Recent Advances in Applied Acoustics*

F. Trendelenburg, Berlin**

Sound Recording. Sound Films

The recording of sound processes for the purpose of their subsequent reproduction can be carried out by various methods. In the technology of sound cinema the principal methods are: electromechanical recording of sound on a disc and electro-optical recording on film. In addition, sound processes can also be recorded electromagnetically on steel wire. Each of these methods has its advantages and its disadvantages, and therefore the choice of one method or another is determined by the goal set.

Recording on a disc^132 is distinguished by its ease of operation. The acoustic qualities of modern records have attained considerable perfection. A record transmits components up to 6000 hertz sufficiently well. The level of the interfering background in recording on wax is relatively low; despite the fact that the maximum amplitude of displacement in transverse recording scarcely reaches 0.1 mm, the intensity can vary in the ratio 1:100, i.e., at an amplitude of about 0.01 mm the recording can still be reproduced satisfactorily. However, from the standpoint of cinematographic requirements, disc recording has the disadvantage that cutting out individual parts of the phonogram during editing is poss—

* For the beginning see Uspekhi fizicheskikh nauk, XI, 4, 1931; XII, 1, 1932; XII 2–3, 1932.

** F. Trendelenburg, “Jahrbuch d. drahtl. Tel. u. Tel.,” Zs. f. Hochfrequenz, 38,5, 1931; translated by N. D. Ershova.

can be done only by the rather complicated method of subsequently transferring the phonogram to another disk.

Photographic sound recording133 can be carried out in two ways. In recording by the variable-density method (formerly the only one used), an instantaneous value of the pressure in the sound field corresponds to a definite photographic density of the phonogram

Fig. 64. Schematic diagram of recording by the variable-density method. F—film, L—lens, M—microphone, Tr—transformer.

(Fig. 64). In recording by the variable-width method, which has recently become widespread, the instantaneous sound pressure corresponds to the width of the exposed part of the phonogram (Fig. 65). The first method of recording imposes serious requirements on the photographic process: only under quite definite development conditions, which we shall discuss below, can nonlinear distortions be reduced to a minimum. As was clarified in detail when considering V. Yanovsky’s work134, it is precisely the struggle against nonlinear distortions that is of the greatest importance.

The frequency range transmitted in recording by the variable-density and variable-width methods is approximately the same. The upper limit of the frequency range, at a film speed of 24 frames per second and an image-slot width of 0.01 mm, lies near 12,000 hertz. With regard to the range of transmitted intensities, however, the two methods differ greatly from one another. In recording by the variable-density method, the sound intensity can

Fig. 65. Schematic diagram of recording by the variable-width method.

vary only in the ratio \(1:20\); greater modulation depth is impossible, since the transparency of the unexposed portions of the phonogram is only 20 times greater than the transparency of the portions with maximum density*.

* One cannot fail to note the error made here. The range of transmitted loudnesses is determined not by the interval between the maximum and minimum transparency of individual portions of the phonogram, but by the interval between the maximum and minimum amplitude of the change in transparency on both sides of some mean value (Ruhetransparenz). Both in recording by the variable-density method and in recording by the variable-width method, the minimum amplitude of the reproduced sound is determined by the level of the interfering background; in both cases modern apparatus makes it possible to vary the loudness over a range of approximately 25 db, which corresponds to an intensity ratio of approximately \(1:300\). Cf. R. Schmidt, Filmtechnik, 5, 194, 1929. — Ed. note.

With recording by the variable-width method one can achieve a greater range of intensities* (especially if one uses the device of masking the unexposed part of the phonogram). In comparison with gramophone recording, recording on film has the disadvantage that wear of the latter is considerably greater; a film that has passed 20 times through projection apparatus is still quite suitable with respect to visual perception, whereas sound reproduction already suffers to a considerable degree from the interfering background noise1. In this respect the intermittent motion of the film, effected by the Maltese-cross system, which is necessary for frame projection, has an especially unfavorable effect. Separation of the frames and the phonogram, when copying them onto separate films, appears expedient from this point of view; in this case the phonogram can move uniformly through the whole apparatus. Under these conditions a sound film can be reproduced several hundred times before the interfering noise becomes strongly noticeable.

Fig. 66. Schematic diagram of magnetic sound recording.

When recording on steel wire[^136] (Fig. 65), the upper frequency limit lies lower than with recording by the methods described above. With a still practically attainable

RECENT ADVANCES IN APPLIED ACOUSTICS

With a slit width of 0.2 mm, transmitting a frequency of 5000 hertz requires a wire speed of 4 m/sec. The intensity can vary only within comparatively narrow limits, since the region of linear dependence between the magnetomotive force and the magnetization is very small; the intensity can vary only in the ratio 1 : 20. The minimum intensity level, owing to the Barkhausen effect, is comparatively high. In practice, the advantage of this kind of recording is that it can be listened to immediately and, without any particular difficulty, erased again. The magnetic recording method is used chiefly for dictaphones.

We would go far beyond the limits of the present survey if we were to consider the numerous individual technical achievements that have made possible the rapid development of various methods of sound recording. We must confine ourselves to examining only those works that are directly connected with various electroacoustic problems.

As in other areas of electroacoustics, methods for the objective investigation of the qualities of apparatus relating to sound recording were developed with special attention.

Buchmann and Meyer ^137 developed a method for investigating gramophone records that makes it possible easily to determine the amplitude of the velocity during recording on a disc. Since recording is carried out in such a way that the amplitude of the pressure in the sound field corresponds to the amplitude of the velocity of the cutter, measurement specifically of the velocity amplitude is of very great importance. Direct proportionality between the velocity amplitude and the pressure amplitude holds for almost the entire range of transmitted frequencies; the only exceptions are very low frequencies (below 200 hertz) and very high frequencies (above 5000 hertz), since at very low frequencies capture of a neighboring groove is possible, while at very high frequencies the radius of curvature of the recorded curve becomes too small.

Buchmann and Meyer used, for measuring the ampli-

hence the magnitude of the velocity is found from the phenomenon of reflection of light when a plane-parallel beam of light falls on a gramophone record. Let, in Fig. 67, \(P\) denote the point at which the observer’s eye is located; on the groove of the recording (assumed, for simplicity, to be sinusoidal) there falls a parallel beam of light in the direction indicated by the arrow. The eye then sees a certain number of luminous points, corresponding to those points of the curve at which the curvature is so great that, upon reflection, the parallel rays are directed to the point \(P\). The number of luminous points is limited by the fact that beyond the extreme points of the phonogram \(B\) and \(D\) there are no such places at which the tangent to the curve would be so steep that reflection to the point \(P\) would be possible. Beyond the points \(B\) and \(D\), reflection is possible only in those directions which pass beyond the point \(P\). The points \(B\) and \(D\) correspond to the points of greatest steepness of the curve; they are points of inflection. Since the steepness of the curve is expressed through the derivative, the steepness at the points of inflection is a measure of the amplitude of the velocity. The steeper the steepest parts of the phonogram, the greater the amplitude of the velocity and the greater the distance between the points \(B\) and \(D\); the width of the luminous row of points is proportional to the amplitude of the velocity. It will be shown below that this method is applicable not only to sinusoidal curves recorded along a straight line, but also to curves recorded along a circumference, as is the case in gramophone records; the magnitude of the radius of the circumference plays no role here, since the diminution of the row of luminous points owing to the decrease of the radius of the circumference as one approaches its center is compensated by an increase in the steepness of the most

Fig. 67. Reflection of light from a sinusoidal phonogram.

of steep points of curves \(i\), which occurs as a result of the decrease in wavelength on approaching the center of the disk.

When the phonogram is in motion—for example, when the disk is rotating—the luminous points merge for the observer into a bright band. The width of the bright band, according to what has been stated above, must be a direct measure of the amplitude of the velocity during recording. In Fig. 68 is shown the reflection from a gramophone disk on which a tone of 435 hertz had been recorded with different amplitudes (related to one another as \(1:2:4:8:16\)). In Fig. 69 is given the frequency characteristic of the velocity amplitude of the recorder cutter; the frequency was varied continuously from high frequencies (the outer edge of the disk) to low ones (the inner edge). The resonance of the cutter at about 6400 hertz is quite distinctly noticeable. Fig. 70 shows a recording of an organ; the changes between piano and forte are clearly visible. It should be noted that with such observations it is easy to establish the absolute value of the amplitude of the curve.

Fig. 68. Tone of 435 hertz with various amplitudes.

Fig. 69. Frequency characteristic of a gramophone recorder.

Meyer and Just\(^{138}\) investigated the frequency curves of electromagnetic adapters (Tonabnehmer). Tests of adapters

can easily be performed with test records having tones of constant displacement and velocity amplitude[^139]; in doing this the pickup works into a valve voltmeter, by means of which the emf developed by the pickup was determined. In Figs. 71a, b, c the frequency characteristics of various pickups are given. Pickup I has a comparatively even frequency characteristic, but the maximum at about 5000 cycles indicates that it transmits the comparatively high components of needle noise rather strongly. The characteristic of pickup II falls steeply, beginning at 2500 cycles. Pickup VI has a clearly expressed resonance near 1500 cycles.

Fig. 70. Recording an organ on a disc.

In the work mentioned above there are also data on the distortion factor of the pickups. The distortion factor of pickup I at very low frequencies (about 150 cycles) is 20%; the distortion factor of pickup II at the same frequency is 5%, which is quite acceptable, especially if one recalls that this figure includes the nonlinear distortions of the recording itself on the disc, and that the frequency 150 cycles practically lies at the lower boundary of the frequency range transmitted by the disc. At higher frequencies the distortion factor proves to be very small.

Fig. 71a. Frequency characteristics of pickups.

In the works of Gofer, Setton, Kofs, and Frederick[^140], numerous characteristics of various adapters are given.

Fig. 71b.

Fig. 71c.

In connection with the work of Maxfield and Harrison, as well as Kellogg,^141 Forstmann^142 clarified the properties of the reproducer on the basis of an electrical equivalent substitution circuit; in doing so he established the conditions for a minimum of frequency and amplitude distortions. It turns out that the requirements concerning dependence on frequency and on amplitude partly contradict one another. Thus, for example, in order to transmit high frequencies without attenuating their loudness, it is necessary for the needle to be as stiff as possible, but then it is difficult to damp its natural oscillations; when excessively tight rubber gaskets are used, additional restoring forces arise that depend on frequency. Thus an improvement in the frequency response is possible only at the cost of increasing nonlinear distortions. The theory of the reproducer was also considered by Seton,^143 who clarified in particular detail the conditions under which the reproducer needle jumps from one groove into the neighboring one.

Fig. 72. Frequency response of a recorder.

The works of Frederick, and also the works of Elmer and Blattner,^144 give indications on the structural design and functioning of electromagnetic recorders. Fig. 72 gives the frequency response of a recorder of a modern type. In the region between 250 and 6500 hertz the deviations of the response amount to only a few percent. Frederick’s work also contains data concerning the shape of the cross-section of the groove and the shape of the cutter used for recording.

Buchmann and Meyer^145 investigated the frequency range of noise

needle. The noise of the needle was observed on a record containing only unmodulated grooves. The acoustic spectrum was determined by Grotmacher’s probing-tone method^146. Figure 73 gives the acoustic spectrum of needle noise at the normal number of revolutions. The distribution of the noise frequencies at the outer edge of the record, at its middle, and at the inner edge is somewhat different. At the inner edge the high frequencies are less noticeable, since here the relative velocity of the needle with respect to the record is small.

Fig. 73. Acoustic spectrum of needle noise at the normal number of revolutions.

At the outer edge of the record, the amplitude of the oscillatory velocity of the needle, beginning with 400–800 hertz, is proportional to its velocity; consequently, the amplitude of the needle displacement for the individual frequencies is constant, amounting to approximately \(3 \cdot 10^{-9}\) cm. At a frequency below 400 hertz we have the opposite picture: as the frequency decreases, the noise increases. The appearance of low components is due to mechanical shocks; shocks of this kind may arise both from the driving mechanism and, possibly, from the reproducing device. In addition, it is possible that the causes of the distortions lie in the waviness of the surface of the gramophone

plate, which is easily noticed by observing the reflection from the plate under normal incidence of light upon it.

The distortions that arise with electro-optical methods of recording have been studied in considerable detail. The distortions may be as follows: 1) nonlinear distortions, such as, for example, those arising as a result of the nonlinearity of the optical effect (Kerr cell, photoelement, distortions associated with development and with the slit), 2) distortions, which include the attenuation of high frequencies owing to the finite width of the slit.

Fig. 74. Characteristic of a Kerr cell.

Data on the physical phenomena connected with the operation of the Kerr cell and the photoelement, and on distortions caused by these elements of the system, are available in the works of Lichte 147, Lichte and Tischner 148, and Gehlhans 149.

Fig. 74 gives the characteristic of a Kerr cell with nitrobenzene. By choosing a bias (constant) voltage of 450 V, we obtain for the alternating voltage—up to an amplitude of 1500 V—a linear dependence between the effect and the applied voltage; in this region the distortion factor in recording with a Kerr cell is negligibly small. The distortion factor of the photoelement can also be made very small. The greatest difficulty is presented by reducing the nonlinear distortions that arise with improper development 150.

The relationship between the density of the developed film and the logarithm of its exposure is given by the so-called characteristic curve; from it the properties of the photographic emulsion can also be determined. By density here is meant the logarithm of the ratio of the intensity of the incident \((J_p)\) to the intensity of the transmitted \((J_l)\) light, and by exposure—the product of the light intensity by the time of its action. At small exposures the characteristic curve runs horizontally, i.e., the density does not depend on

Fig. 75. Characteristic curve.

exposure; at large exposures the curve rises and then, over a comparatively broad region, runs rectilinearly. This straight-line part can be described by the following equation:

\[ S = \gamma \lg (J \cdot t), \]

where \(\gamma\) is the slope of the curve.

The value of \(\gamma\) depends on the thickness of the emulsion layer, as well as on the composition and temperature of the developer. This relation, for the case when the exposure time, owing to the uniform motion of the film, is constant, can be written as:

\[ S = \mathrm{const}\,\lg J^\gamma. \]

Denoting the slope, exposure, etc. of the negative by the index \(N\), and the same quantities for the positive by the index \(P\), we have for

rectilinear portions of the characteristic curves of the negative and the positive:

\[ S_N=\mathrm{const}_N\cdot \lg J_N^{\gamma_N}, \]

\[ S_P=\mathrm{const}_P\cdot \lg J_P^{\gamma_P}. \]

Between the intensity of the light transmitted by the positive to the photoelement \((I_{Ph})\), and the intensity of the light incident on the negative \((I_N)\), the following relation holds:

\[ J_{Ph}=\mathrm{const}_{Ph}\cdot J_N^{\gamma_N\gamma_P}. \]

This relation shows that a linear dependence between the intensity of the light incident on the photoelement and the initial intensity of the light that acted on the negative can exist only when

\[ \gamma_N\gamma_P=1. \]

Fig. 76. Correct transmission of the curve shape at \(\gamma=1\).
Distortion of the curve shape at \(\gamma=2\).

This is the condition derived by Goldberg \(^{151}\).

When there are deviations from this condition, nonlinear distortions become very noticeable.

Fig. 76 shows the distortion of the form of a harmonic oscillation at \(\gamma=2\); the drawing shows with extreme clarity how large the nonlinear distortions are even with such deviations from the Goldberg condition.

Frieser and Pistor \(^{152}\) point out that, depending on whether the blackening measurements are made in diffuse or directed light, different results are obtained (the Callier effect). When reproducing a sound film, the phonogram is illuminated by a directed beam of light, while the characteristic is determined, for the most part, in dif-

fused light, for example by means of Goldberg's densometer. Precise measurements showed that the actual value of the product \(\gamma_N\cdot\gamma_P\) is approximately 1.18 times greater than that obtained from the characteristic curve taken in diffuse light. Thus nonlinear distortions must become noticeable even when the product \(\gamma_N\cdot\gamma_P\) appears to be exactly equal to unity. The error caused by the Callier effect is all the more appreciable because, for practical reasons, values of \(\gamma_N\cdot\gamma_P\) exceeding unity are often allowed.

In the following table the values of \(\gamma_N\cdot\gamma_P\) measured in diffuse and in directed light, and the corresponding values of the distortion factor, are compared:

The linear distortions of the Kerr condenser, as well as of the photocell, are extremely small: up to \(10^9\) hertz both systems operate practically without distortion.

Considerable difficulties are caused by the optical slit, both with respect to nonlinear and to linear distortions. Defects of the frequency characteristic caused by the optical slit are analyzed in detail in Joachim's work \(^{15}\).

For the luminous flux passing through the film, when recording by the variable-density method, the following equation holds*:

\[ A = 2A_0 \cdot b + a_1 \frac{\gamma}{\pi}\sin 2\pi \frac{b}{\lambda}\sin 2\pi \frac{l}{\lambda}, \]

* This equation is also valid for the case of recording by the variable-width method—see the cited work of Joachim. Ed. note.

Fig. 77. Dependence of the amplitude of the light current on the height of the tone.

Fig. 78. Drop in intensity for slits of different widths.

where \(A_0\) is the mean luminous flux, \(2b\) is the width of the slit, \(\lambda\) is the wavelength of the recording, and \(l\) is the coordinate measured along the length of the phonogram. For very small \(b\), the sine may be replaced by its arc; then we have:

\[ A = 2 A_0 a_1 2b \sin 2\pi \frac{l}{\lambda}. \]

Thus, for very narrow slits, the periodically varying component of the luminous flux is directly proportional to the amplitude of the transparency of the film; with a sufficiently narrow slit, the amplitude of the luminous flux does not depend on frequency.

Fig. 79. Dependence of the clear factor on frequency for various positions of the slit; \(s = 30\,\mu\).

As the wavelength of the recording is decreased, i.e., as the frequency increases, this approximation becomes inadmissible, and the amplitude begins to depend on frequency.

Figs. 77 and 78 clearly show the properties of various slits. It turns out that the amplitude of the luminous flux is equal

zero when \(b = \dfrac{\lambda}{2}\), i.e., when the slit width \(2b = \lambda\).

This phenomenon is clearly noticeable on the curve \(2b = 32\) (Fig. 78). With a further increase in frequency, the amplitude becomes negative, i.e., the phase of the oscillation is shifted by \(180^\circ\) relative to the phase at the center of the slit. It should be noted that in practice slits about \(20\ \mu\) wide are most commonly used; in this case the intensity at 7000 cycles drops by 70% (Fig. 79). The above considerations are also valid for recording by the variable-width method.

Fig. 80. Distortion factor in reproducing a variable-width type phonogram with a nonuniformly illuminated slit.

Distortions may also arise as a result of the oblique position of the slit of the reproducing apparatus relative to the slit of the recording apparatus. Friser and Pistor investigated the distortions caused by the oblique position of the slit.

For the ratio \(\dfrac{A'}{A}\) of the amplitude with the oblique position of the slit to the amplitude with the correct position, the following equality holds:

\[ \frac{A'}{A}=\frac{\lambda}{\pi h_1 \tg \alpha}\sin \frac{\pi h_1 \tg \alpha}{\lambda}, \]

where \(h_1\) is the width of the image and \(\alpha\) is the angle between the slits of the reproducing and recording apparatus.

As final results, we note that with a deviation of only \(0.5^\circ\), the intensity at 10,000 cycles drops by 35%, i.e., the attenuation is quite clearly noticeable. In contrast to recording by the variable-density method, in recording by the variable-width method

as a result of improper adjustment, nonlinear distortions arise. From the results of the work of Friser and Pistor we shall reproduce here a diagram giving the dependence of the clip factor on frequency for different positions of the angle between the slits.

In recording by the variable-width method, nonlinear distortions also arise as a result of nonuniform illumination of the slit. The calculation can be carried out on the basis of the diagram in Fig. 80, where curve a is constructed on the assumption that the intensity falls symmetrically from the middle toward the edges, and curve b on the assumption that the intensity falls linearly from one edge to the other.

LITERATURE

1. On the technique of gramophone recording, see the following articles:
   E. W. Kellog, Journ. Amer. Inst. El. Eng., 46, 1041, 1927;
   L. Hajek, Monatsschrift für Ohrenheilkunde und Laryngo-Rhinologie, 62, 808, 1928;
   L. A. Elmer and D. G. Blattner, Trans. Mot. Pict. Eng., 13, 227, 1929;
   H. A. Frederick, Bell System Techn. Journ., 8, 159, 1929;
   E. Lübcke, Z. d. V. D. I., 73, 333, 1929;
   H. Vogt, Kinotechnik, 12, 385, 1930;
   P. Hatschek, Kinotechnik, 12, 302, 332, 361, 1930.

2. On photographic recording, see the following works:
   F. Lüschen, E. T. Z., 50, 693, 1928, 1929;
   H. Lichte and H. Tischner, Jahrb. Forsch.-Inst. A. E. G., 1, 13, 1930;
   C. Kemna and H. Kluge, Siemens-Jahrb., 4, 361, 1930. From the last work a number of the above-mentioned indications and Figures 64 to 66 have been borrowed.

3. See note 9, “Advances in Physical Sciences,” Vol. XI, Issue 4, 1931.

4. See especially: Homer G. Tasker, Electronics, 273, 1930;
   G. Sandvik, Kodak Scientif. Publ., 12, 260, 1928;
   J. I. Crabtree, O. Sandvik and C. I. Ives, Kinotechnik, 12, 330, 320, 1930 (a detailed abstract on the possibility of reducing film wear by suitable treatment, such as, for example, paraffining).

5. C. Still, E. T. Z., 51, 449, 1930.

6. G. Buchmann and E. Meyer, E. N. T., 7, 147, 1930.

7. E. Meyer and P. Just, E. N. T., 6, 264, 1929.

8. Determination of the velocity amplitude of measuring gramophone records can be performed either by the method indicated above, or (as in the work under consideration by Meyer and Just) by a method consisting in playing gramophone records with tones of different pitch at different speeds, so that the frequency of the force actually applied to the adapter remains constant; in this case the properties of the adapter itself are excluded.

1. A. Hofer, “Funkbastler,” 7, 621, 1930; G. W. Sutton, “Journ. Inst. El. Eng.,” 68, 566, 1930; A. Kofes, “Funkbastler,” 6, 621, 1929; H. A. Frederick, “Bell System Techn. Journ.,” 8, 159, 1929. See also the article “Grammophone Pickups tested,” “Wireless World,” 26, 321 and 356, 1930.

2. J. P. Maxfield and H. C. Harrison, “Bell System Technical Journ.,” 5, 493, 1926; E. W. Kellog, “Journ. Amer. Inst. El. Eng.,” 46, 1041, 1927.

3. A. Forstmann. “E. N. T.,” 7, 426, 1930.

4. G. W. Sutton. “Journ. Inst. El. Eng.,” 68, 566, 1930.

5. H. A. Fredrick, “Bell. System. Techn. Journ.,” 8, 159, 1929; L. A. Elmer and D. G. Blattner, “Trans. Soc. Mot. Pit. Eng.,” 13, 227, 1929.

6. E. Meyer and G. Buchmann, “E. N. T.,” 8, 218, 1931.

7. See “Uspekhi fizich. nauk,” XI, 1931, note 9.

8. H. Lichte, Photographische Probleme des Tonfilms, revised by F. Hehlgans, “Kinotechnik,” 12, 615, 641, 1930.

9. H. Lichte and H. Tischner, “Jahrb. Forsch.-Inst. A. E. G.,” 1, 13, 1930.

10. F. Hehlgans, “Kinotechnik,” 12, 615, 641, 1930 (an exhaustive work on Kerr-condenser recording. See also E. F. Kingsberg, “Rev. Scient. Inst.,” 1, 22, 1930).

11. On this question, in addition to the works indicated in notes 16 and 17 (“Uspekhi fizich. nauk,” XI, 4, 1931), see the article by J. Eggert, Über die photographischen Erfordernisse des Tonfilms, “Kinotechnik,” 12, 549, 1930. On characteristics, see the abstract of the works of L. A. Jones and O. Sandvik, “Kinotechnik,” 12, 216, 1930.

12. Borrowed from the work of J. Eggert. “Kinotechnik, 12, 549,” 1930. The cited work also contains a description of an apparatus monitoring the processes of exposure and development, the “Agfa-Gammameter.”

13. H. Frieser and W. Pistor, “Kinotechnik,” 12, 601, 1930; see also Küster and R. Schmidt, “Kinotechnik,” 12, 602, 1930.

14. H. Joachim, “Z. f. techn. Phys.,” 11, 168, 1930.

15. H. Friser and W. Pistor, “Z. f. techn. Phys.,” 12, 116, 1931.

1. This assertion is hardly correct.—see the preceding footnote. Ed. note. ↩