THE DUALISTIC NATURE OF SOUND

To hear is to interpret sound.

To the physicist, sound is a form of energy, an organized movement of particles within any medium. The physicist’s sound can be measured and controlled to do work, or it can alter the position of objects and generate heat.

To the psychologist, sound is a sensation, something that exists only within ourselves. Such sensations create emotions and change our conduct. Sound is real but intangible. One cannot weigh it or see it; one can only feel the effects of it.

Where the physicist’s sound can be controlled, measured, and organized, the psychologist’s sound is conceptual. It may be high or low, loud or soft, pleasant or unpleasant. The psychologist who wishes to relate the sensation of sound to objects and events in the physical world is forced to compare the pitch, loudness, or timbre, as reported by a subject, with the intensity (in decibles), frequency (in cycles per second), and the complex wave form (or analysis of the sound spectra).

The physiologist interprets for both the physicist and psychologist how the sound waves are received and passed through the outer and middle ears into the cochlea; there the sound is transformed into nerve impulses to be received by the brain. The physiologist interprets for the physicist how such neural impulses correspond in patterns of time to the original pattern of the physicist’s sound wave, and for the psychologist, how such nerve impulses generate our subjective sensations. Such a study, a blending of objective and subjective data, is known as psychophysics.

The physical properties of a sound are inherent in the sound waves and can always be measured independent of any human observer. The subjective properties of a sound are characteristic of the sensations experienced by a human listener and cannot be measured without him.

Hearing must be discussed in psychophysical terms, for such terms will always indicate a relationship between the objective and subjective aspects of sound and their impact upon human conduct.

THE SENSITIVITY OF THE EAR

Man has not been able to create a mechanical implement that is able to transfer motion from one point to another as effectively and efficiently as do the ossicles of the middle ear when they transfer pressure variations from the outer ear to the hydraulic system of the inner ear. The manner in which such a transfer of motion is accomplished never fails to bring to the thoughtful observer a sense of awe and leads him to a new respect for his ability to hear and interpret the sounds of life about him.

The sensitivity of the ear is remarkable. Judson and Weaver¹ hold that at the most favorable pitch (3,000 cps) the ear will detect periodic pressure changes of less than one one-thousandth of a dyne per square centimeter. Such a pressure is equivalent to the weight of a human hair one-third as long as its diameter. Since the normal weight of the air is about one million dynes per square centimeter, the ear responds to a periodic change of one-billionth part of the value of this pressure. Hallowell Davis states:

The human ear is so sensitive that at its best it can almost hear the individual air molecules bump against the ear drum in their random thermal flight. The distance that the eardrum moves in and out with each wave when we hear just the faintest audible tone at the most favorable frequency is less than one-tenth of the diameter of a single hydrogen molecule. This distance is, of course, far less than we can see under the best microscope. We cannot think of it in terms of inches for it is less than a hundred millionth of an inch. If the capital ‘I’ at the beginning of this sentence were enlarged to the height of the Empire State Building a hundred millionth of an inch would correspond to about the thickness of a piece of cigarette paper.²

Animals have an even more efficient means of collecting sound energy. Their outer ears are much larger and are able to gather in more of the sound signal. But the inner ear of man is as sensitive as it can usefully be. If the inner ear were more acute, the sound of molecular motion would create a continuous hiss that would mask the meaningful faint sounds around us, and the threshold of hearing would be raised.

To interpret properly the listening process, one must define the constituents of audible sound in physical and psychophysical terms.

THE PHYSICAL ASPECTS OF FREQUENCY

Frequency is the measure of the number of times per second that a vibrating particle executes a complete cycle. As illustrated by Fig. 50. Frequency is measured in cycles per second (cps).³

Frequency is not synonymous with pitch. Frequency is an observation of an aspect of sound which is determined by assistance of instruments; whereas pitch is determined by a direct observation of an aspect of sound as it affects the ear and is entirely subjective.

The Measurement of Frequency

The musical scale is a scale of frequency. Fig. 81 shows the frequency of notes of the musical scale which are mathematically constructed in order to provide for all possible changes of key. The system of intervals is based upon an equally tempered scale in which each octave consists of twelve equal intervals.⁴ The frequency of a note is determined by multiplying the frequency of any note by one of the following factors:

Each octave thus attained will be the exact multiple of another octave.

Fig. 81. Frequency of Notes of the Musical Scale

Chart courtesy of Conn Corporation, Elkhart, Indiana, world’s largest manufacturer of band instruments.

Frequency Limits of Audible Sound⁵

The range of audible frequencies extends from about 20 to 20,000 cps. For the ear the most sensitive range is from 500 to 4,000 cps; this range is shown in Fig. 82 to be almost the same range as that which is important in understanding speech. Above 4,000 and below 500 cps, the sensitivity of the ear declines more and more rapidly with the increase in age. Young people are able to distinguish sounds well between 18,000 and 20,000 cps where a man or woman of forty has difficulty hearing frequencies above 11,000 or 12,000 cps. In Fig. 82 the lowest line divides the audible tones from the inaudible and shows how both low frequency and high frequency sounds must be made more intense to be heard.

The low threshold curve of hearing⁶ suggests hearing sounds under ideal conditions: Young adults with healthy ears, extremely quiet environment, and a subject who is skilled in the process of listening to faint sounds.

The average threshold curve of hearing is represented by the broken line in Fig. 82. This line is not fixed. Hearing acuity can vary fifteen decibels above and below this line and still be normal; the threshold depends upon the frequency and the person who is being tested.

Fig. 82. Thresholds of Hearing

Source: Hallowell Davis, Hearing and Deafness (4th ed.; New York: Rinehart Books, Inc., 1951).

The best threshold of hearing curve bounds the area of audibility. Below the line sounds are not heard. Above the line sounds are heard with varying degrees of acuity that depend upon frequency and intensity. As an example, the average best acuity of hearing occurs between 1,000 and 4,000 cps at an intensity level of 20 decibels. For tones above 4,000 cps and below 1,000 cps the intensity of each tone has to be raised to be perceived aurally. The area of audible speech is bounded above by thresholds of discomfort (tickling and pain); such thresholds are sensed only when the intensity level is 120 decibels or greater.

THE PSYCHOPHYSICAL ASPECTS OF PITCH

Pitch is that aspect of auditory sensation which the listener organizes upon a scale running from low to high. Pitch is chiefly a function of the frequency of the sound, but it is also dependent upon the intensity and the timbre of the sound.⁷

Pitch is used for a relative subjective comparison between musical sounds; one depends upon the timbre of the sound to detect the difference between two notes of the same pitch produced by different instruments such as a piano or a violin, an oboe or a clarinet.

For the singer, pitch depends upon intensity to a profound degree. Stevens quotes Miles⁸ in describing an experiment in which the singer is required to reproduce vocally the pitch of a tuning fork (middle C). When the fork is held close to the ear, in his attempt to match the pitch, the singer sings a lower pitch. He actually hears the louder tone as lower.

Fig. 83. Contours Showing How Pitch Changes with Intensity

The percentage change in frequency necessary to keep the pitch of a tone constant in the face of a given change in intensity can be taken as a measure of the effect of intensity upon pitch. Source: Stanley Smith Stevens and Hallowell Davis, Hearing (New York: John Wiley & Sons, Inc., 1963).

In an experiment conducted by Stevens⁹ tones ranging from 150 cps to 1,200 cps were tested to determine the effects of intensity upon the audible range of hearing. Two tones of slightly different frequencies were presented alternately to an observer. He was allowed to adjust the intensity of one tone until the pitch of the two tones appeared equal. Although the frequency of the vibrator was not altered, the observer psychophysically compensated for the difference in intensity, thereby making the two tones sound equal in pitch.

One should note that this phenomenon does not occur when complex tones are used. The pitch is held constant because one or more of the partials are stable and do not change with changes of intensity.

Fig. 83 illustrates the relationship between pitch and intensity which must be maintained in order to keep a tone at a constant level of pitch. It also shows what happens to the pitch of tones of various frequencies when the intensities are altered. For low tones the pitch lowers with intensity. For high tones the pitch raises with intensity.

The Measurement of Pitch

The relation of pitch to frequency is not one to one. In 1937 Harvard University psychophysicists devised an electronic piano with knob adjustments on the keys which permitted a wide range of frequency variation for each key. Subjects faced the task of tuning the piano to equal appearing pitch intervals evenly spaced along the scale. The frequency of each tone was then measured. Stevens describes the research experiment as follows:

The subjects did not tune the piano to equal steps of the physicist, nor . . . to that of musical intervals. A new scale of pitch measurement was devised. To measure the intervals of the new pitch scale, units called “mels” from the word “melody” were created. A 1,000 mel tone was determined to be a sound with a frequency of 1,000 cycles and an intensity of 40 db.¹⁰

An examination of the graph in Fig. 84, will show that in the lower parts of the scale an equally spaced octave determined by the mel scale will vary 100 mels when compared with the frequency scale, but at the upper end of the piano (2,000 to 3,000 cycles) the octave represents a 700 mel variation when compared with the frequency scale. “These measurements confirm the feeling often expressed by pianists that the higher musical octaves sound larger than the lower ones.¹¹

Fig. 84. The Mel Scale of Pitch Showing How Subjective Pitch in Mels Is Related to
Frequency (cps) for Pure Tones

Source: The Speech Chain by P. B. Denes and E. N. Pinson, published by Bell Telephone Laboratories, Inc. (1963).

S. S. Stevens describes the research effort as follows:

Was there a physical explanation of this? To account for the form of the mel scale the researchers studied the structure of the human ear. Asking: Where are the points at which different frequencies stimulate the basilar membrane of the inner ear? Comparing the mel scale with a sort of anatomical map showing the membrane where each frequency sets up its maximum vibration, they found an amazing coincidence. In tuning the electronic piano, the listeners had adjusted the tones so that the points of stimulation on the basilar membrane were equally separated. Equal pitch extent, therefore, meant equal separation along the membrane.

The Organ of Corti behaves like a specialized piece of skin. Just as a touch anywhere on the skin produces a sensation that seems to be localized in a particular place, so a “touch” on the sensitive cells of the inner ear produces a sensation localized in a kind of subjective space that we call pitch. The “mel” scale of pitch provides an accurate map of the cochlea, in which a distance of one millimeter on the basilar membrane corresponds to 100 mels.

When musicians are asked to set a pure tone precisely one octave above another pure tone, they tend to set the upper tone a little sharp. Many musical egos are shaken when the musician discovers he is unable to produce a perfect octave by ear.¹²

THE PHYSICAL ASPECTS OF INTENSITY

Intensity refers to a dimension of a stimulus. It is a measure of the strength or magnitude of the stimulating agent. In plane progressive sound waves, intensity is measured in terms of pressure or energy flow (power).¹³ “Sound pressure, therefore, in a specified direction at a point, is the average rate of sound energy transmitted in the specified direction through a unit area normal to this direction at the point considered.”¹⁴

Intensity is not synonymous with loudness. Intensity, like frequency, is a physical aspect of sound which must be observed with the aid of instruments; loudness, like pitch, is a subjective aspect of sound which may be observed directly.

Intensity is difficult to define because the values of a sinusoidal (See definition on p. 104.) sound wave must be specified in order to completely determine the sound wave. Sound is two dimensional and intensity is one of its dimensions,¹⁵ frequency is the other.

The propagation of sound involves the rapid oscillation of air particles in an elastic medium.

This oscillation involves a transfer of energy through the medium, and it ends by exerting a minute force against any surface which the wave strikes. Since this force or pressure varies during each to-and-fro oscillation, the term intensity derives from the amplitude or amount of increase or decrease in pressure in each oscillation of the particle.

The Measurement of Amplitude or
Pressure of Intensity

In considering the movement of air particles one also must consider the force which disturbs them from their positions of rest. Such a force is called pressure. It is measured by a force unit called the dyne. “The dyne is a force which will produce a change in velocity of one centimeter per second in a gram mass in one second.”¹⁶ The force of gravity exerts a pressure of 1,000 dynes upon one square centimeter mass. Normal atmospheric pressure is equal to about one million dynes per square centimeter.

Pressures within sound waves are very small. The smallest pressures sufficient to produce an audible sound within the human threshold of hearing is .0002 dynes per square centimeter.

The Measurement of Power of Intensity

As an air particle is disturbed it transfers its energy to an increasing number of particles which tend to dissipate the energy and particle velocity. To measure the energy available at a point away from the sound source, one must use a measure of power which will indicate the sound’s intensity, or particle velocity, in very small quantities.

When the application force results in the displacement of a particle, work is done. Power is the amount of work accomplished in a given time. Its unit is the erg per second. Since the erg per second is too small for practical use the power or intensity of a sound wave is measured in watts per square centimeter. A just audible sound within the human threshold of hearing has a sound intensity of 10-16 watts or ten billionths of a watt.¹⁷

The Decibel Scale of Intensity

The human ear is extremely sensitive to variations in the amplitude of sound waves, which are interpreted here as variations in air pressure.

Variations in air pressure may cause the amplitude to increase while the frequency remains constant. In this case, the movement of the point of the pendulum is analogous to the oscillation of an air particle. Variation in amplitude of an oscillating body may be illustrated by hanging two pendulums, each of the same length, and starting them swinging, one in a long arc, the other in a short arc. Both will cross the point of rest at the center at the same moment; i.e., frequency is constant while the amplitudes are different.

Likewise, variation in air pressure may cause the frequency to change while the amplitude remains constant. The oscillations of the air particle may be illustrated by shortening the string of one pendulum by one half. The number of complete oscillations, cps, will be doubled in the shorter pendulum, but the amplitude will be the same, provided each weight is released at the same point. (Fig. 86).

Since the ear responds to an extremely wide range of intensities from a just audible sound to one with an intensity ten billion times more powerful, acoustic engineers have found it convenient to use a logarythmic system that will compare the relative value of one sound to another. First, they had to establish a reference level of intensity with which all other sounds could be compared.

Fig. 85. Two sounds, one with twice the amplitude of the other

Source: Peter Ladefoged, Elements of Acoustic Phonetics (Chicago: University of Chicago Press, 1962).

Such a reference sound was determined by listening to a 1,000-cycle tone at an intensity level where the sound first becomes audible. Such a sound has the acoustic power of 10-16 watts per square centimeter and the acoustic pressure of .0002 dynes per square centimeter. This point of just audible sound was called zero decibels. Once such a reference level was established, considering the amplitude or power of any sound as being so much more or less than that of the reference sound was a simple task.

Fig. 86. Two Sounds with Equal Amplitudes, But One with a Frequency of 100 cps, and the Other with a Frequency of 300 cps

Source: Peter Ladefoged, Elements of Acoustic Phonetics (Chicago: University of Chicago Press, 1962).

The following graph by Ladefoged (Fig. 87) shows approximately thirteen equal steps to intensity, starting from the reference pressure of .0002 dynes per square centimeter, and the intensity power level of 10–¹⁶ watts per square centimeter to the threshold of pain. One can see that the difference in power (in actual watts per square centimeter) is far greater between steps twelve and thirteen than it is between steps one and two; but the power ratio between any two adjacent steps remains the same.

One logarithmic unit to the base of ten, of the ratio of one acoustic power to another is known as a bel. Since the bel is a rather large unit, in practice a unit whose value is one-tenth of a bel is used. It is called the decibel. The following table explains this statement:

Fig. 87. The Powers of Sounds Constituting Thirteen Approximately Equal Steps of Loudness

The power of each sound in watts per square centimeter is proportionate to the area of each block. Source: Peter Ladefoged, Elements of Acoustic Phonetics (Chicago: University of Chicago Press, 1962).

All that one has to do to find the common logarithm of the power ratios shown in the above table is to count the number of zeros. The difference in decibels between the two sounds can then be found by multiplying this number by ten.

When this system is applied to the power ratios in Fig. 87, the common logarithm of the sound at the threshold of pain and the reference level is 13 because the number has 13 zeros in it. The difference between the two sounds is 10 multiplied by 13 or 130 decibels. The difference between step three and step five is 20 db since the power at step five is 100 times greater than at step three and the common logarithm of 100 is 2.

When the power ratio between two sounds is some intermediate value such as 47 to 1, logarithm tables are used to find the proper differences between the sounds.

THE PSYCHOPHYSICAL ASPECTS OF LOUDNESS

Loudness is the intensive attribute of an auditory sensation, in terms of which sounds may be ordered on a scale extending from soft to loud. Loudness depends primarily upon the sound pressure of the stimulus, but it also depends upon the frequency and wave form of the stimulus.¹⁸

Loudness depends upon the amplitude of a sound wave. Fig. 87 shows a loud sound in which the pressure variations are large and a softer sound in which they are much smaller.

The Measurement of Loudness

Gustav Theodore Fechner of Leipzig, Germany, published Elements of Psychophysics in 1860. In this work the author set forth a law known as the Weber-Fechner law which expressed the relation between stimulus and sensation by a simple rule:

As stimuli are multiplied to greater magnitude sensations increase by addition; i.e., each time the intensity of the sound is doubled, one step is added to the sensation of loudness. This is a logarithmic process and Fechner’s law states that sensation grows as the logarithm of the stimulus.¹⁹

Since the law applied to a stimulus of any kind—light, vision, taste, touch, and smell—the “just noticeable differences” between stimulus and the sensation could be measured and experimental psychology was established as a science.

Fig. 88. Two Sounds, One Twice as Loud as the Other and One with Twice the Amplitude of the Other

Source: Peter Ladefoged, Elements of Acoustic Phonetics (Chicago: University of Chicago Press, 1962).

Loudness Level Scale

To determine the psychophysical relationship between loudness and intensity levels, it was necessary to create a new scale of measurement that would be wholly compatible with the loudness level and the intensity level as shown in Fig. 89. The empirical choice for such a unit of measurement was the phon.

To establish a sound level scale, many listeners with headphones, heard a 1,000 cycle tone at 40 db. A second tone was fed into the earphones, at say 200 cps. By turning a dial the listener could adjust the 200 cps tone until the two tones were equally as loud. Other tones of various frequencies were Fig. 85. Two sounds, one with twice the amplitude of the other matched in loudness with the 1,000 cps-40 db sound, and their positions were recorded. For example, all points on the 60 phon contour were rated equal in loudness to a 1,000 cps sound at 4 db. The loudness level of a given tone was defined as the intensity (measured in decibels) of a 1,000 cps tone that sounded equal in loudness to a given tone. The unit of loudness level was named the phon. The numbers on each of the contours in Fig. 89 are the number of phons corresponding to that particular contour.

Fig. 89. Loudness Level Contours Adopted by the
American Standards Association, 1936

Loudness levels in phons are indicated in the center of the chart. Source: The Speech Chain by P. B. Denes and E. N. Pinson, published by Bell Telephone Laboratories, Inc. (1963).

Thus a 100 cps tone must have an intensity of about 62 db to have a loudness level of 40 phons, while a 30 cps tone will have to have an intensity of about 80 db of 40 phons.

Loudness level becomes apparent when one listens to present day highfidelity music. If the volume decreases both bass and treble seem to fade; accordingly, the volume of the bass and treble portions of the spectrum are raised to bring the total sound into balance. The reason is that the threshold of hearing is lowest between 1,000 and 4,000 cps (Fig. 82, p. 147) and when the loudness of the music is reduced the musical sounds reproduced within this range are heard where frequencies below 1,000 cps and above 4,000 cps are not heard.

The Numerical Loudness Scale

The phon scale of loudness level (Fig. 89) is used to arrange sensations in order of increasing magnitude. It cannot tell the scientist how much greater in magnitude one tone is than another; it can only tell him that one is greater than another.

The Weber-Fechner²⁰ law was disproved in the nineteen-thirties by acoustic engineers who required a means of measuring loudness. The decibel measured sound energy in logarithmic units, but it did not prove to be the proper scale for listening comparisons. “It was apparent to anyone who listened that a loudness of 50 decibels was not one-half the loudness of 100 decibels; 50 db is defined as the quiet buzz of a normal room, and 100 db is equivalent to the din of a boiler factory.”²¹

A scale was needed which would express numerical relations between magnitudes of sensations measured. In the case of loudness the numerical scale devised by the psychoacoustic laboratory at Harvard University was identified by the word sone (Latin for sound) as its unit of loudness measurement. It is known as the sone scale. By definition one sone is the loudness of a 1,000 cps tone at 40 db.

Researchers²² found that each increase of 10 db in the intensity of a sound stimulus doubles the sensation of loudness. The experiments showed that the sensation of loudness grows by multiplication and not by addition, as was claimed by Fechner.

To evaluate the loudness relationship a listener is asked to compare two tones and to adjust the intensity of one of them until it is twice as loud (or half as loud as the other). Experimenters²² have found that the perceived loudness is not proportional to the loudness level (Fig. 90). To increase the loudness from 0.1 sones to 10 sones one must increase the loudness level from 20 to 66 db Stevens now believes²³ that the relation of loudness to the intensity of a 1,000-cps tone can be expressed by the rule: An intensity increase of 10 db corresponds to a loudness ratio of two to one, and to a typical listener, loudness is a power function of sound pressure. The power exponent or multiplying factor for loudness is about .03 power of its sound energy. An increase of 10 db (between 40 and 50 cps) at the intensity of a 1,000 cps tone at 40 db increases the sone level six times from the original base of 40 db. A second 10 db increase (between 80 and 90 db) increases the sone level by twenty sones (25 to 45) (Fig. 89).

Fig. 90. The Loudness Function

Perceived loudness in sones depends upon the loudness level of the stimulus in db. Calibration on the ordinate is in logarithmic division of fifths. Source: The Speech Chain by P. B. Denes and E. N. Pinson, published by Bell Telephone Laboratories, Inc. (1963).

THE ANATOMY AND PHYSIOLOGY OF THE EAR

The Outer Ear

The external ear, the pinna, is mainly an ornament. Man has never developed it to use as a focusing device as do most animals. The human ear canal is irregularly oval in cross-section and varies from man to man in size and shape. It is approximately twenty-five centimeters in length. Acoustic waves falling on the external ear funnel down the ear canal and set the eardrum into vibration. Denes and Pinson state:

Because the ear canal is an acoustic resonator it amplifies frequencies near its own frequency. Thus the pressure at the ear drum for tones near this resonance (from 3,000 to 4,000 cps) may be two to four times greater than the pressure at the entrance to the canal. This effect permits us to detect many sounds that would be imperceptive if the drum were located at the surface of the head.²⁴

The tympanic membrane, the eardrum, lies at the end of the auditory canal. It is a pearl gray wall composed of a thin, tough fibrous membrane that is fastened to the bony wall of the canal by a ring of tough fibrous tissue (Fig. 91).

The membrane is cone-shaped inward toward the middle cavity. The handle of the hammer (the malleus), the first of the three ossicles that transmit the vibrations of the drum to the middle ear, is attached to the inner surface of the drum. It keeps the membrane stretched tightly and cone-shaped. This tension is increased by the aid of the tensor tympani muscle (Fig. 92).

Fig. 91. The Outer, Middle, and Inner Ears After Hallowell Davis.

Fig. 92. The Middle Ear After Hallowell Davis.

The Middle Ear

The middle ear is a cavity in the bony structure of the skull. This cavity contains three small bones called the auditory ossicles—the malleus, the incus, and the stapes. These ossicles, which form the mechanical linkage between the eardrum and the inner ear, are suspended from the cavity walls by ligaments (Fig. 92).

Motions of the eardrum are transmitted through the malleus, which is attached to the eardrum, to the incus (anvil), the second of the ossicles. The incus ends in a long curved tip and is connected to the head of the stapes (stirrup), the last of the three ossicles.

The stapes is shaped like a stirrup, and its oval base fits into the oval window of the inner ear. The variation of air pressure causes the tympanic membrane to move back and forth, a motion transmitted through the first two ossicles to the stapes. It rocks back and forth in the oval window and compresses the fluid of the inner ear. The stapedius muscle attached to the neck of stapes pulls the stapes outward and backward; it thus acts as an antagonist muscle to the tensor tympani muscle, which pulls in the opposite direction. The combined action of these two muscles tends to suspend the ossicles and hold them steady during their rapid movement of complex vibrations.

The round window is located beneath the oval window. It is covered with an elastic membrane stretched flat. Its function as a resilient shock absorber will be explained later.

The eustachian tube running between the middle ear and the mouth cavity effectively links the middle ear with the outside air, equalizing the pressures in the middle ear and permitting the ossicles to work freely. Swallowing normally causes the eustachian tube to open momentarily, allowing the pressures to equalize.

Denes and Pinson²⁵ have revealed that the mechanics of the middle ear accomplish amplification of the outside sound. Their studies have led to the following conclusions, briefly stated. The middle ear increases the amount of acoustic energy entering the fluid-filled inner ear by increasing the amplitude of the pressure variations at the oval window. The ossicles behave like a lever, producing greater force at the footplate of stapes than the force applied at the malleus. This pressure amplification in the middle ear enables us to hear sounds whose energies are about one thousand times weaker than could otherwise be heard (Fig. 93).

Fig. 93. Mechanics of the Middle Ear

Source: Stanley Smith Stevens and Hallowell Davis, Hearing (New York: John Wiley & Sons, Inc., 1963).

The Inner Ear²⁶

The inner ear is contained within the temporal bone, the hardest bone structure of the body. It is a series of channels filled with a clear watery fluid containing delicate membranous sacs, which are themselves filled with a watery fluid and contain sensory cells, each having its own function. The vestibule is a central portion that lies immediately behind the oval window. On one side it joins the cochlea, which is the organ of hearing, and on another side, the loops of three semicircular canals that form the sense organs of balance and turning (Figs. 91 and 94A).

The cochlea is coiled like a snail shell in a flat spiral of two and one-half turns. The canal within the cochlea is slightly over one inch in length (thirty-five millimeters) and ends at the apex of the spiral. The canal is partly divided into two galleries by a spiral shelf of bone protruding from the inner wall of the canal. This shelf is called the spiral lamina. The division is completed by a fibrous, flexible basilar membrane, which stretches from the edge of the bony shelf to the spiral ligament. This ligament attaches it to the outer wall of the canal. The upper gallery is called scala vestibuli, the lower, scala tympani. Both galleries are filled with watery fluid called perlymph, which makes both galleries an incompressible hydraulic system (Fig. 95A and 95B). The oval opening provides a window into the vestibule, which is continuous with the scala vestibuli, and the round window is the termination of the scala tympani.

Fig. 94A. The Cochlear Portion of the Inner Ear

Source: The Speech Chain by P. B. Denes and E. N. Pinson, published by Bell Telephone Laboratories, Inc. (1963).

Fig. 94B. Diagram of a Section Through the Core of the Cochlea

Source: The Speech Chain by P. B. Denes and E. N. Pinson, published by Bell Telephone Laboratories, Inc. (1963).

The basilar membrane and the bony shelf terminate before the end of the spiral canal is reached, so that both galleries are continuous and permit the fluids to pass freely between them. This opening at the apex of the canals is called the helicotrema (Fig. 95A and 95B). The basilar membrane is thirty-two millimeters in length, it is broadest at the apex of the spiral canal (one-half millimeter) and narrowest at the base of the canal near the oval window (one-twentieth of a millimeter). The membrane is thin and taut at its base near the stirrup and thick and loose near the helicotrema.

Fig. 95A. Cross Section of Cochlear Canal After Hallowell Davis.

Fig. 95B. Cross Section of Spiral Organ (Papilla) or Organ of Corti

Source: Andrew Theodore Rasmussen, Outlines of Neuro-Anatomy (Dubuque, Iowa: Wm. C. Brown Co., Pub., 1947).

Upon the surface of the basilar membrane within the scala vestibuli lie the sensory cells of hearing known as the organ of Corti (Fig. 95A). Separating the organ of Corti from the fluid of the scala vestibuli is a thin resilient membrane called Reissner’s membrane (Fig. 95A). The area within the organ of Corti is filled with a heavy thick fluid called endolymph.

The sensory cells are hair cells, each with dozens of microscopic protruding hairs arranged in four parallel rows that run the full length of the basilar membrane in its spiral ascent to the helicotrema. About 3,500 hair cells stand side by side in an inner row, and approximately 20,000 slightly smaller hair cells are evenly spaced in orderly arrangement in three outer rows.²⁷ The rods of Corti form a triangle to supply support and stiffness to the organ (Fig. 95B).

Stretching out above the hair cells is the tectorial membrane, soft, gelatinous, and yielding. The tiny hairs of each cell are imbedded in this soft membrane. Any bending or movement of the hair cells sets off nerve impulses in the nerve fibers attached to the lower end of each hair cell (Fig. 95B).

The nerve fibers run from the hair cells to the central core of the cochlea, where they join like strands of rope to form the auditory nerve and pass to the brain.

Each nerve fiber connects with more than one hair cell, and each hair cell connects with several nerve fibers in adjacent but overlapping zones. Thus no hair cell is responsible for a single frequency. Several cells and fibers send impulses to the brain simultaneously, even if the sound is sinusoidal.

ANALYSES OF SOUNDS BY THE EAR

The experiments of George Von Békésy²⁸ have revealed that when a sound pressure impulse causes the footplate of stapes to rock in the oval window the fluid within the cochlea is suddenly compressed causing the basilar membrane at the vestibule to bulge into the scala tympani. This sudden downward thrust creates an undulating wave which sweeps along the basilar membrane. The wave turns at the helicotrema, traverses the fluid of the tympani gallery where the shock of the wave is absorbed by the bulging of the round window.

As the wave moves along the basilar membrane its amplitude increases until it reaches a maximum then falls off sharply as the wave dies out. The frequency of sound is detected by the ear (Fig. 96) at the point that this wave reaches its greatest amplitude upon the basilar membrane. For high frequencies, the wave height is greatest at the oval window where the basilar membrane is lightest and stiffest. For the lower frequencies, the wave height is greatest at the upper end where the membrane is broader and more elastic.

Fig. 96. The Envelopes Indicate the Extent of Basilar Membrane Displacement for Different Frequencies of Sinusoidal Excitation Applied at the Stapes

Source: The Speech Chain by P. B. Denes and E. N. Pinson, published by Bell Telephone Laboratories, Inc. (1963).

The action which creates the energy necessary for the transmission of a signal to the brain is a shearing action between the organ of Corti (Fig. 97), which rests upon the basilar membrane, and the tectorial membrane, which is suspended over it. Each moves in the opposite direction. This shearing action causes the hairs to bend and their cells generate electrochemical impulses for transmission by the auditory nerves to the brain.²⁹

When a complex wave strikes the eardrum, the motion of stapes responds to each sinusoid within the waves tonal spectrum and the undulation of the basilar membrane becomes as complex as the spectrum. The energy of each partial then creates a certain wave height which determines the number of nerve cells that will fire at that particular point of the wave crest. If the signal is weak, one or two nerve cells will fire. If it is strong many will be affected. Denes and Pinson³⁰ state that the sensation of loudness may be determined by the number of pulses reaching the brain’s auditory areas each second. The fact that different fibers have different thresholds may play an important role in determining such a sensation; however, only further research will provide factual evidence of this subtle aspect of hearing.

Fig. 97. Shearing Actions of Membranes

Fig. 98. Auditory Patterns for Four Notes of Taps Played on a Bugle

The width of the black area is proportional to the loudness contributed by that particular bit of the organ of Corti. Source: Bell Telephone Laboratories, Inc.; courtesy, H. Fletcher.

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^* To demonstrate the singer’s dependence upon auditory feedback a simple experiment may be performed. Attach a speaker system to a tape recorder through output jacks on the recorder. Record as usual, but turn on the speaker system while recording. The sound will emerge from the speaker a fraction of a second later than the sung word, causing the singer considerable confusion. Such an experiment will reveal just how much the singer relies upon auditory feedback rather than upon proprioceptive feedback for sensing the desired position for the resonators and the articulators.