Chapter 2

ACOUSTICS

Telephony is the art of reproducing at a distant point, usually by the agency of electricity, sounds produced at a sending point. In this art the elements of two general divisions of physical science are concerned, sound and electricity.

Sound is the effect of vibrations of matter upon the ear. The vibrations may be those of air or other matter. Various forms of matter transmit sound vibrations in varying degrees, at different specific speeds, and with different effects upon the vibrations. Any form of matter may serve as a transmitting medium for sound vibrations. Sound itself is an effect of sound vibrations upon the ear.

Propagation of Sound. Since human beings communicate with each other by means of speech and hearing through the air, it is with air that the acoustics of telephony principally is concerned. In air, sound vibrations consist of successive condensations and rarefactions tending to proceed outwardly from the source in all directions. The source is the center of a sphere of sound vibrations. Whatever may be the nature of the sounds or of the medium transmitting them, they consist of waves emitted by the source and observed by the ear. A sound wave is one complete condensation and rarefaction of the transmitting medium. It is produced by one complete vibration of the sound-producing thing.

Sound waves in air travel at a rate of about 1,090 feet per second. The rate of propagation of sound waves in other materials varies with the density of the material. For example, the speed of transmission is much greater in water than in air, and is much less in highly rarefied air than in air at ordinary density. The propagation of sound waves in a vacuum may be said not to take place at all.

Characteristics of Sound. Three qualities distinguish sound: loudness, pitch, and timbre.

_Loudness._ Loudness depends upon the violence of the effect upon the ear; sounds may be alike in their other qualities and differ in loudness, the louder sounds being produced by the stronger vibrations of the air or other medium at the ear. Other things being equal, the louder sound is produced by the source radiating the greater energy and so producing the greater _degree_ of condensation and rarefaction of the medium.

_Pitch._ Pitch depends upon the frequency at which the sound waves strike the ear. Pitches are referred to as _high_ or _low_ as the frequency of waves reaching the ear are greater or fewer. Familiar low pitches are the left-hand strings of a piano; the larger ones of stringed instruments generally; bass voices; and large bells. Familiar high pitches are right-hand piano strings; smaller ones of other stringed instruments; soprano voices; small bells; and the voices of most birds and insects.

Doppler's Principle:--As pitch depends upon the frequency at which sound waves strike the ear, an object may emit sound waves at a constant frequency, yet may produce different pitches in ears differently situated. Such a case is not usual, but an example of it will serve a useful purpose in fixing certain facts as to pitch. Conceive two railroad trains to pass each other, running in opposite directions, the engine bells of both trains ringing. Passengers on each train will hear the bell of the other, first as a _rising_ pitch, then as a _falling_ one. Passengers on each train will hear the bell of their own train at a _constant_ pitch.

The difference in the observations in such a case is due to relative positions between the ear and the source of the sound. As to the bell of their own train, the passengers are a fixed distance from it, whether the train moves or stands; as to the bell of the other train, the passengers first rapidly approach it, then pass it, then recede from it. The distances at which it is heard vary as the secants of a circle, the radius in this case being a length which is the closest approach of the ear to the bell.

If the bell have a constant intrinsic fundamental pitch of 200 waves per second (a wave-length of about 5.5 feet), it first will be heard at a pitch of about 200 waves per second. But this pitch rises rapidly, as if the bell were changing its own pitch, which bells do not do. The rising pitch is heard because the ear is rushing down the wave-train, every instant nearer to the source. At a speed of 45 miles an hour, the pitch rises rapidly, about 12 vibrations per second. If the _rate of approach_ between the ear and the bell were constant, the pitch of the bell would be heard at 212 waves per second. But suddenly the ear passes the bell, hears the pitch stop rising and begin to fall; and the tone drops 12 waves per second as it had risen. Such a circumflex is an excellent example of the bearing of wavelengths and frequencies upon pitch.

Vibration of Diaphragms:--Sound waves in air have the power to move other diaphragms than that of the ear. Sound waves constantly vibrate such diaphragms as panes of windows and the walls of houses. The recording diaphragm of a phonograph is a window pane bearing a stylus adapted to engrave a groove in a record blank. In the cylinder form of record, the groove varies in depth with the vibrations of the diaphragm. In the disk type of phonograph, the groove varies sidewise from its normal true spiral.

If the disk record be dusted with talcum powder, wiped, and examined with a magnifying glass, the waving spiral line may be seen. Its variations are the result of the blows struck upon the diaphragm by a train of sound waves.

In reproducing a phonograph record, increasing the speed of the record rotation causes the pitch to rise, because the blows upon the air are increased in frequency and the wave-lengths shortened. A transitory decrease in speed in recording will cause a transitory rise in pitch when that record is reproduced at uniform speed.

_Timbre._ Character of sound denotes that difference of effect produced upon the ear by sounds otherwise alike in pitch and loudness. This characteristic is called timbre. It is extraordinarily useful in human affairs, human voices being distinguished from each other by it, and a great part of the joy of music lying in it.

A bell, a stretched string, a reed, or other sound-producing body, emits a certain lowest possible tone when vibrated. This is called its _fundamental tone_. The pitch, loudness, and timbre of this tone depend upon various controlling causes. Usually this fundamental tone is accompanied by a number of others of higher pitch, blending with it to form the general tone of that object. These higher tones are called _harmonics_. The Germans call them _overtones_. They are always of a frequency which is some multiple of the fundamental frequency. That is, the rate of vibration of a harmonic is 2, 3, 4, 5, or some other integral number, times as great as the fundamental itself. A tone having no harmonics is rare in nature and is not an attractive one. The tones of the human voice are rich in harmonics.

In any tone having a fundamental and harmonics (multiples), the wave-train consists of a complex series of condensations and rarefactions of the air or other transmitting medium. In the case of mere noises the train of vibrations is irregular and follows no definite order. This is the difference between vowel sounds and other musical tones on the one hand and all unmusical sounds (or noises) on the other.

Human Voice. Human beings communicate with each other in various ways. The chief method is by speech. Voice is sound vibration produced by the vocal cords, these being two ligaments in the larynx. The vocal cords in man are actuated by the air from the lungs. The size and tension of the vocal cords and the volume and the velocity of the air from the lungs control the tones of the voice. The more tightly the vocal cords be drawn, other things being equal, the higher will be the pitch of the sound; that is, the higher the frequency of vibration produced by the voice. The pitches of the human voice lie, in general, between the frequencies of 87 and 768 per second. These are the extremes of pitch, and it is not to be understood that any such range of pitch is utilized in ordinary speech. An average man speaks mostly between the fundamental frequencies of 85 and 160 per second. Many female speaking voices use fundamental frequencies between 150 and 320 vibrations per second. It is obvious from what has been said that in all cases these speaking fundamentals are accompanied by their multiples, giving complexity to the resulting wave-trains and character to the speaking voice.

Speech-sounds result from shocks given to the air by the organs of speech; these organs are principally the mouth cavity, the tongue, and the teeth. The vocal cords are _voice-organs_; that is, man only truly speaks, yet the lower animals have voice. Speech may be whispered, using no voice. Note the distinction between speech and voice, and the organs of both.

The speech of adults has a mean pitch lower than that of children; of adult males, lower than that of females.

There is no close analogue for the voice-organ in artificial mechanism, but the use of the lips in playing a bugle, trumpet, cornet, or trombone is a fairly close one. Here the lips, in contact with each other, are stretched across one end of a tube (the mouthpiece) while the air is blown between the lips by the lungs. A musical tone results; if the instrument be a bugle or a trumpet of fixed tube length, the pitch will be some one of several certain tones, depending on the tension on the lips. The loudness depends on the force of the blast of air; the character depends largely on the bugle.

Human Ear. The human ear, the organ of hearing in man, is a complex mechanism of three general parts, relative to sound waves: a wave-collecting part; a wave-observing part, and a wave-interpreting part.

The outer ear collects and reflects the waves inwardly to beat upon the tympanum, or ear drum, a membrane diaphragm. The uses of the rolls or convolutions of the outer ear are not conclusively known, but it is observed that when they are filled up evenly with a wax or its equivalent, the sense of direction of sound is impaired, and usually of loudness also.

The diaphragm of the ear vibrates when struck by sound waves, as does any other diaphragm. By means of bone and nerve mechanism, the vibration of the diaphragm finally is made known to the brain and is interpretable therein.

The human ear can appreciate and interpret sound waves at frequencies from 32 to about 32,000 vibrations per second. Below the lesser-number, the tendency is to appreciate the separate vibrations as separate sounds. Above the higher number, the vibrations are inaudible to the human ear. The most acute perception of sound differences lies at about 3,000 vibrations per second. It may be that the range of hearing of organisms other than man lies far above the range with which human beings are familiar. Some trained musicians are able to discriminate between two sounds as differing one from the other when the difference in frequency is less than one-thousandth of either number. Other ears are unable to detect a difference in two sounds when they differ by as much as one full step of the chromatic scale. Whatever faculty an individual may possess as to tone discrimination, it can be improved by training and practice.