RECENT ADVANCES IN APPLIED ACOUSTICS*

F. Trendelenburg, Berlin

Contents

I. Introduction.
II. Methods of measurement.
    1. Sound analysis.
    2. Compensation methods for the exact determination of the phase and amplitude of periodic pressure oscillations.
    3. Other methods for determining quantities characterizing the sound field. Measurement of the acoustic power of a sound emitter. Acoustic measurements in rooms.
III. Sound emitters and sound receivers.
    1. Sound receivers.
    2. General questions concerning electrical sound generators.
    3. Musical instruments and their sound.
IV. Hearing and speech.
V. Architectural acoustics and room acoustics.
VI. Sound recording. Sound films.

I. Introduction

In 1926 and 1928 the author published review articles on questions of acoustics. The first of these articles was limited to the field of sound analysis, which at that time, owing to the introduction of precise physical methods, was undergoing considerable development. The second review² covered a somewhat broader field: the most recent acoustical and especially electroacoustical work. In the present article the order of presentation has been somewhat modified; in addition, questions of sound recording and the technology of sound cinema, which in recent times have received

* Z. Hochfrequenz, technik, 1931. Translated by N. D. Ershova.

...of great technical and economic significance have been set apart in a special section. In the last two years acoustic research has developed greatly. The interest shown in acoustics on all sides is confirmed by the fact that in the work program of the Hertz Institute[^3] a large place was assigned to acoustic investigations. Within the limits of this condensed review article it is impossible to cover all work in the various bordering fields of acoustics,[^4] and therefore we shall confine ourselves to considering only those works that are of significance for applied acoustics.

II. Methods of Measurement

1. Analysis of Sound

In the field of methods of measurement, methods of automatic sound analysis have been considerably improved. E. Meyer[^5] gave a particularly simple method of automatic analysis, also applicable for determining the nonlinear distortion of microphones. A carbon microphone (Fig. 1) is connected in an arm of a bridge, the remaining arms of which are ohmic resistances \(W_1, W_2, W_3\). Through the carbon microphone there is passed not a direct current, as usual, but an alternating current. If the alternating current is represented in the form \(J \sin 2\pi s t\), and if a sound wave of frequency \(p\) (which, for simplicity, we shall take to be sinusoidal) falls on the microphone, then the microphone experiences resistance oscillations of the form \(2R \sin 2\pi p t\), and the voltage on the microphone will be:

Fig. 1. Automatic analysis of sound with the aid of a carbon microphone.

\[ E = (R + \Delta R \sin 2\pi p t) J \sin 2\pi s t, \tag{1} \]

where \(R\) is the constant component of the microphone resistance. Equation (1) may be transformed as follows:

\[ E = JR \sin 2\pi s t + \frac{J\Delta R}{2}\cos 2\pi(s-p)t - \frac{J\Delta R}{2}\cos 2\pi(s+p)t. \tag{2} \]

In performing sound analysis, the frequency \(s\) (the test frequency, Suchfrequenz) of the alternating current passing through the microphone is made to traverse the entire range of sound frequencies.

Using alternating-current instruments tuned to a low frequency, one measures the strength of the difference tone of frequency \((s-p)\), which is proportional to \(\Delta R\), if the amplitude of the current \(J\) is constant over the whole frequency range and consequently proportional to the amplitude of the sound wave of frequency \(p\). If the sound process is not sinusoidal but is a complex sound, then in exactly the same way one can successively determine the strength of the individual components by passing through the range of sound frequencies.

The summation tone \((s+p)\) [the last term of equation (2)] is not registered by measuring instruments tuned to a low frequency. The current of the test frequency cannot produce deflections, since the measuring instrument is connected into the diagonal of the bridge and, when the bridge is properly balanced, cannot respond to the current of this frequency. To measure the current in the bridge, Hart’s string galvanometer is used, or sometimes the rotary instrument of Kipp and Zonen. By this method, with the aid of the Reiss microphone and without using an amplifier, components can be determined whose effective pressure amplitude is approximately \(0.1\ \mathrm{dyn}/\mathrm{cm}^{2}\).

The same circuit can be used to test the nonlinearity of a microphone. For this purpose, the microphone under test (in the method described, connected into the measuring bridge) is acted upon by two tones from two high-quality loudspeakers with frequencies \(p\) and \(q\); and, with the aid of the test frequency, it is determined when and with what strength combination tones arise that are caused by the nonlinearity of the microphone.

Fig. 2 gives the results of measurements of carbon microphones. A double microphone gives very insignificant distortions, somewhat larger ones are given by the Reiss microphone* and very

* At a small pressure amplitude (\(6\ \mathrm{dyn}/\mathrm{cm}^{2}\)), the nonlinear distortions produced by the Reiss microphone are nevertheless very insignificant.

significant distortions are produced by an ordinary telephone microphone.

Fig. 2. Nonlinear distortions of microphones.
(Pressure amplitude 80 dyn/cm².)

The method described by E. Meyer is a further development of earlier methods of automatic sound analysis.

[In the diagram: “mixture of frequencies”; “test frequency”; “generation of combination oscillations”; “filter”; “measuring instrument.”]

Fig. 3. Schematic diagram of sound analysis by means of a test frequency.

This method is based on the occurrence of combination oscillations between the test frequency and the various components of the sound under investigation. Fig. 3 gives a diagram of Meyer’s method.

where the combination tones arise directly in the microphone receiving the sound. In the earlier methods this occurred in an amplifying tube operating on the quadratic part of its characteristic, so that the combination tones needed for measurement were obtained. A filter was connected to the amplifier, filtering out the first difference tone; measuring instruments were connected to the filter1.

N. Salinger2 theoretically clarified the question of frequency analysis by means of a test frequency. The amplitudes of the various components can be determined by an analogous method only if their frequencies lie farther apart from one another than the limiting frequencies passed by the filter. In addition, changes of the test frequency \(\gamma\) (hertz/sec.) must take place so slowly that the relation remains valid

\[ \frac{F}{\sqrt{\gamma}} > 4, \]

where \(F\) is the width of the band passed by the filter. By this method one can investigate both purely periodic and nearly periodic processes. An example of a process of the latter kind is the sound produced by a “howling” buzzer; these also include voiced consonants, such as \(L, M, N, R\). Noises can be investigated by this method only if they are repeated in a regular sequence. Irregular sound processes, such as, for example, continuous spoken text, the hiss produced by the outflow of gas, etc., cannot be analyzed by this method, since noises in the general case contain a large number of components lying arbitrarily close to one another, so that there is not even a small frequency interval between them (corresponding to the frequency of the fundamental tone). Therefore, when difference tones arise in the quadratically operating element of the apparatus, arbitrarily low difference tones may occur, which are then passed by the low-frequency filter and cause a prolonged deflection of the instrument.

This drawback is absent from the push-pull circuit,* proposed by M. Grützmacher. Fig. 4 shows how combination tones arise in this circuit. If the tubes operate on the quadratic part of the characteristic, then the voltages at the output will have values respectively proportional to

\[ [e_g-e_s+(e_g-e_s)^2] \]

and

\[ [e_g+e_s+(e_g+e_s)^2]. \]

Subtracting one from the other, we obtain:

\[ \begin{gathered} e_g-e_s+e_g^2-2e_g e_s+e_s^2\\ {}-e_g-e_s-e_g^2-2e_g e_s-e_s^2\\ \hline -2e_s-4e_g e_s, \end{gathered} \]

that is, the resulting voltage in this case will not contain the square of the voltage originating from the noise. Consequently, difference oscillations caused by the noise do not enter the filter.

Fig. 4. Sound analysis by means of a push-pull circuit, after M. Grützmacher.

Fig. 5. Spectrum of the noise of a hissing bus \(S\).

Fig. 6. Spectrum of the noise of a Bunsen burner.

* The method of sound analysis by means of a test frequency, which has the advantage that operation with it does not depend on the amplitude of the test-frequency voltage, was recently developed at the Werner works. The analysis is carried out according to a rectifier-bridge circuit.⁹

A thermoelement with a mirror galvanometer, at a sufficiently low rate of change of the test frequency, faithfully records noise spectra. Fig. 5 shows the spectrum of the hissing sound \(S\), extending up to 13,000 hertz in the case of particularly sharp pronunciation. Fig. 6 gives the spectrum of a Bunsen burner; Fig. 7, the spectrum of a vacuum cleaner.

M. Grützmacher \(^{10}\) gave yet another very simple method of automatic sound analysis, in which the beats are produced not in an electrical circuit, but arise directly in the recording electromechanical system—in a string electrometer. Fig. 8 gives the circuit diagram

Fig. 7. Spectrum of the noise of a vacuum cleaner.

Fig. 8. Sound analysis by means of an electrometer, according to Grützmacher.

for connecting the string electrometer. A simple calculation shows that the force applied to the string is proportional to \(e_s e\), where \(e_s\) is the voltage of the test frequency, and \(e\) is the voltage due to the sound process. If the natural frequency of the string is very low, then each time the test frequency begins to coincide with some component of the sound, the string will oscillate in the rhythm of the beat oscillation.

Louder \(^{11}\) carried out, with the aid of a system of filters, extensive statistical investigations of the composition of human speech and of the properties of musical sounds, especially orchestral music. We shall give here a brief description of this work.

A ribbon microphone with an artificially flattened freq-

…operates, with a frequency characteristic, through a suitable amplifier and rectifier, on two instruments with a rotating coil possessing sufficiently large inertia. One of these instruments makes it possible, by means of a lever transmission (Fallbügelapparatur), to record the mean value of the pressure exerted on the strip over a given interval of time.* The other instrument is connected into the circuit for measuring the impulse and records, likewise with the aid of a transmission, the largest values of the pressure over a given interval of time[^12]. Nine sections of the filter may be connected to the amplifier in turn, and the measuring instruments will give readings only for that part of the process whose frequency lies within the range of frequencies passed at that moment by the given section of the filter. In this way statistical investigations can be made of the mean and extreme values of pressures over a given interval of time.

The sections of the filter are constructed so that, as far as possible, they pass the frequency region of only one octave. The range of the lowest octave lies between 25–50 hertz; the next between 50 and 100 hertz, etc. The upper octave lies between 6,400 and 12,800 hertz. The absorption curves of the individual filter sections are shown in Fig. 9, from which it is evident that only in the high octaves is a rectangular form of the filter transmission curve attained. The various results of investigations carried out with this instrument will be discussed in Section III.

The methods of oscillographic investigation of sound have found extensive application in various fields for the precise study of a complex sound process. Along with the investigation of musical sounds[^13], investigations were carried out on the noise of airplanes[^14]. Objective investiga—

* Usually in acoustics the root-mean-square value of the pressure is given; it should be noted that, in contrast to this, Löder gives the arithmetic mean value. Since the arithmetic mean value of the pressure over a whole period is necessarily equal to zero, the circuit is arranged so that the value of the pressure is obtained over half a period, for example, during the time of increase of the pressure.

…recording of sound made it possible to give an explanation of cardiac and pulmonary murmurs.^15

The sound pattern of the heartbeat is an important criterion for determining pathological changes in individual parts of the heart. The closing of a heart valve produces a sound phenomenon known as a heart tone.

Fig. 9. Frequency ranges passed by an octave filter.

Sclerosis of a valve is recognized from the sound pattern by the fact that, in contrast to a healthy heart, the heart tones are detected in the form of series of prolonged, weakly damped oscillations. Of especially great importance for diagnosis are cardiac murmurs that arise when blood flows through narrowed or hardened valves; in the sound pattern of the normal heart only heart tones are detected, caused by the closing of a heart valve. Precise observation of cardiac murmurs, and especially the precise determination of their position in time within the period of the heartbeat,

of the heart can be made with the aid of an objective recording of sound, with great accuracy, but nevertheless certain difficulties arose here. These difficulties consist in the fact that many noises which, under direct, subjective observation, seem loud, are either not noticeable at all on the oscillogram or are noticeable only very slightly; at the same time, in the objective representation the heart tones predominate, which are either barely perceived by the ear or not perceived at all.

Fig. 10. Sound picture of the noise of a motor exhaust.

This is explained by the great dependence of human hearing on frequency; the ear is very sensitive to high tones and insensitive to low ones. Therefore heart tones, lying in the region of low frequencies, are perceived by hearing much more weakly than higher heart noises.

The difference between objective-physical and subjective observation disappeared after the recording apparatus was supplemented with a special amplifier with capacitive coupling (with capacitors of small capacitance), so that the frequenc—

…characteristic of the device began to correspond to the characteristic of the human ear[^16].

Amplifiers operating like the human ear have been successfully used for investigating various sound phenomena[^17].

Fig. 10 gives the sound picture of the exhaust noise of an automobile engine. Curves b and d give a physically objective picture of the exhaust with and without a muffler. Curves a and c give the same thing, but with the use of an amplifier operating like the human ear. From the curves the action of the muffler is clearly visible. Without a muffler the engine noise contains low frequencies, whose frequency corresponds to the frequency of the flashes, and in addition a series of high components of the same amplitude (curve d).

Hearing perceives almost exclusively the high frequencies (curve c); by switching on the muffler, we damp the high tones, leaving the low tones almost unchanged (curve b), but the ear perceives these low tones as considerably weakened (curve a).

Recently in America, with the aid of amplifiers operating like the ear, investigations have been carried out of street noise[^18] and machine noise[^19].

2. Compensation methods for the exact determination of the phase and amplitude of periodic pressure oscillations.

The compensation method can be applied with great success in all acoustical problems where it is necessary to determine, with sufficient accuracy, the amplitude and phase of the pressure of a purely periodic acoustical process. Acoustical measurements by the compensation method were first carried out by E. Gerlach[^20] in his work with a ribbon microphone, where compensation of the forces of the sound field applied to the ribbon was achieved electrodynamically. E. Meyer[^21] compensated the force applied to the membrane of a condenser microphone by an electrostatic method. K. A. Hartmann[^22] likewise used the electrostatic principle for compensation measurements. Mi-

microphone (Fig. 11) is connected according to Riegger’s circuit; a constant voltage is applied to \(V_0\), and to \(v\) an alternating voltage of the frequency of the received sound, small in comparison with the constant voltage; by this latter voltage the force of the sound field applied to the membrane will be compensated. Adjustment to zero can be carried out with the aid of a telephone connected into the low-frequency amplifier following the rectifier. In this way the frequency characteristics of microphones, telephones, and loudspeakers are determined. A simple method, especially suitable for measuring pressure oscillations in closed acoustic systems (such as, for example, a pipeline, etc.), was given by Tishner[^23]. His compensating device consists of a telephone and a sound-receiving system. The motion of the telephone membrane can be compensated electromagnetically by means of a tone of the corresponding phase and amplitude, passed through the induction coil of the telephone.

Fig. 11. Circuit of the compensation method with a condenser microphone.

For observing the compensation, a small microphone contact is brought to the reverse side of the telephone membrane, to which a telephone for listening is connected; with this telephone the compensation is set subjectively. This method is so sensitive that there is no need for an amplifier between the microphone contact and the headphones.

Fig. 12 gives a diagram of a device for measuring pressure oscillations in water pipes. The tube generator \(RS\) operates through the phase regulator \(P\) and the voltage divider \(S_2\) into the telephone \(T_1\). The telephone serves to excite sound waves in the pipe. The voltage divider \(S_1\) can load the compensating microphone \(T_2\) with current; adjustment to zero is carried out by the telephone \(T_3\).

By the method described, the theory of propagation was verified—

of sound propagation in tubes. The equations of sound propagation in tubes are analogous to the equations of propagation of electrical waves along wires, known as the telegraph equations. Pressure oscillations in acoustic systems correspond to alternating voltage in electrical systems, while the velocity of particles in the acoustic system is equivalent to current in the electrical system.

Fig. 12. Diagram of Tishner’s compensation method.

For a purely periodic process the telegraph equation may be written in the form:

\[ \frac{\partial^{2}U}{\partial x^{2}}=\gamma^{2}U, \]

where \(U\) may denote either voltage or current (or either pressure or particle velocity); the propagation constant \(\gamma\) is, generally speaking, a complex quantity,

\[ \gamma=\beta+i\alpha, \]

where \(\alpha\) is the factor determining the phase, and \(\beta\) is the measure of attenuation. The attenuation of the acoustic conductor \(\beta_{ak}\) can be calculated on the basis of Helmholtz’s theory\({}^{24}\) or on the basis of Kirchhoff’s theory.

graph. ^26 According to Helmholtz’s theory,

\[ \beta_{ak}=\sqrt{\frac{\mu}{\rho}}\cdot \sqrt{\frac{\omega}{2}}\cdot \frac{1}{cr}, \]

where \(\mu\) is the coefficient of internal friction, \(\rho\) is the density of air, \(\omega\) is the angular frequency, \(c\) is the speed of sound in free space, and \(r\) is the radius of the tube.

According to Kirchhoff’s theory it is also necessary to take thermal conductivity into account; then one must put

\[ \sqrt{\frac{\mu}{\rho}}=\sqrt{\frac{\mu}{\rho}+\left(\sqrt{k}-\frac{1}{\sqrt{k}}\right)\nu}, \]

where \(k=c_p/c_v\), and \(\nu=5\mu/2\rho\) is Maxwell’s kinematic coefficient of viscosity.

Precise observations of standing waves in tubes by the compensation-microphone method, carried out by Tischer, showed that the solution of the differential equation given by Kirchhoff corresponds more closely to reality, and consequently heat transfer must be taken into account. ^26

With the aid of the compensation microphone, the effect of damping surfaces in tubes was also determined; the results of these investigations will be discussed in Section V.

II. Treger ^27 investigated, with the aid of a compensation microphone, the formation of standing waves in tubes to one end of which the ear was applied, and in this way determined the physical properties of the tympanic membrane; we shall speak of these investigations in the section “Hearing and Speech.”

3. Other methods of determining quantities characterizing the sound field

The method of measuring, by means of Rayleigh’s disk, the mean square value of the particle velocity is still of great importance. The advantage of this method is that here it is easy to express the measurement results in absolute units. The disadvantage of this method is its great sensitivity to air currents; measurements with the disk are possible only with careful precautions and in an enclosed room.

L. Sivian^28 describes a method of measurement with Rayleigh’s disk in which air currents do not so strongly affect the results. In this method the amplitude of the sound wave under investigation (taken, for simplicity, to be sinusoidal) was modulated by an oscillation whose frequency coincided with the natural frequency of the disk. Then the amplitude of the torsional oscillations of the disk, occurring at its natural frequency, can be used as a measure of the intensity of the standing waves under investigation. Goldbaum and Wittman^29 attempted to determine the intensity of sound in absolute units by measuring, in the sound field, the mean cooling of a heated wire. The investigations were carried out in standing waves excited in a tube by a telephone as the sound generator. The pressure amplitude in the standing wave was measured by a membrane manometer according to M. Wien, so that the intensity of the sound could be calculated in absolute units. In measuring the cooling of a measuring wire 20 mm long, heated by a direct current and included in a bridge circuit, it was found that the cooling effect decreases considerably as the frequency is increased, and therefore the possibility of making direct absolute measurements by this method is extremely small.

In 1927 it was recognized^30 as impossible to determine directly, by acoustic measurement, the power emitted by a sound source. Nevertheless E. Meyer and P. Just^31 very simply solved this problem by a purely acoustic method. The sound source under investigation is placed in a closed, highly reflecting space. According to the well-known equation of architectural acoustics for the mean energy density in an enclosed space in the case of a stationary state, we have:

\[ E=\frac{4L}{Ac}, \]

where \(L\) is the power of the sound source, \(A\) is the total absorption of the space, and \(c\) is the speed of sound. The mean energy density is conveniently determined by means of a sound receiver calibrated in absolute units, for example by means of a condenser microphone. The energy density and the effective-

the pressure value are related by the following relation:

\[ E=\frac{p^{2}}{c^{2}\rho}. \]

The value of the total absorption is most conveniently determined by measuring the reverberation time. Between the reverberation time and the total absorption there exists the following dependence:

\[ AT=kV, \]

where \(V\) is the volume in \(m^{3}\) and \(k=0.16\) is a constant. The newest methods of measuring reverberation will be discussed below.

The difficulty that arises when this method is applied is that, in a room with strongly reflecting walls, a system of standing waves arises and the energy density changes from point to point. Therefore it is most advantageous to work with non-sinusoidal tones; best of all—with “warbling” tones, i.e. with tones whose frequency varies within certain narrow limits. If the sound source is a buzzer, then, in order to obtain the “warbling” effect, a small variable-capacitance condenser is used, set in rotation by an electric motor. By its rotation the condenser continuously varies the frequency of the sound \(^{32}\).

The Acoust. Soc. “Lidstrem” introduced into use gramophone records recorded with warbling tones. These records, together with electrical adapters, may be used to excite loudspeakers in various acoustical investigations \(^{33}\). Further, in order to avoid errors connected with the occurrence of standing waves, it is recommended in various acoustical measurements to use moving loudspeakers and microphones and to employ a large reflecting screen, which must likewise be set in motion. Snek and Zwinér \(^{34}\) found that the average error when this method is used in the range from 100 to 500 hertz is equal to 14%, whereas when warbling tones are used it is reduced to 9%.

Methods for the indirect determination of the acoustic power of a sound radiator have also been developed. To determine the efficiency coefficient of electrical

For sound emitters Graf[^35] applied a method known from hydroacoustic technology: recording resonance curves in air and in vacuum without excitation of the field. In this way, by means of purely electrical measurements, he determined the efficiency of a ribbon loudspeaker, whose ribbon had been tuned by tensioning to a frequency of 800 hertz.

To determine the acoustic properties of rooms in which speech or music is performed, it is extremely important to know the reverberation time; therefore many attempts were made to measure reverberation objectively, so as thereby to reduce the errors arising in subjective observations. A. Meyer and P. Just[^36] recorded sound-decay curves oscillographically, but since usually the amplitude, decreasing according to an exponential law, became very small within a short interval of time, after a certain interval an amplifier was switched in (by means of an automatic relay), increasing the sensitivity by a definite number of times, for example by 10. In addition, it is more convenient to carry out measurements not with pure tones, but with warbling tones (the significance of which for measuring room acoustics was discussed above). In this way one can avoid noticeable irregularities in the course of the sound-decay curve, which on average is determined by an exponential law.

Fig. 13. Method of automatic measurement of reverberation.

M. Strutt[^37] describes an automatic method for recording reverberation curves (Fig. 13). In this method, when the sound source is switched on, a clock is switched on automatically; the clock is switched off after the sound energy reaches a definite value, by means of a relay connected to the microphone. This method is sufficiently accurate, so that measurements can be made with an accuracy of up to 0.01 sec.

In addition to what has been set forth above, one may also point to a very simple method for determining the sound permeability of materials. Fig. 14 gives a diagram of Meyer’s method^38: two rooms are separated by a wall made of the material being tested; in one of the rooms there is a loudspeaker serving as the source of sound. Two identical microphones serve to receive the sound: one receives the sound in the same room in which the loudspeaker is located, the other—the sound that has passed through the wall into the other room.

Fig. 14. Measurement of sound permeability by Meyer’s method.

Subjective comparison of loudness and equalization of loudnesses by introducing a certain attenuation makes it possible to determine the magnitude of the sound permeability, the measure of which is the introduced attenuation.

BIBLIOGRAPHY

1. Z. Hochfr., 28, 54 and 84, 1926.

2. Z. Hochfr., 32, 27, 94, 131, 173 and 202, 1928; Russian translation, UFN, 10, 593, 1930.

3. K. W. Wagner, E. N. T. 7, 174, 1930.

4. Questions of recent acoustics are treated in:
   Hdb. d. Phys., hrsg. v. H. Geiger u. K. Scheel, Bd. VIII, Berlin 1927; Müller-Pouillers, Lehrb. d. Phys., hrsg. v. E. Waetzmann, Bd. 1/3, Braunschweig 1929.

5. E. Meyer, E. N. T. 5, 398, 1928.

6. Cf., for example, M. Grützmacher, E. N. T. 4, 533, 1927; E. Gerlach, Z. f. techn. Phys. 8, 515, 1927; C. R. Moore and A. S. Curtis, Bell Syst. Techn. Journ. 6, 216, 1927.

7. H. Salinger, E. N. T. 6, 293, 1929.

8. M. Grützmacher, Z. f. techn. Phys. 10, 570, 1929.

9. The device will be described in the work:
   C. H. Walter, “Über eine neue Gleichrichteranordnung und ihre Verwendung in der Messtechnik.”
   Grützmacher, Z. f. techn. Phys. 10, 577, 1929.
   H. Luder, Wiss. Veröffentlich. a. d. Siemens-Konz. IX/2, 167, 1930;
   a similar device: L. J. Sivian, Bell Syst. Techn. J. 8, 646, 1929.
   On the question of amplitude statistics, see H. G. Baerwald, E. N. T. 7, 862, 1930.

1. H. Backhaus, Naturwiss. 17, 811, 1929.

2. J. Obata and Y. Yosida, Rep. Aeron. Res. Ins. Tōkyō Imp.-Univ., V/6, 144, 1930.

3. F. Trendelenburg, Wiss. Veröff. a. d. Siemens-Konz. VI/2, 184, 1928. K. Posener and F. Trendelenburg, Wiss. Veröff. a. d. Siemens-Konz., VIII/2, 228, 1929; E. Bass, Z. f. exp. Med. 59, 133, 1928; 63, 578, 1928; A. Pierach, Klin. Wochschr. 9, 645, 1930; F. M. Groedel, Verhdl. d. Ges. f. inn. Med. 41 Kongr. 372, 1929.

4. See K. Posener and F. Trendelenburg, Z. f. t. Ph. 9, 495, 1928.

5. H. Gerdien, H. Pauli, and F. Trendelenburg, Z. f. techn. Phys. 10, 374, 1929.

6. “City Noise” ed. by the Noise Abatement Commission Dep. of Health. City of New York 1930. Cf. R. H. Galt, Journ. Ac. Soc. Amer. 2, 30, 1930.

7. B. A. G. Churcher and A. J. King, J. I. E. E. 68, 97, 1930.

8. E. Gerlach, Wiss. Veröff. a. d. Siemens-Konz. Bd. 111/1, 139, 1923.

9. E. Meyer, E. N. T. 3, 230, 1926.

10. C. A. Hartmann, E. N. T. 4, 86, 1927.

11. H. Tischner, E. N. T. 7, 102, 1930.

12. H. V. Helmholtz, Crelles Journal 57, 1860.

13. G. Kirchhof, Pogg. Annal. 134, 177, 1868.

14. The results obtained by Lichte, who investigated the propagation of sound in tubes, agree with this: H. Lichte, E. N. T. 44, 304, 1927.

15. J. Tröger, Phys. Z. 31, 26, 1930.

16. L. J. Sivian, Phil Mag. (VII) 5, 615, 1928.

17. G. Golbaum and E. Waetzmann, Z. Physik 54, 179, 1929; H. Muller and E. Waetzmann (I. Physik 62, 167, 1930).

18. F. Trendelenburg in Handbuch. d. Physik by H. Geiger and K. Scheel, VIII, Berlin, 1927.

19. E. Meyer and P. Just, Z. f. techn. Phys. 10, 309, 1929.

20. Mitteilungen a. d. R. P. Z. Z. Hochfr. 33, 184, 1929.

21. E. Meyer and P. Just, E. N. T. 5, 293, 1928.

22. J. L. Snoek and C. Zwikker, Physica 10, 219, 1930.

23. Z. Graf, Z. f. techn. Physik. 10, 334, 1929. Cf. E. D. Cook, Gen. El. Rev. 53, 509, 1930.

24. E. Meyer and P. Just, E. N. T. 5, 293, 1928.

25. M. J. O. Strutt, E. N. T. 7, 280, 1930.

26. E. Meyer, Z. d. V. d. J. 74, 273, 1930; measurements of sound transmission by means of a thermomicrophone were carried out by Keo, Phys. Z. 30, 145, 1929; on the measurement of sound transmission, cf. A. E. Knöwler, Phil Mag. 10, 342, 1930, and N. F. Hopkins, Filmtechnik 6, 15, 1930.