheres, Helmholtz resonators are placed, responding to the tone of the propagating wave. Kasterin gives a complete theory of this phenomenon. Kasterin’s experiments, interesting from the point of view of acoustics, are decisive in the theory of dispersion of light, where light waves, propagating in an inhomogeneous medium, encounter resonator-molecules responding to pe-

period of an electromagnetic light wave. The theory given by Kasterin is the complete solution of the resonance theory of the dispersion of light.

The question of the absorption of acoustic vibrations was investigated for purely practical purposes, in order to find materials capable of providing the best acoustic insulation. But of particular interest is the work carried out in Lebedev’s laboratory by N. P. Neklepaev. In it the author investigates the absorption by air of short acoustic waves \((\lambda = 0.250\) and \(\lambda = 0.083\) mm.). The source of the sound vibrations is a spark discharge. To measure the wavelength a diffraction grating was used, and the intensity was determined by a pressure instrument. It turned out that the order of magnitude of the absorption \(A = c\lambda^{2}\) for short waves is the same as that given by theory, although somewhat greater than might be expected on the basis of calculation. The absorption coefficient \(c\) increases as the wavelength decreases, while \(A = c\lambda^{2}\) remains constant. Taking the data of this work, P. N. Lebedev draws the following conclusion: “In general outline, experiment and theory agree in showing that sound of medium pitch is not absorbed by air to any noticeable extent. For short acoustic waves this situation already becomes noticeable.” Assuming that the absorption \(A = c\lambda^{2}\) found by Neklepaev remains unchanged also for still shorter waves, P. N. Lebedev calculates “that distance, after traversing which the sound wave is weakened to one hundredth of its initial strength”; these distances are:

\[ \begin{aligned} \text{for } \lambda_{1} &= 0.8\ \text{mm.} \quad &\ldots\ldots&\ 40\ \text{cm.}\\ \text{” } \lambda_{2} &= 0.4\ \text{”} \quad &\ldots\ldots&\ 10\ \text{”}\\ \text{” } \lambda_{3} &= 0.2\ \text{”} \quad &\ldots\ldots&\ 2.5\ \text{”}\\ \text{” } \lambda_{4} &= 0.1\ \text{”} \quad &\ldots\ldots&\ 0.6\ \text{”} \end{aligned} \]

Here, says Lebedev, we approach the limiting values of short acoustic vibrations. That is, practically such a wave cannot propagate over any appreciable distance while retaining a noticeable intensity.

The question of determining the strength of sound in absolute measure has also, in recent years, received an exhaustive solution.

First of all, let us establish what we mean by the strength of sound in absolute measure. At the present time the strength of sound in absolute measure is usually understood as the amount of sound energy contained in a unit volume of the medium through which the sound propagates, or the so-called density of sound energy. We have already seen that the magnitude of the sound pressure on a reflecting wall can serve as a measure of the density of sound energy; the size of the reflecting wall on which the pressure is determined must be large in comparison with

wavelength, and since the wavelengths of tones of medium pitch are already very considerable (the wavelength of the tone \(do_3\), for example, is approximately 130 centimeters), the method can be applied to a freely propagating wave only for very high tones. Be that as it may, the sound-pressure method is a reliable means of determining the intensity of sound in absolute measure.

Methods have also been proposed for determining the intensity of sound based on transforming a sound oscillation into an oscillation of the strength of an electric current. The sound is received by a microphone, and the electric current is investigated in a telephone. The most original of these methods is the one proposed by Geindelgoffer. A sound wave falls upon an extremely thin gold leaf, and the adiabatic compression and expansion in the wave produce the effect of heating and cooling the leaf. This leaf is included in the circuit of a galvanic cell in series with the primary winding of a Ruhmkorff coil. As a result of the change in the temperature of the leaf, its electrical resistance changes, and a current of variable strength flows in the primary winding of the coil. The current induced in the secondary coil is then investigated galvanometrically. Although these methods may yield satisfactory results, they are nevertheless of little practical applicability because of the complexity of the arrangement, which may itself be a source of considerable errors, especially in absolute measurements.

The most universal and technically simplest method is the so-called Rayleigh disk. Rayleigh noticed that a plate placed in a medium through which a sound wave propagates is deflected, tending to stand perpendicular to the direction of propagation of the wave. The rotating forces are proportional to the intensity of the sound; consequently, the angle of deflection of the plate, suspended on a torsion thread, serves as a measure of the intensity of the sound. The explanation of the very phenomenon of rotation of the disk is as follows: it is known from hydrodynamics that if a plate is placed in a stream of liquid at some angle to the direction of the stream, then rotating forces act on the plate, tending to set it perpendicular to the direction of the stream. If the plate is suspended on a torsion thread or on a bifilar suspension, then the deflection, within the limits of small angles, is proportional to the kinetic energy of the stream. It is easy to see that when the sign of the stream is changed, i.e., when the direction of the stream is changed to the opposite, the direction of rotation does not change. Sound oscillations may be regarded as a stream of alternating direction. The velocity of the particles changes both in magnitude and in sign. As we have seen, the direction of rotation of the disk does not depend on the sign of the stream, while the magnitude of the deflection is proportional to the maximum velocity of the oscillating particles. If from the deflection of the disk we are able to calculate the maxi-

low velocity, then by this the absolute sound intensity is also determined for the propagating wave from the formula \(E=\frac{\mu v^2}{2}\), where \(\mu\) is the density of the medium and \(v\) is the maximum velocity of the oscillating particle. This method was proposed by Rayleigh as early as 1882, but was applied only for relative measurements. In 1891 Walter König derived a formula by means of which it was possible to determine the density of sound energy, provided one used a disk of infinitely small thickness, representing the limiting form of an ellipsoid of revolution with an infinitely small axis of rotation. The disk method, however, even after that was not used for a long time for absolute measurements. In 1908 the author of the present review published a work, carried out in P. N. Lebedev’s laboratory, in which he subjected to experimental investigation the applicability of W. König’s formula both to the case of an ellipsoid of revolution and to the case of a plate (disk). It turned out that in the case of the ellipsoid König’s formula is satisfied within the limits of observational error; in the case of a disk of finite thickness, as was to be expected, a correction must be made, calculated on the basis of an empirical formula.

The investigation itself was carried out in the following way: an ellipsoid of revolution or a disk, on a thin glass rod bearing a mirror, was introduced into a cylinder oscillating together with the stem of a large electromagnetic tuning fork. The amplitude of the cylinder was measured directly, and from it the energy density of the vibrations of the air located inside the cylinder was determined. On the other hand, the same density was calculated from the deflections and dimensions of the disk or ellipsoid introduced into the cylinder. As has already been said, it proved entirely possible to use Rayleigh’s disk for absolute measurements.

For measuring sound intensity of medium pitch, such as, for example, the intensity of the human voice, an instrument—a phoneter—was constructed in the following way: on a high stand (see Fig. 1) \(F\) there is fixed a copper disk \(S\), which serves as the base for two supports \(T_1\) and \(T_2\), carrying a second copper disk. On a thin quartz thread is suspended a galvanometer mirror \(R\) (diam. 3 mm), to the rear side of which a small magnet is glued. By means of the movable magnet \(M\) one can (by raising or lowering the magnet \(M\)) impart to the mirror a greater or smaller period of oscillation and set the mirror at the required angle (by rotating the same magnet about the vertical axis). This mirror serves as Rayleigh’s disk; by means of it the angle of deflection of the disk-mirror itself is also measured. At a distance of two meters from the disk, for loud singing

Fig. 1.

the energy density is found to be up to \(2.0\cdot 10^{-4}\) erg per cubic cm. Assuming that sound propagates equally in all directions, one can calculate what energy is radiated by a person singing loudly in the form of sound vibrations. For this quantity we obtain approximately \(10^{-5}\) horsepower. In other words, 100,000 singers, singing loudly at the same time, radiate energy in the form of a sound wave equal to the energy of an engine with a power of one horsepower. Knowing the energy density, it is easy to calculate what, for example, will be the amplitude of the particles for the tone \(d o_3\), and for the energy value \(E = 2.0\cdot 10^{-4}\) erg per cubic cm, the strength of sound that we perceive as a sound of very great intensity. The result is approximately \(A = 0.00085\) cm. The unexpectedly small value of the amplitude gives the impression of a strong sound.

The author of the review also examined other methods, namely: the method of sound pressure and the so-called method of Wien’s vibration manometer. All the methods give concordant results, but the most convenient and quite sufficiently sensitive is nevertheless Rayleigh’s disk method.

According to the design of Prof. P. N. Lebedev, on the principle of Rayleigh’s disk, a very convenient portable phonometer was constructed, in which the disk is replaced by a long mirror plate (the plate is 15 mm long, 3 mm wide, and as thick as a cover glass). With the aid of a damper, the oscillations of the system are made aperiodic. The convenience and universality of the method is characterized by the fact that, following the publication of the investigations mentioned, a whole series of works appeared in which the authors, for determining the strength of sound, used precisely Rayleigh’s disk.

At the present time the question of measuring the strength of sound in absolute measure may be considered quite exhausted.

Many works have been devoted to the question of investigating the timbre, or composition, of sound. A considerable number of authors use for this purpose the transformation of a sound oscillation into an oscillation of electric current, and then record the oscillations of the latter. Here, too, the sound is received by a microphone, and the change in current strength is recorded by an oscillograph (Divo, Charbonnel, and others).

One of the works of this series (Hochstetter) is especially original in its arrangement: the alternating current of the microphone flows through a spiral, inside which is placed a bar of glass containing a considerable quantity of lead. The optical properties of such glass change in a magnetic field, with the appearance of double refraction and its change depending on the change in the strength of the field being observed. The glass bar is placed between crossed Nicols. When double refraction appears in the bar, light begins to pass through the analyzer, and the more so the stronger the current in the spiral.

In another series of works the authors use the method of photographing the vibrations of a membrane (a plate reproducing sound vibrations) by means of an apparatus proposed by the physiologist Hermann, which enabled him to record the sounds of the human voice. The bottom of the horn (see Fig. 2) \(R\) is a resilient plate (cork, thin glass, mica, etc.); a pin \(h\), glued to the plate, rests against the mirror \(M\), which rotates about the point \(C\). A ray of light from the source \(S\) falls on the mirror \(M\) and, after being reflected from it, falls on the rotating cylinder \(B\), over which a sensitive film is placed. When the membrane vibrates, reproducing the sound vibration incident upon it, the mirror rotates, and the reflected ray \(MB\) glides over the rotating drum, leaving on the photographic film a record—the so-called phonogram. The resulting curve is then subjected to analysis.

Fig. 2.

It is precisely by this method that the accompanying phonograms were obtained (see Fig. 3), showing curves for the vowel \(A\), sung into the horn. Curve 1) for the tone \(la_1\); 2) for the tone \(re_2\); 3) for the tone \(fa_2\); 4) for the tone \(la_2\), and 5) for the tone \(do_3\).

Fig. 3.

Phonograms of the human voice show that curves with a clearly expressed period are obtained only with singing and with slow pronunciation of words. It can also be seen from the phonograms that each vowel is characterized by a definite overtone pitch; its pitch changes little when the pitch of the fundamental tone changes. Such an overtone, characteristic of a given vowel, is called a formant. Helmholtz, in studying the composition of vowels by means of a set of resonators, had already established the presence of these formants. Now this circumstance is once again confirmed. Proctor Hall discovers the same formants for nasal consonants.

All methods of registering vibrations by means of a vibrating membrane (both the microphone and Hermann’s method) suffer from the fact that what is actually registered is the vibration of the membrane itself, and in each individual case we cannot be entirely certain that the membrane accurately repeats the vibrations sent by the sound source. In order that the membrane reproduce the vibrations as accurately as possible,

…its own tone must be high in comparison with the tones that it repeats.

Free from the indicated defect is the method of direct photographing of sound vibrations, used by Fallet and Zuder. The sound wave, propagating from a spark discharge, is illuminated by an electric spark, and the shadows produced by the non-uniform density of the air in the wave are fixed photographically. This method, of interest for very short and strong vibrations propagating from a spark discharge, is not applicable to tones of medium pitch, whose composition is what chiefly interests us.

Also free from the indicated defects is Edwards’s method. This is a modified method of investigating the composition of sound by Helmholtz. A set of resonators, tuned in a sequence of harmonic overtones, is used; but instead of the ordinary Koenig flames, by whose vibrations one judges which of the resonators responds to one of the overtones of the fundamental tone, a disk is suspended, according to Rayleigh, in front of the aperture of each resonator, and when the resonator is excited, the corresponding disk is deflected from its position of equilibrium. Such a modification is valuable in that, from the deflection of the disks, we can judge not only the qualitative composition of the sound, but also answer precisely the question of the relative strength of the overtones of the given tone.

A very large number of works is devoted to the investigation of the tone of various musical instruments and to the investigation of the vibrations of the separate parts of an instrument. More often than others we meet the name of Barton, who, in collaboration with a whole series of other investigators, examined in the greatest detail the vibrations of the strings of the monochord and the violin, the vibrations of the bridge, the body of the instrument, and the air enclosed within it. The recording of the vibrations is carried out photographically, and the dependence is investigated of the form of vibration on the various kinds of excitation of the string’s vibration and on the force of pressure of the bow. The vibrations of the body of the violin and of the air inside it differ considerably from the form of vibration of the string. In the investigation of the vibration of the bridge (Raman), there is obtained, at first glance, the strange circumstance that the bridge generally repeats the vibrations of the string, but shows the greatest amplitude for vibrations with a number twice as large as the fundamental number of vibrations of the string; but this circumstance is evidently easily explained by the fact that the bridge inclines forward through the greatest angle each time the string is farthest from its position of equilibrium, and there are two such positions for one fundamental vibration of the string. Among the works devoted to the investigation of the tone of the violin, the work of Hewlett is of interest; he, using…

by Edwards’s method (resonators with Rayleigh disks), attempts to establish the composition of an ideal violin sound and determines, if not the ideal composition, then at any rate the composition of the sound of first-class instruments.

In studying the vibrations of piano strings (Berry), it has been possible to establish that, in order to obtain the best composition of the vibration, it is necessary to excite the string by the blow of the hammer at a quite definite place on it, namely: at one ninth of its length from the point of attachment. Piano makers arrived at the same result by a purely empirical route.

For the resolution of the general question of the cause of the different timbre of different musical instruments, interesting results are found in Goldhammer. He studies the composition of the sound of wooden wind instruments and finds that each type of instrument is characterized by a peculiar formant, i.e. an overtone of definite pitch which accompanies all the tones of the given instrument. Thus this question is resolved in the same way as the question of the formation of vowels.

To this same series of works one must also assign the investigation of von Nies, who studied the composition of the sound of the bells in Amsterdam Cathedral. The author establishes the dependence of the pitch of the principal tone on the manner of excitation. When the concave side is struck, the principal tone is an octave higher than when the convex side of the bell is struck. The principal tone is always accompanied by a large number (up to seven) of overtones and sometimes by one lower tone. Immediately after the blow, the first overtone sounds most strongly, and only later does the principal tone become predominant.

Also of interest are attempts to investigate experimentally the acoustic properties of rooms. Exner constructed for this purpose a special apparatus, the “Acoumeter,” by means of which the strength of sound at different points of a given room is determined from the resistance that must be introduced into the telephone circuit in order to render a definite sound inaudible. A shot from a child’s pistol was used as the source of sound. In the works of Sabine and Marage it is established that, in a room good in the acoustic sense, the sound produced must be sustained (reverberate) for a definite time. For piano playing Sabine sets this time at 1.1 seconds, while for the vowels of human speech Marage gives a time from 0.5 to 1.0 seconds, different for different vowels. This last result has very great practical significance, since it is known that, in advance, when building an auditorium or concert hall, it is very difficult to foresee what the acoustics of this room will be. If the hall proves unsuccessful in the acoustic respect,

then, by regulating the reverberation time (by placing special resonators in the hall, or, conversely, curtains that absorb sound), it is apparently possible to correct this shortcoming.

In conclusion, I shall point to one question, newly raised, from the field of physiological acoustics. This is the question of why an observer can not only estimate the intensity of a sound, its pitch and timbre, but can also determine the direction from which the sound wave comes. This question was raised by Rayleigh, and he also gives the most satisfactory answer to it. For tones that are not too high, apparently, we judge the direction of propagation of a sound wave by the difference of phase with which the wave reaches one and the other ear of the observer. This question has given rise to a considerable literature, but one may think that if, for high tones, another cause can also be indicated, such as, for example, a difference in intensity, then for tones of medium pitch the solution of the question given by Rayleigh is the most probable.