SOUND. —
I. PHYSICAL GENESIS OF ACOUSTIC STIMULI
The energy adequate to stimulate the auditory apparatus is a particular form of mechanical energy, namely vibratory energy. A conservative mechanical system containing elastic potential energy tends to return it in the form of kinetic energy; and this, when certain conditions of symmetry are satisfied, may be transformed into potential energy according to a closed cycle of energy exchange, giving rise to a periodic vibratory movement of the material masses of the system around their position of rest. Parasitic dissipation of the energy contained in the system means that this cycle can be repeated only a limited number of times, so that, if the vibrating system is not supplied with energy, the vibrations are damped over a shorter or longer period.The amplitude of the vibrations and the number of vibrations that the system itself performs in the unit of time (frequency) depend on the mechanical quantities involved, in particular on the masses and the restoring forces that continuously urge them toward the position of rest. One complete vibration per second, that is, one period per second, is the unit of frequency and is called the Hertz (Hz).
If the vibrating system is situated in an elastic medium (solid, liquid, or gaseous), it is also a “source of vibrations,” insofar as its alternating movements are communicated to the medium and transmitted through it by pressure waves. It is in this way that vibrations reach the auditory apparatus, through the air, directly, setting the tympanic membrane in vibration and consequently, in succession, the structures of the middle and inner ear; a small part of the vibratory energy arrives by direct conduction through solids (e.g., the ground), reaching the inner ear directly by bone conduction, as also occurs with a modest fraction of that conducted by the gaseous medium.
The tympanic membrane is sensitive to the “pressure” of the incoming waves, and the vibratory stimulus is adequate only if this pressure lies within certain limits (“auditory threshold” and “threshold of pain”), while its frequency likewise lies within other defined limits (the lower and upper limits of the tonal auditory field). An increase in the pressure of the stimulus is perceived as an increase in the (subjective) intensity of sound, while a rise in its frequency is perceived as a rise in the so-called (subjective) pitch of sound.
Through the external and middle ear, mechanical vibrations at acoustic frequencies reach the cochlea, where the conditions are established for excitation of the VIII nerve; the nerve impulses travel, undergoing various modifications, through a chain of four neurons and their synapses, and reach the auditory radiations and the auditory cortical area. The conscious subjective process then begins, during which sound arises as a result of the highest associative, perceptive, and apperceptive processes.
There is no basis for speaking of sound as present in the environment surrounding us. In that environment, the vibratory phenomenon has physical reality. It should also be noted that the sensation of sound may arise even in the total absence of vibrations in the external environment, for example through the application of electric currents to the auditory apparatus (the electrodonic phenomenon); here the electrical stimulus is inadequate but sufficient.
II. VIBRATING BODIES
Taut strings, metal plates, rods, bells, and almost all the objects surrounding us are mechanical systems capable of vibrating at an acoustic frequency; air, too, can become a vibrating body when enclosed within cavities, as in organ pipes and sound boxes.A remarkable vibrating system is that constituted by the “vocal cords,” more accurately called the “vocal lips.”
III. SPEED OF VIBRATION
The amplitude and frequency of vibratory motion determine the speed at which the particles of the vibrating body follow their alternating periodic motion around the position of rest, toward which, as stated, they are urged at every instant by the elastic restoring forces.In a tuning fork having a frequency of 100 Hz, excited so that the vibration amplitude of the end of the prongs is one millimetre, each particle of that end travels, in one second, 100 times over distances of one millimetre each, amounting to a total path of 200 mm, and therefore has an average speed of 20 cm per second, equivalent to 0.72 km per hour.
The tympanic membrane, which at a frequency of 3000 Hz can be set vibrating with an energy of barely one-billionth of a microwatt per square centimetre, has, according to Wilska, a vibration amplitude equal to 5.2 hundred-billionths of a centimetre; under these conditions it has, as is easy to calculate, an average speed of 3.12 millionths of a millimetre per second, that is, approximately 12 microns per hour.
IV. SPEED OF PROPAGATION
Calculations of this kind can also be repeated for the particles of the medium (gaseous, liquid, or solid) in which the vibratory motion propagates. In air, for example, the speed of the particles reaches at most fractions of a millimetre per second, since, although the movement is rapid, their displacement around the position of rest is always extremely small.The speed, however, at which the vibratory motion propagates (commonly designated by the term « speed of s. ») depends on the physical characteristics of the medium, more precisely on its density and its modulus of elasticity—quantities that are themselves related to various factors, such as temperature and pressure. In air, the speed of propagation is 331.45 metres per second at zero degrees centigrade under the normal atmospheric pressure of 760 mm. of Hg., and increases by 0.607 m. per second for every degree of increase in temperature; thus one may take its average value to be approximately 340 m. per second in relation to the average ambient temperature at our latitudes. In liquid media the speed is greater (in distilled water, for example, it is 1430 m./second at 5° C); in solids it is several times greater still.
The speed of propagation does not depend, within broad limits of approximation, on the frequency of mechanical vibrations (at least within the limits of the acoustic range); a close dependence between frequency and speed would make it almost impossible to hear words and music at a distance, since tones of different pitch would reach the listener’s ear with different delays. The speed of propagation is not perceived as such by the ear, but we are accustomed to appreciate it as an indirect consequence in the fact, for example, of hearing the s. with a greater or lesser delay (in relation to distance) from the moment at which we see the act that generated the mechanical vibrations. This speed is also of primary importance in determining the direction from which a vibration at acoustic frequency originates, a determination connected with differences in the time and phase of perception in the two ears.
The vibratory displacement of the particles takes place in the very direction of propagation; in this sense, there are no waves in the medium as such—that is, not in the way we are led to imagine by taking as a model the waves on the surface of water, in which the motion of each particle occurs in a direction perpendicular to the direction in which the disturbance propagates over the surface.
In the propagation of elastic waves in a homogeneous medium, therefore, there exist only zones of compression and rarefaction, following one another in orderly succession and spaced at equal intervals in the direction of propagation of the elastic disturbance. The length of this interval is called « wavelength » and is inversely proportional to frequency. At 100 periods per second, with a speed of 340 m. per second, each wave is 3.4 m. long; at 1000 periods per second, with the same speed, each wave is 34 cm. long.
V. SIMPLE AND COMPOUND MOTIONS: TIMBRE
The mechanical vibrations of bodies at acoustic frequency are periodic movements similar to pendular movements, but they attain the latter’s regularity and simplicity only in the rare cases in which particular conditions of structural simplicity and symmetry are indeed realized (as, for example, in a tuning fork).The course of the vibratory motion over time is in such cases representable by a sinusoidal function of the type y = sin X.
An elastic body of any shape, on the other hand, vibrates by dividing itself into various vibrating portions (compound vibratory motion), so that vibrations having various frequencies and amplitudes are produced simultaneously. Simple ratios of multiplicity (harmonic ratios) may or may not exist among these frequencies. The component whose frequency is twice that of the fundamental frequency is called the second harmonic, that whose frequency is three times as great the third, and so on. Any compound motion can always be decomposed into a series of simple, that is, sinusoidal, vibratory motions which, coexisting, determine the compound motion itself. The investigation of these components is commonly called « analysis of s. ».
It is to the « composition » of vibratory motion that the subjective appreciation of timbre corresponds. Timbre varies as a consequence of changes in the number, frequency, and amplitude of the vibrations composing the complex vibration. Differences in phase are of lesser importance.
When the component vibrations are not in harmonic ratios but are completely independent of any law of mathematical relationship, especially when the vibratory motion is rapidly damped, the listener defines his auditory sensation more as noise than as s. A typical example is provided by the « Savart wheel », that is, a toothed wheel against which a piece of card may be placed. When the wheel turns, as each tooth passes, the card undergoes an oscillation, producing a definite noise; but if the successive impacts on the teeth follow one another rapidly, the auditory sensation may more properly be defined as s. of a pitch dependent on the number of impacts per second, that is, on the speed and the number of teeth on the wheel.
Hearing is endowed with considerable powers of analysis and can distinguish the individual components in a complex s., appreciating their pitch and intensity. This analysis takes place as though the ear consisted of a complete and exceedingly numerous series of resonators and should, according to the law of acoustic Ohm, be independent of the phase relationships of the component tones. This is true within limits of first approximation, since, strictly speaking, the ear is not a perfect analyser: contiguous regions of the basilar membrane, to which the most recent research by Bekesy assigns this function, are found to respond to a lesser degree also to stimuli of a frequency close to that for which they are specifically tuned. While this guarantees, on the one hand, a response to stimuli of any frequency (within the acoustic range), it gives rise, on the other, to the possibility that simultaneous stimulation by two stimuli of slightly different frequency may produce periodic effects of reinforcement and weakening of the s. at the rhythm of the difference between the two frequencies (subjective beats).
Modifications of timbre caused by phase shifts of the individual components of a complex tone may arise through phenomena of interferential combination with auricular harmonics; that is, the stimulus actually applied to the cochlear organ is modified, and consequently the subjective appreciation is different. Severe modifications of timbre result from substantial reductions in the amplitude of the field of tonal audibility due to disorders of the auditory organ in the numerous forms of deafness.
VI. PSYCHOLOGICAL ATTRIBUTES OF SOUND
The principal ones are intensity and pitch, respectively rendered in the subject’s judgment by indications of “loud” and “soft” and by indications of “high” and “low.” (Subjective) intensity corresponds, for a given vibratory stimulus, to the acoustic pressure at the level of the tympanic membrane and thus to the amplitude of vibration, generally to the number of ergs transmitted through one square centimetre in each second. Pitch, on the other hand, corresponds to the frequency of the vibratory stimulus. These two correspondences are not, however, as close and, above all, as univocal as had been believed until some time ago and is still stated in many treatises; both pitch and intensity are each functions of the two variables, acoustic pressure and frequency; thus it is, for example, possible to induce variations in pitch by modifying the intensity of a sound. These variations are small in percentage terms, but account for many phenomena of physiological acoustics.The acoustic-pressure level of a vibratory stimulus may be expressed by the number of decibels (dB), which indicates by how much it exceeds the value of the reference threshold, that is, the minimum acoustic pressure capable of generating an auditory sensation, a threshold conventionally assumed to refer to a frequency of 1000 Hz. On this scale:
| zero dB | 10⁻¹⁶ watt cm⁻² |
|---|---|
| " " | 0.000204 dyne cm⁻² |
| " " | 73.8 dB below 1 dyne per cm². |
These reference levels represent the auditory threshold for a normal ear, but do not constitute starting values for a strictly understood (subjective) “intensity scale.” The audible field extends, on average, between 16 Hz and 19,000 Hz for normal hearing; that is, between wavelengths of 21.3 m and 1.8 cm, respectively.
VII. OTHER PSYCHOLOGICAL ATTRIBUTES OF SOUND
In addition to timbre, which has already been mentioned, there are other attributes; it may be observed that, in order to define a new one, it is sufficient for the organism’s reaction to variations in the stimulus to be systematic and for the corresponding values to be representable in a graph. In 1916 Rich clearly formulated the fact that sounds possess a subjective character of “breadth” or “extension” (volume) which, according to his observations, depends on pitch. In 1924 Halverson highlighted the dependence of volume on intensity. In 1934 Stevens demonstrated that it is possible for two sounds to appear equal in volume while differing in pitch and intensity, precisely because, if the volume is to remain constant, the higher sound must have greater intensity. Thus, for the volume to remain constant, starting from a vibratory stimulus with a frequency of 900 Hz and a pressure at the tympanic membrane 55 dB above threshold, an increase of 100 Hz in frequency must be followed by an increase of 10 dB in pressure.Many subjects also tend to attribute to pure sounds the subjective quality of “compactness” or “density,” and this was the object of detailed research by Stevens (1934). Density varies inversely with volume, in the sense that an increase in frequency is compensated by a decrease in pressure. Thus, for density to remain constant, an increase in frequency from 500 to 600 Hz in a vibratory stimulus producing at the tympanic membrane a pressure of 60 dB above threshold must be compensated by a decrease of approximately 4 dB in the pressure just mentioned.
It is not easy to indicate through which mechanisms the perception of volume and density is achieved. It is obvious that the fact that the responses are differentiated implies a different neural and cortical excitation. Thus one may suppose that density is linked to the density of nervous excitation in the cortex, whereas volume (Boring, 1926) would depend on the “breadth” of the cortical area involved.
The possibility of judging sounds as “bright” and “dull” has led some authors to define the brightness of sound as another attribute. It does not, however, appear that this attribute can possess an independent existence, since as early as 1929 Troland indicated that it was closely connected with pitch, whereas for Stevens it must, on the basis of more rigorous analysis, be regarded as identical with density. He in fact found that producing tones of varying brightness is possible only by varying timbre: brightness is therefore more a subjective appraisal of timbre than a new attribute of sound. Other highly important attributes of sounds are the “musical” ones, consisting in the fact that two or more sounds of different frequency may be judged consonant or dissonant, whether produced simultaneously or successively, and that the relative interval may be judged equal to, greater than, or smaller than another, all of this leading to the formation of musical scales and, together with judgments concerning the intervals of time between one sound and another, to harmony, counterpoint, orchestration—in a word, to music in general.
VIII. REFLECTION. ECHO. – If, during its propagation, the vibratory motion of the air particles encounters an elastic wall, such as, for example, a marble slab, a polished wall, etc., it is reflected according to laws similar to those governing the reflection of light by a mirror. Reflection gives rise to an echo under particular environmental conditions.
The vibratory motion reaching the ear is always different from that produced by the source, as a result of the various successive reflections from the walls of the surroundings and from the objects contained therein. Thus there is a persistence of acoustic energy in the environment: the phenomenon of reverberation, which is always present unless one operates in a free field, that is, in a theoretical environment in which reflecting walls do not exist and are infinitely distant; or in which such walls, although present and at a finite distance, are completely absorbent, reflecting none of the energy incident upon them. The existence of “absorbent” materials such as, for example, glass wool, mineral wool, etc., makes it possible to construct chambers called precisely “absorbent,” in which the energy reflected by the walls may amount to only a small percentage of the incident energy. No wall is so reflective as to reflect all the energy incident upon it; there are, however, “reflective” materials (marble, for example, is typical) that make it possible to construct chambers known as “reverberant” chambers for purposes of acoustic investigation. The proportioning of reflective and absorbent materials in the environment is of the utmost importance for the acoustics of auditoriums and theatres.
IX. RESONANCE
A material system can enter into oscillation under the action of periodic external forces (forced vibration). In this case, the period and amplitude of vibration are not those proper to the system when it vibrates on its own, but those proper to the external forces, though partly modified by the very presence of the material system upon which they act.The vibrations of the latter can become very large when its own period coincides with that of the external forces; in this case the system enters into resonance, and even a small force can generate considerable oscillations. Thus, two pendulums oscillating with the same period stimulate each other to oscillate if placed near one another; and if one of them is at rest while the other is set into oscillation, after a little while the first too will be seen to oscillate as a result of the rhythmic pushes it receives through the air. A similar experiment can be carried out with two tuning forks having the same frequency: if one is excited and placed near the other, it will be observed that the latter begins to vibrate. The same can be observed with two musical instruments, for example two violins, whose strings have been tuned in unison, placed in the same room even several metres apart: if the strings of the first are excited one by one and then stopped by placing the fingers upon them, the corresponding strings of the other respond in sequence. This is understood to mean exciting them by « plucking », and not with a bow or other means, which may induce variations in the frequency of the string being rubbed.
A mass of air enclosed within a cavity can also enter into resonance; that contained in a tube, for example, resonates at a frequency dependent upon the length of the tube. In a complex manner, the air contained in the cavities called « sound boxes » in musical instruments resonates. These cavities—those of violins being a typical example—have been studied empirically so that the air contained within them resonates as uniformly as possible throughout the broad range of frequencies produced by the instrument; because of their complex shape, the lengths of the air columns and the air masses differ in different directions. Of considerable importance for the uses made of them in acoustics are the « Helmholtz resonators », hollow spheres equipped with two diametrically opposite openings through which the internal air communicates with the surrounding air and with the listener’s ear. The internal air resonates at a frequency determined by the diameter of the cavity.