PHYSICAL PROBLEMS OF THE PHYSIOLOGY OF HEARING *

Georg von Békésy-Budapest

1. Anatomy of the Ear

Although physicists ought not to concern themselves with questions of anatomy, nevertheless they have to encounter these questions even when studying purely physical problems of hearing. And then one can appreciate the full harmony of the anatomy of the ear and the difference between the ways in which nature and technology solve one and the same problems. In the present state of the physiology of hearing, which is still far from being able to give direct answers, knowledge of this kind plays a major role. For there are not infrequent cases in which, after a physicist has solved a problem well to his own satisfaction, on closer acquaintance with the anatomy of the ear he cannot rid himself of the feeling that the phenomena must proceed in an entirely different manner.

Fig. 1. Schematic section of the middle and inner ear.
1 — temporal bone, 2 — auditory canal, 3 — tympanic membrane, 4 — round window, 5 — semicircular canal, 6 — bony labyrinth, 7 — basilar membrane, 8 — helicotrema, 9 — Eustachian tube.

In Fig. 1 is shown a schematic section of the middle and inner ear, compiled from two drawings given in the well-known work of H. Helmholtz, On the Sensations of Tone¹. The auditory canal, 2.5 cm long and 0.7 cm wide, terminates in the tympanic membrane, which has a conical shape. The tympanic membrane is connected with three auditory ossicles—the malleus, incus, and stapes—situated in the cavity of the temporal bone, called the middle ear. The ossicles are attached to the walls of the cavity by elastic ligaments. The middle ear is connected by the Eustachian tube with the oral cavity. In a healthy person, however, this tube is usually closed; it

* Elektrische Nachrichten-Technik, 12, 71–83, 1935. Translated by A. V. Rabinovich.

opens only during swallowing, whereby the possible difference in pressures on the two sides of the tympanic membrane is equalized. This can be demonstrated experimentally. A small buzzer is fastened to a tube and the tube is placed in the mouth. If the Eustachian tube is closed, the sound from the buzzer is barely audible; when the Eustachian tube is opened, a loud noise is obtained.

Thus the tympanic membrane is subjected to the one-sided action of changes in the pressure of the sound field, and its vibrations are transmitted through the base of the stapes into the inner ear. In man the latter consists chiefly of a round canal about 3.5 cm long and about 0.25 cm wide, coiled in a spiral and therefore called the cochlea. The canal is divided along its length by a partition into two equal parts. This partition does not reach the end of the canal, so that an opening is formed (the so-called helicotrema), through which the fluid can flow from the upper part of the canal into the lower. This ensures that, when there is excessive pressure of the stapes at the beginning of the upper part of the canal, the fluid does not exert prolonged pressure on the partition, being equalized through the helicotrema and the round window (an opening in the lower half of the canal, closed by a membrane). The inner part of the partition, perpendicular to the axis of the cochlea, is bony, whereas the outer part consists of a membrane—the so-called basilar membrane. Near the stapes the basilar membrane has a width of about 0.16 mm; approaching the helicotrema, it widens to 0.5 mm.

Into the upper half of the cochlear canal open the apertures of three mutually perpendicular so-called semicircular canals (in Fig. 1 only one of them is shown), filled, like the cochlea, with fluid. Injuries of the skull extending to the semicircular canals cause dizziness—hence their importance for maintaining equilibrium is clear.

When the head rotates about an axis perpendicular to the plane of a semicircular canal, the fluid, owing to inertia, lags behind; its displacement relative to the walls of the semicircular canal irritates the nerve endings situated on these walls.

If, near the stapes, as a result of the rectification of vibrations of the fluid, currents of fluid are produced, then, because of the proximity of the openings of the semicircular canals, they are carried into these canals, which may also be a cause of disturbance of equilibrium.

Fig. 2 is a photographic image of the auditory ossicles, freed from the softer parts, such as skin, ligaments, and cartilage.

The handle of the malleus, designated in the figure by the number 4, is fused along its entire length with the tympanic membrane, while the head of the malleus is fused with the plane of the incus, designated by the number 1. It was formerly supposed that the head of the malleus and the incus were not rigidly connected, and that they formed something like a ratchet joint, transmitting completely only small

oscillations and loses contact during excessively large oscillations. However, later studies on fresh temporal bones did not confirm this point of view. The lower narrow process of the incus is connected to the stapes by means of a joint.

Fig. 2. Auditory ossicles. 1—surface of fusion of the head of the malleus with the incus, 2—incus, 3—base of the stapes, 4—handle of the malleus.

In Fig. 3 the tympanic membrane and the auditory ossicles are shown in their natural position. The conical form of the tympanic membrane 3 and the handle of the malleus 4 fused with it are clearly visible. In the figure, besides the site of fusion between the head of the malleus and the incus, it is also visible how the short crus of the incus 1 is flexibly connected with the wall of the temporal bone. Near the articular surface adjoining the stapes 2 there is a thin muscle fiber running to the temporal bone. This fiber is fused with the apex of the stapes and contracts under the action of strong sounds. In the middle ear there is also another muscle, namely the muscle that begins from the handle of the malleus and tenses the tympanic membrane toward the interior of the head. It has been observed that some people can tense this muscle voluntarily.

In Fig. 4 the stapes, its base 2, and the articular head 1 are visible. Since the oval window 4 lies so deeply that the stapes cannot be photographed in its normal position, in this preparation it has been bent outward, as a result of which it became possible to see the form of the oval window itself. The round window 3 is visible

Fig. 3. Tympanic membrane and auditory ossicles in normal position. 1—incus, 2—surface of the joint adjoining the stapes, 3—tympanic membrane, 4—handle of the malleus, 5—head of the malleus.

vibrations and losing contact at excessively large vibrations. However, later investigations on fresh temporal bones did not confirm this point of view. The lower narrow process of the incus is connected with the stapes by means of a joint.

Fig. 2. Auditory ossicles. 1—surface of fusion of the head of the malleus with the incus, 2—incus, 3—base of the stapes, 4—handle of the malleus.

In Fig. 3 the tympanic membrane and the auditory ossicles are shown in their natural position. The cone-shaped form of the tympanic membrane 3 and the handle of the malleus 4 fused with it are distinctly visible. In the figure, besides the place of fusion between the head of the malleus and the incus, it is also visible how the short crus of the incus 1 is flexibly connected with the wall of the temporal bone. Next to the articular surface in contact with the stapes 2 there is a thin muscular fiber running to the temporal bone. This fiber is fused with the apex of the stapes and contracts under the action of strong sounds.

There is also one more muscle in the middle ear, namely the muscle that begins at the handle of the malleus and tightens the tympanic membrane toward the inner part of the head. It has been observed that some people can tighten this muscle voluntarily.

In Fig. 4 the stapes, its base 2, and the articular head 1 are visible. Since the oval window 4 lies so deep that the stapes cannot be photographed in its normal position, in this specimen it has been taken out, as a result of which it became possible to see the shape of the oval window itself. The round window 3 is visible

Fig. 3. The tympanic membrane and auditory ossicles in the normal position. 1—incus, 2—surface of the joint in contact with the stapes, 3—tympanic membrane, 4—handle of the malleus, 5—head of the malleus.

in lateral projection. The tympanic membrane and the auditory ossicles, as was especially emphasized by Frank,^2 contribute to the fact that the sound does not arrive simultaneously at the oval and round windows.

Otherwise there would be no difference in pressure between the two windows, and consequently no deflection of the fluid would occur in the cochlea. Nothing definite can be said, however, about the expediency and necessity of both internal muscles and about the intricate arrangement of the auditory ossicles. Probably the developmental history of man plays a role with respect to their form, since in man the auditory ossicles developed from the skeleton of the fish jaws and gills.

Fig. 4. Stapes removed from the oval window. 1—articular head of the stapes, 2—base of the stapes, 3—round window. 4—Oval window.

In Fig. 5, on the left side, the bony parts of the cochlea are shown. In the lower turn there is visible, perpendicular to the axis of the cochlea, the bony part of the septum,^5 which divides the canal into two equal parts; the soft continuation of the bony septum—the basilar membrane—has been removed. The upper turn reaches the apex of the cochlea, from where, through the helicotrema, one can trace the transition from the lower to the upper part of the canal. On the right in the figure are visible the three mutually perpendicular planes of the semicircular canals.

Fig. 5. Bony part of the cochlea and three semicircular canals arranged mutually perpendicular to one another

In Fig. 6 the cochlea is reproduced in its normal form. In the middle is located the axis of the cochlea 2, the so-called modiolus, into which the auditory nerve enters. It is clearly seen that in the lower turns of the cochlea, which lie closer to the stapes, the soft and thin part of the septum is narrower than in the upper turns. In addition, the figure shows the tip of the basilar membrane, fused with the apex of the cochlea, with

located in front of it, the helicotrema. The number of turns of the cochlea varies: in the whale there are \(1^{1}/_{2}\) turns, in man \(2^{3}/_{4}\), in the guinea pig 4.

Fig. 6. Transverse section of the cochlea.
1—upper turn of the basilar membrane,
2—modiolus

Owing to its cochlea-like shape the canal is protected from deformation.

If the apex of the cochlea is sawn off, the helicotrema can be seen together with an entire turn (Fig. 7). The end of the basilar membrane is visible, fused with the apex of the cochlea and here reaching its maximum width. If the apex of the cochlea is filled with liquid and the opening closed with a thin glass plate, then in this way it is possible to observe the oscillations of the basilar membrane along the whole turn, without thereby disturbing the normal relationships.

In Fig. 8 there is shown, enlarged, a transverse section of the cochlear canal of the guinea pig. The lower, in the guinea pig relatively small, part of the cochlear canal is bounded above by the basilar membrane 3, on which lies a row of cells with hairs; still higher is situated the tectorial membrane 4. Since this membrane is mechanically relatively stable, when the basilar membrane is displaced pressure is exerted on the cells lying beneath the tectorial membrane, between which, as Corti showed, there are also the endings of the auditory nerve. On this observation of Corti’s is based the supposition that deformation of the basilar membrane determines the auditory process. Farther upward runs Reissner’s membrane, exceedingly thin and invisible in Fig. 6. The intermediate space

Fig. 7. Upper turn of the cochlea. 1—helicotrema, 2—modiolus, 3—beginning of the lower turn, 4—end of the basilar membrane

between Reissner’s and the basilar membranes, the so-called ductus cochlearis, is filled with a viscous fluid.

Observations made on the preparation shown in Fig. 7, in which Reissner’s membrane had been preserved, showed that both membranes—the tectorial and the basilar—oscillate with exactly the same phases, so that from a physical point of view

Fig. 8. Transverse section of the cochlear canal of a guinea pig. 1—Reissner’s membrane, 2—ductus cochlearis, 3—basilar membrane, 4—tectorial membrane, 5—auditory nerve.

there will be no significant error if we replace all three membranes by one membrane with the corresponding mechanical properties.

The cochlea of the guinea pig is valuable for physiological experiments because it is located in an easily accessible and comparatively thin-walled capsule, which, owing to its external form, makes it possible to orient oneself readily. Therefore Geld and Kleynknecht³ were able to drill through the bony wall indicated in Fig. 8 by line 3 and to weaken at this point the tension of the basilar membrane, as a result of which hearing at the drilled site exhibited characteristic tonal gaps.

2. Various Theories of Hearing

Slow oscillations of pressure in the auditory canal cause, as a result of the deflection of the stapes in the upper part of the cochlear canal, a flow of fluid which penetrates through the helicotrema into the lower part of the canal; as a result of this, according to Poiseuille’s law, along the basilar membrane there arises a pressure difference which is proportional to the velocity of motion of the fluid and is in the same phase as this motion.

The so-called telephone theory assumes that this proportionality and coincidence of phases of the pressure action along the entire basilar membrane occur not only at very low frequencies (of the order of 20 hertz), but at all frequencies, so that the basilar membrane is likened to a telephone membrane, oscillating in the same phase over the entire membrane. In the auditory nerves, as in a telephone receiver, electric currents arise that are proportional to the strength of the sound and are then subjected in the brain to further analysis. In this theory the special form of the basilar membrane remains unexplained. The theory of the “sound pattern” (Schallbildtheorie), developed by Ewald^4, assumes that oscillatory patterns arise on the basilar membrane, having for each separate frequency a different form, on the basis of which the determination of pitch is carried out in the brain.

Since the activity of the brain has been little studied and, consequently, no conclusions can be drawn from the above theories that could be tested, the physicist Helmholtz and subsequently Guildemeister^5 put forward the so-called place theory (Einortstheorie). According to this theory, frequency analysis takes place not in the brain but, to a certain extent, mechanically in the cochlea: each tone excites on the basilar membrane one single narrowly limited region, and by this place on the basilar membrane the pitch of the tone is determined.

Thus the regions of excitation of individual tones are spatially separated, and consequently the mutual phase relation of tones when sounding together has no influence on timbre.

Since the study of the perception of the direction of sound clearly shows that the auditory nerves transmit the phases of tones, and for very low frequencies even the anatomical structure of the cochlea confirms the “telephone” theory, one should not draw a sharp opposition between the different views, for, while giving preference to the place theory, it is nevertheless possible that at very high tones frequency analysis is carried out exclusively through the determination of place on the basilar membrane, whereas at very low tones the frequency of the nerve currents contributes to this to a significant degree.

3. Electrical currents in the auditory nerve

The development of amplifier technology made it possible to measure directly the currents in the auditory nerve and, in this way, to settle the question of their frequency analysis. Such an experiment was first carried out by Wever and Bray⁶, who found that in the tissues surrounding a freely exposed auditory nerve there arise alternating voltages quite proportional to the sound pressure, up to the very highest frequencies. A repetition of this very difficult experiment was made by Saul and Davis⁷ and showed that, alongside the currents observed by Wever and Bray and arising mainly in the tissues surrounding the auditory nerve, there are currents of a completely different character, spreading along the nerve. These currents reproduce the stimulating frequencies no higher than up to 2,000 Hz and are similar to the nerve currents characteristic of other sense organs.

4. Phenomena indicating the existence of mechanical frequency analysis in the cochlea

The presence of mechanical frequency analysis in the cochlea is confirmed by the following circumstances: the alternating potentials found by Wever and Bray at the apex of the cochlea are greater at low frequencies than at high ones, whereas on the lower turn of the cochlea, on the contrary, they are greater at high frequencies than at low ones. This indicates that high tones excite chiefly the part of the basilar membrane close to the stapes, while low tones act on the part close to the helicotrema.

The very fact that the dimensions of the cochlea in the newborn are as large as in the adult human, whereas the bones surrounding the cochlea grow more than twice as large, points to the important role for hearing of the dimensions and mechanical properties of the cochlea.

If mechanical frequency analysis takes place, then, according to the one-place theory, when hearing is lost in a narrow frequency range only some small segment of the basilar membrane undergoes change. Crowe, Guild, and Polvogt⁸ determined the dependence of the threshold of audibility on frequency in patients for whom it had been established that they could not recover.

After the death of these persons, the changes that had occurred in the cochlea were determined by means of histological examination. Figure 9 gives one of a large number of cases studied, where, for frequencies above 1,000 Hz, there was hardness of hearing increasing with frequency. In this figure a projection of the cochlea onto a plane perpendicular to its axis is given; for the lower (closest to the stapes) turn, the width of the black bands indicates to what extent (in percent) the nerve endings, the organ of Corti, and the corresponding segment of the basilar membrane had not yet undergone destruction. It is clearly seen how, with approach to the stapes, i.e., with increasing frequency and, consequently, hardness of hearing, the destruction increases.

From a large number of observations it was established that impairment of hearing for frequencies of 8,192, 4,096, and 2,048 Hz corresponds to destruction of the cochlea in the regions indicated by the brackets.

The above-mentioned experiments of Held and Kleinknecht, in which the basilar membrane of guinea pigs was damaged in certain narrowly circumscribed places, yielded completely identical results with respect to the frequency dependence of hearing losses.

Fig. 9. Deafness for high frequencies corresponds in the human ear to destruction of the nerve endings near the stirrup.

The further conclusions of the theory of a single place are also confirmed. It is known that a nerve, under excessively prolonged and strong stimulation, becomes fatigued. Fatigue acts first and most strongly on the nerve endings. Since each tone stimulates only one place of the basilar membrane, one should expect that, with prior fatigue by a pure tone of constant frequency, the influence of fatigue will be found only for tones very close in frequency to the fatiguing tone.

This was indeed demonstrated; moreover, the loss of loudness at unchanged sound pressure is greatest for the frequency of the fatiguing tone (a decrease in loudness under strong fatigue is equivalent to that from reducing the sound pressure by a factor of 3–5), and for frequencies somewhat higher or lower it gradually diminishes in both directions.

Fig. 10. Change in pitch with preceding fatigue.

At the same time it was observed that with preceding fatigue a slight change in pitch occurs. As shown in Fig. 10, preceding fatigue in a narrow region (the degree of fatigue and its distribution along the basilar membrane are depicted by the thick curved line in the center of the figure, with a maximum at 800 Hz) changes the distribution of the stimulation from the subse—

...of the tones, close in frequency to the fatiguing tone, in such a way that the stimulus is reduced on the side facing the fatigued place. Therefore the place of maximal excitation, which also determines the sensation of pitch, is displaced; all tones with a frequency higher than that of the fatiguing tone are raised, while those with a frequency lower than that of the fatiguing tone are lowered. This phenomenon is confirmed experimentally.

5. Similarity between the perception of sound propagated in air and that conducted directly through a solid body

For the further development of the theory of a single place it is important to determine the relation existing between the ordinary auditory perception of sound propagated in air, in which the tympanic membrane and the stirrup come into oscillation relative to the body of the cochlea, and the auditory perception of so-called body sound. The latter term refers to the case in which, by touching an oscillating body to the cranial bones—for example, the stem of a sounding tuning fork—not only the stirrup but the entire body of the cochlea is set into oscillation (transverse and longitudinal). In this case there is a completely normal perception of tones. It is even possible to construct a “bone telephone” by setting the teeth into oscillation by means of currents of sound frequency through a rigid oscillating system.

In order to establish whether the perception of sound arriving through the air differs in a fundamental way from the perception of bone-conducted sound, and whether the form of oscillations of the basilar membrane is identical in both cases, we apply one and the same tone simultaneously by means of an ordinary telephone and by means of a bone telephone. If the oscillations of the basilar membrane under the action of the sound applied to the ear by each of these methods had the same form, then, by properly selecting the amplitudes and phase relations of both telephone currents, complete compensation of the oscillations applied to the ear by the two different methods ought to have been achieved, and the ear would not have perceived any sound.

Since this experiment was entirely successful, the identity of the oscillations of the fluid in both cases should be regarded as proven.^10

Judging from the anatomical structure of the cochlea, this was to be expected, for with uniform compression of the cochlea and the symmetry of both canals of the cochlea, as is seen in Fig. 11, no displacement of the basilar membrane occurs. But since the upper canal of the cochlea is loaded with the tympanic membrane and the auditory ossicles, the symmetry is broken. The asymmetry is further increased by the fact that the semicircular canals adjoin the upper canal of the cochlea, their openings being situated near the stirrup; as a result, when the semicircular canals are pressed upon, the fluid is forced into the cochlea in exactly the same way as by the inward movement of the stirrup.

Bone-conducted sound is of great importance for establishing diagnoses of diseases in the field of hearing. These diseases are divided into two groups: hardness of hearing due to lesions of the nerves and hardness of hearing due to inflammation of the middle ear. These two groups must be considered separately, since they require entirely different treatment. In the presence of inflammation of the middle ear, the mobility of the auditory ossicles and of the tympanic membrane is usually reduced, as a result of which, in comparison with the normal state, the loudness of sound conducted through bone increases (Fig. 11b), while the loudness of sound perceived through the air decreases. Such a phenomenon may occur in a healthy ear if the tympanic membrane is subjected to a constant unilateral pressure of 10 cm water column; in this case the loudness of the sound conducted through the bones of the skull increases greatly, which is caused by fixation of the auditory ossicles owing to a strong decrease in the mobility of the tympanic membrane, as shown by impedance measurements.

Fig. 11. Occurrence of deflection of the basilar membrane when the cochlea is compressed owing to asymmetry of the two canals of the cochlea

If the auditory canal is stopped with a finger, the loudness of bone-conducted sound very often increases still more, since the finger and the lower jaw, owing to the absence of a rigid connection with the temporal bone, oscillate not in the same phase and not with the same amplitude as the latter. In this case the auditory canal is compressed, and sound vibrations conducted through the air act upon the tympanic membrane, as happens in ordinary hearing. The stapes in this case is pressed inward into the cochlea.

Thus the empirical discovery of Weber, often used in medical practice, becomes understandable; it consists in the following: the stem of a sounding tuning fork is applied to the middle of the head; with normal hearing in both ears, a sound of equal loudness is obtained, whereas in disease of the middle ear the sound seems louder precisely in the affected ear.

6. Investigations of Fluid Oscillations in the Ear on a Model

Since direct observation of fluid oscillations in the cochlea of the human ear, owing to the difficulties of prepar-

...the imperfection of preparations and the spiral form of the cochlea is very difficult, so in order to elucidate the physical principles of the motion of the fluid, experiments have long been carried out with the aid of simplified models.

Figure 12 presents three variants of the theory of a single place. In Fig. 12a there is shown Wilkinson’s model[^11], whose basilar membrane consists of a row of wires lying next to one another and glued together with a thin sheet of parchment; the natural frequency of these wires continuously decreases in the direction from the stapes to the helicotrema. Such a device is essentially a phramic reed frequency meter: at each frequency of oscillation of the stapes, a definite place of the basilar membrane oscillates with maximum amplitude. At the same time, four small vortices are formed in the fluid. This model is best suited for explaining Helmholtz’s resonance theory of hearing. According to this theory the place of maximum oscillations is determined only by the mechanical properties of the membrane, while the dimensions of the cochlear canal play no role.

Fig. 12. Various variants of the theory of a single place

The problem of bringing the model membrane as close as possible to the actual anatomical proportions was accomplished by Ewald[^12], who applied a rubber solution to a thin stiff plate having, in section, the shape of the basilar membrane. Taking into account the thinning of the rubber solution, the manner of applying it, and the degree of drying, it is possible to make membranes that have an almost uniform tension in all directions, as well as membranes in which the transverse tension considerably exceeds the longitudinal tension. At the edges of the membrane the rubber solution dries faster than in the middle; therefore the middle part of the membrane contracts during drying and often bursts along its length.

With the aid of various membranes made in this way and ear models, the size of which has recently been brought to the actual dimensions of the cochlea, the form of oscillation of the basilar membrane shown in Fig. 12b was obtained[^13]. The part of the membrane nearest the stapes oscillates in the same phase as the stapes, whereas in its more remote parts traveling waves with great damping arise. At the place where the series of waves originates two vortices are formed, which, as the frequency increases, approach the stapes. If the oscillations imparted to the stapes are not free from overtones, then the two vortices mentioned above are situated opposite one another. With elongation of the canal...

of the cochlea by attaching, for example, to the lower half of the model a small piece of tube, with the membrane of the round window transferred to its end, the place where the vortices arise does not change.

A mathematical analysis of this form of fluid oscillation was made by Ranke ^14, who explained the causes of the occurrence of the vortex.

The form of oscillations shown in the lower part of Fig. 12 was proposed by Lux ^15 and Roaf ^16, and its mathematical analysis was made by Fletcher and Kharkovsky ^17. The oscillations of the fluid take place inside a column separated out in the fluid, the mass of the liquid columns and the elasticity of the membrane at the site of oscillation determining the natural resonant frequency. The site of oscillation at high frequencies comes very close to the stirrup, as a result of which the length of the liquid columns is considerably shortened. Therefore, when the lower window is covered with fluid (as may occur in inflammation of the middle ear), we should have expected changes in the pitch of tones, since the oscillating columns of fluid are lengthened. We have not yet succeeded in proving this effect.

Whether columnar oscillations of the fluid represent a stable form of its motion, and which of the three variants of the theory of a single site corresponds to the dimensions and mechanical properties taken into account here—all this will be finally clarified only after a general mathematical analysis.

The openings of the semicircular canals lie very close to the stirrup, and therefore it seems possible in principle to study whether, at a certain amplitude, oscillations of the fluid occur in one or the other direction within the column, or whether there occurs some kind of rectification of the fluid oscillations associated with its vortex-like streams, since, if this phenomenon is present, it should also propagate to the semicircular canals and cause a disturbance of equilibrium. The experiment consists in simultaneously applying to one ear two tones of equal and, moreover, very great intensity; the frequency of the first tone is 1000 Hz, and the frequency of the second differs somewhat from that of the first. If the period of the beats arising in this way is greater than 2 sec, then we are dealing with a pure auditory sensation. With an increase in the beat frequency, however, in the majority of subjects a clearly perceived disturbance of equilibrium arises, and it seems to them that the head is rocking from side to side in time with the beats.

At a beat frequency of 3 Hz this phenomenon reaches its maximum value; then, with a further increase in frequency, it decreases continuously, almost disappearing at 30 Hz. If a tone with three beats per second is suddenly switched on, it is easy to discern that the auditory sensation arises at once in full measure, whereas in order for the disturbance of equilibrium to reach its full magnitude, not fewer than 10 beats must pass.

In addition to the statements of the subjects, reflex eye movements associated with the disturbance of equilibrium may also be demonstrated. Since under normal conditions the described

...the phenomenon is small, it was necessary to use a very large number of subjects, 80% of whom showed disturbance of equilibrium. The degree of disturbance of equilibrium, however, varied greatly with time. Pietro Tullio¹⁸ wrote an interesting book about this phenomenon. Strong oscillations of sound pressure at a frequency of 3 Hz and howling tones with the same modulation frequency do not affect the organs of equilibrium.

Whereas in the ear model in Fig. 12b no vortex motion is observed near the stirrup, generally speaking, it is nevertheless not improbable—as Hensen¹⁶, Helmholtz’s contemporary, already pointed out—that in the human ear such a motion takes place.

The deviation of the stirrup from its normal position, caused by the one-sided action of pressure on the tympanic membrane, is associated with a change in the degree of disturbance of equilibrium even when the accompanying changes in the loudness of the beat tones are compensated.

7. The Process of the Origin of Oscillations in the Ear

Alongside the problem of mechanical frequency analysis, the process by which oscillations arise in the middle ear

Fig. 13. Oscillations of the tympanic membrane and the membrane of a telephone receiver.

and in the cochlea also assumes importance. The damping of an oscillatory system, for example the string of a musical instrument, is best judged by how rapidly the oscillations of a system set into motion by a pluck die away. On a telephone membrane this can be achieved (at Sell’s²⁰ suggestion) by the sudden interruption of the direct current passing through the telephone receiver and by recording the oscillations that arise, for example with the aid of a microphone. The damping curve for a modern postal telephone is given in Fig. 13.

The tympanic membrane can also be set into vibration by means of forceps, although this is not so easy to do. The oscillatory process is shown at left in Fig. 13, and the natural frequency of the middle ear proved to be about \(1300\ \mathrm{Hz}\) \(^{21}\). As we see, telephone technology in this respect can still develop, since the damping time of the vibrations of a telephone diaphragm is too great.

If one follows the vibrations of the liquid arising in a model of the ear when the stapes is displaced once and freely outward (Fig. 14), it is seen that the basilar membrane near the stapes moves together with it, while the more distant part remains in complete rest. After a short time the part of the membrane near the stapes aperiodically comes to rest, while the traveling wave (shown in Fig. 14 by a thick dotted line) approaches the helicotrema, so as to become completely leveled out there after approximately \(1/20\) sec. Particles of coal dust situated on the membrane are pushed, with each movement of the stapes away, by a definite distance in the direction of the helicotrema, independently of the direction of this movement.

Fig. 14. Traveling waves on the basilar membrane.

It is now necessary to prove the existence of such a traveling wave in the human ear and to determine the velocity of propagation of this wave. It is known that the phenomenon of perceiving the direction of sound (the binaural effect) is connected with the possibility of detecting, by the two ears, very small differences in time; if a short sound impulse (a click) is applied simultaneously to both ears, the impression is created that it has come from a certain sound source situated in the median plane with respect to the head; in the case, however, when the sound impulse reaches one ear \(0.0001\) sec earlier than the other, the direction in which the apparent sound source is located already changes perceptibly.

If a very brief sound impulse acts on the tympanic membrane, then the stapes executes a rapidly damped series of oscillations (Fig. 15a). At the same time, on the portion of the basilar membrane close to the stapes, the rise and fall of excitation proceed according to the curve shown in Fig. 15b. If, however, a traveling wave arises with a finite propagation velocity, then the process of rise and fall of the sound energy over the whole basilar membrane is very greatly stretched out. Thus there is a difference in time between the maximum of excitation over the whole basilar mem-

brane (Fig. 15c) and with the maximum of excitation in the case when only the region of the membrane in the immediate vicinity of the stirrup is excited. The latter can be achieved by applying to the ear a strong low tone, which, according to the theory of one place, will especially strongly excite the basilar membrane near the helicotrema. If the low tone is sufficiently strong, it will mask in this region of the basilar membrane a weak short impulse, as was established by Wegel and Lane[^22] with respect to prolonged tones.

The time difference discussed above can be demonstrated in the experiment of shifting the apparent source of sound when a short sound impulse is simultaneously delivered to both ears and a strong low tone is applied to one ear.

§ 8. Nonlinear Distortions in the Ear

Fig. 15. On the observation, by means of a short sound impulse, of the velocity of propagation of traveling waves arising under its action.

With regard to nonlinear distortions in the ear, it may be considered established that they are not of nervous origin, since they remain unchanged when the ear is fatigued. Nonlinear distortions therefore represent a purely physical phenomenon, and one may hope that in time it will be possible, by means of them, to make a quite objective inference concerning the motion of the fluid in the cochlea, since the magnitude of the overtones and combination tones arising in the ear is very readily measurable. For this purpose the method of auxiliary tones producing beats is used. It consists in the following: an auxiliary tone is presented to the ear simultaneously with the tone under investigation; its frequency differs by only a few hertz from the frequency of the overtone or combination tone being measured; the beats thereby arising reach a maximum when the amplitudes of the auxiliary and measured tones are equal.

In Fig. 16, for a fundamental tone of 200 Hz and a sound pressure of 10 dyn/cm², the amplitude spectrum of overtones obtained by the indicated method is shown[^23]. As is evident from the figure, the first overtone is, in amplitude, more than one third of the fundamental tone, so that the nonlinear distortions of the ear must in any case be regarded as a very characteristic phenomenon of the cochlear mechanism.

Previously there existed the point of view that nonlinear distortions are caused chiefly by the conical form of the tympanic membrane. If, therefore, the tympanic membrane is subjected to the action...

…by strong, entirely sinusoidal oscillations of the air pressure, then in this case it should radiate the overtones and combination tones that arise not only inward, but also outward, into the auditory canal. Experiment, however, has shown that this outward radiation is ten times smaller than would have been expected, so that the cause of nonlinear distortions must, chiefly, be sought in the motion of the stapes and in the cochlea. This point of view is further confirmed by the fact that, in the absence of the tympanic membrane, no sharply noticeable reduction of distortions is observed.

Fig. 16. Overtones arising in the ear with a fundamental tone of 200 Hz and 10 dyn/cm² of sound pressure

arise, probably, at the base of the stapes either as a result of the nonlinearity of the elastic forces in the tissues connecting the base of the stapes with the temporal bone, or as a result of the vortices that arise (Fig. 12a), producing mechanical rectification, which Wegel[^24] regards as a necessary condition for the occurrence of combination tones. One can demonstrate experimentally the role of the stapes by applying a unilateral air pressure to the tympanic membrane and thereby withdrawing the stapes from its normal position. Fig. 17 gives curves of the change in time of the loudness of two primary tones, 2,000 and 2,260 Hz, of the corresponding first difference tone (260 Hz), and of the normal tone at 260 Hz, when the sound pressure in the auditory canal is decreased.

Combination tones

Fig. 17. Changes in loudness of the fundamental tone, the difference tone, and the ordinary tone identical in frequency with the difference tone, when the sound pressure in the auditory canal is changed.

air pressure in the external auditory canal. As can be seen from the figure, the increase in the loudness of the difference tone during deflection of the auditory ossicles is very great, whereas a normal tone of the same frequency produces a relatively small change in loudness.

In our brief article, which does not claim to be exhaustive, an attempt has been made to illuminate the modern scientific theories in this field. Whether it will be possible to obtain definitive exact results will depend on the possibility of carrying out a mathematical analysis of the motion of fluid in a double canal with elastic walls.

PRINCIPAL LITERATURE ON HEARING

1. H. v. Helmholtz, Die Lehre von der Tonenempfindungen; G. Wilkinson a. A. A. Gray, The Mechanism of Cochlea, 1924; T. Wrightson, The analytical mechanism of the internal ear, 1918; H. Fletcher, Speech and Hearing, 1929; Journ. Acoust. Soc. 1, 311, 1930; E. Waetzmann, Resonanztheorie des Hörens, Müller-Pouillets Lehrb. d. Physik, Akust. Band, p. 141, 1929; Bethe-Bergmann, Handb. d. Physiologie, XI, 1926; E. Meyer, Geiger, Scheel, Handb. d. Hals- usw. Heilkunde, VI, Gehörorgan I; E. M. v. Hornbostel, Neue Beiträge zur physiologischen Hörtheorie, Jahresb. d. Physik u. exp. Pharmakologie, IX, p. 753, 1928; I. Tröger, Die Schallaufnahme durch das äussere Ohr, Phys. Z. 31, 26, 1930; R. T. Beatty, Hearing in man and animals, 1932.

2. O. Frank, Sitzungber. d. Münchener Akad. d. Wiss. 1923, p. 71.

3. H. Held u. F. Kleinknecht, Pflügers Archiv. 216, 1, 1927.

4. J. R. Ewald, Pflüg. Arch. 124, 29, 1908.

5. M. Gildemeister, Kongressber. Basel. Z. Hals-usw. Heilkunde, 27, 305, 1930.

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7. L. J. Saul u. H. Davis, Arch. of Neur. 28, 1104, 1932.

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11. G. Wilkinson a. A. A. Gray, The Mechanism of the Cochlea, 1934.

12. J. R. Ewald, Pflüg. Arch. 93, 485, 1903; 124, 29, 1908.

13. G. v. Békésy, Phys. Z. 29, 793, 1928.

14. O. F. Ranke, Die Gleichrichterresonanztheorie, Habilitationsschrift, Heidelberg, 1931; Berendes, Z. Hals-usw. Heilkunde 36, 388, 1934.

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17. H. Fletcher, J. Acous. Soc. Am. 1, 311, 1930; W. Kucharski, Phys. Z. 31, 264, 1930.

18. Pietro Tullio, Das Ohr, 1929.

19. V. Hensen, Ergebnisse d. Physiol. 1, 2, 873, 1891.

20. H. Sell, Z. tech. Phys. 8, 226, 1927.

21. G. v. Békésy, Phys. Z. 34, 577, 1933.

22. R. L. Wegel u. C. E. Lane, Phys. Rev. 23, 266, 1924.

23. H. Fletcher, J. Acous. Soc. Am. 1, 313, 1930; Ann. d. Phys. 5, 809, 1934.

24. E. Waetzmann, Ton, Klang und sekundäre Klangerscheinungen, A. Bethe-Bergmann, Hand. d. norm. u. path. Physiol. 2, Rezeptions-Organe 1, 579, 1926.