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Table of Contents

THE EAR, AND HEARING—PHYSIOLOGY OF HEARING AND SOUND—SOUND AS COMPARED WITH LIGHT—WHAT IS SOUND?—VELOCITY OF SOUND—CONDUCTIBILITY—THE HARMONOGRAPH.

Before entering upon the science of Acoustics, a short description of the ear, and the mode in which sound is conveyed to our brain, will be no doubt acceptable to our readers. The study of the organs of hearing is not an easy one; although we can see the exterior portion, the interior and delicate membranes are hidden from us in the very hardest bone of the body—the petrous bone, the temporal and rock-like bone of the head.

Fig. 170- 1. Temple bone. 2. Outer surface of temple. 3. Upper wall of bony part of hearing canal. 4. Ligature holding “hammer” bone to roof of drum cavity. 5. Roof to drum cavity. 6. Semicircular canals. 7. Anvil bone. 8. Hammer bone. 9. Stirrup bone. 10. Cochlea. 11. Drum-head cut across. 12. Isthmus of Eustachian tube. 13. Mouth of tube in the throat. 14. Auditory canal. 15. Lower wall of canal. 16. Lower wall of cartilaginous part of canal. 17. Wax glands. 18. Lobule. 19. Upper wall of cartilaginous portion of canal. 20. Mouth of auditory canal. 21. Anti-tragus.

The ear (external) is composed of the auricle, the visible ear, the auditory canal, and the drum-head, or membra tympani. The tympanum, or “drum,” is situated between the external and the internal portions of the ear. This part is the “middle ear,” and is an air cavity, and through it pass two nerves, one to the face, and the other to the tongue. The internal ear is called the “labyrinth,” from its intricate structure. We give an illustration of the auditory apparatus of man (fig. 170).

The auricle, or exterior ear, is also represented, but we need not go into any minute description of the parts. We will just name them (fig. 171).

Sound is the motion imparted to the auditory nerve, and we shall see in a moment how sound is produced. The undulations enter the auditory canal, having been taken up by the auricle; the waves or vibrations move at the rate of 1,100 feet a second, and reach the drum-head, which has motion imparted to it. This motion or oscillation is imparted to other portions, and through the liquid in the labyrinth. The impressions of the sound wave are conveyed to the nerve, and this perception of the movement in the water of the labyrinth by the nerve threads and the brain causes what we term “hearing.”

Fig. 171.—1. Pit of anti-helix. 2, 6, 10. Curved edge of the auricle. 3. Mouth of auditory canal. 4. Tragus. 5. Lobe. 7. Anti-helix. 8. Concha. 9. Anti-tragus.

Let us now endeavour to explain what sound is, and how it arises. There are some curious parallels between sound and light. When speaking of light we mentioned some of the analogies between sound and light, and as we proceed to consider sound, we will not lose sight of the light we have just passed by.

Sound is the influence of air in motion upon the hearing or auditory nerves. Light, as we have seen, is the ether in motion, the vibrations striking the nerves of the eye.

There are musical and unmusical sounds. The former are audible when the vibrations of the air reach our nerves at regular intervals. Unmusical sounds, or irregular vibrations, create noise. Now, musical tones bear the same relation to the ear as colours do to the eye. We must have a certain number of vibrations of ether to give us a certain colour (vide table). “About four hundred and fifty billion impulses in a second” give red light. The violet rays require nearly double. So we obtain colours by the different rate of the impingement of impulses on the retina. The eyes, as we have already learned, cannot receive any more rapidly-recurring impressions than those producing violet, although as proved, the spectrum is by no means exhausted, even if they are invisible. In the consideration of Calorescence we pointed this out. These invisible rays work great chemical changes when they get beyond violet, and are shown to be heat. So the rays which do not reach the velocity of red rays are also heat, which is the effect of motion.

Thus we have Heat, Light, and Sound, all the ascertained results of vibratory motion. The stillness of the ether around us is known as “Darkness”; the stillness of the air is “Silence”; the comparative absence of heat, or molecular motion of bodies is “Cold”!

In the first part we showed how coins impart motion to each other.

VELOCITY OF LIGHT WAVES.
According to Sir J. Herschel.
Colour of the Spectrum.	No. of Undulations in an inch.	No. of Undulations in a second.
Extreme Red	37,640	458,000,000,000,000
Red	39,180	477,000,000,000,000
Intermediate	40,720	495,000,000,000,000
Orange	41,610	506,000,000,000,000
Intermediate	42,510	517,000,000,000,000
Yellow	44,000	535,000,000,000,000
Intermediate	45,600	555,000,000,000,000
Green	47,460	577,000,000,000,000
Intermediate	49,320	600,000,000,000,000
Blue	51,110	622,000,000,000,000
Intermediate	52,910	644,000,000,000,000
Indigo	54,070	658,000,000,000,000
Intermediate	55,240	672,000,000,000,000
Violet	57,490	699,000,000,000,000
Extreme Violet	59,750	727,000,000,000,000

When an impulse was given the motion was carried from coin to coin, and at length the last one in the row flew out. This is the case with sound. The air molecules strike one upon another, and the wave of “sound” reaches the tympanum, and thus the impression is conveyed to the brain. We say we hear—but why we hear, in what manner the movement of certain particles affects our consciousness, we cannot determine.

That the air is absolutely necessary to enable us to hear can readily be proved. The experiment has frequently been made; place a bell under the receiver of an air-pump, and we can hear it ring. But if we exhaust the air the sound will get fainter and fainter. Similarly, as many of us have experienced upon high mountains, sounds are less marked. Sound diminishes in its intensity, just as heat and light do. Sound is reflected and refracted, as are light and radiant heat. We have already shown the effect of reflectors upon heat. Sound is caught and reflected in the same way as light from mirrors, or as the heat waves in the reflectors. We have what we term “sounding boards” in pulpits, and speaking tubes will carry sound for us without loss of power. Echoes are merely reflected sounds.

The velocity of sound is accepted as 1,100 feet in a second, which is far inferior to the velocity of light. Fogs will retard sound, while water will carry it. Those who have ever rowed upon a lake will remember how easily the sound of their voices reached from boat to boat, and Dr. Hutton says that at Chelsea, on the Thames, he heard a person reading from a distance of a hundred and forty feet. Some extraordinary instances could be deduced of the enormous distances sound is said to have travelled. Guns have been heard at eighty miles distant, and the noise of a battle between the English and Dutch, in 1672, was heard even in Wales, a distance of two hundred miles from the scene of action.

Sound always travels with uniform velocity in the air in the same temperature. But sound! What is the cause of it? How does it arise? These questions can now be fully answered with reference to the foregoing observations. Phenomena of vibration render themselves visible by light, heat, and sound, and to arrive at some definite ideas of sound vibrations we may compare them to waves, such as may be produced by throwing a stone into a pond.

There are, so to speak, “standing” waves and “progressive” waves. The former can be produced (for instance) by thrumming a fiddle-string, and when the equilibrium of the cord is disturbed, the position of the equilibrium is passed simultaneously by the string-waves. In water the waves or vibrating points pass the position of equilibrium in succession.

Waves consist of elevations and depressions alternately, and when we obtain two “systems” of waves by throwing two stones into water, we can observe some curious effects. It can be seen how one series of depressions will come in contact with the other series of depressions, and the elevations will likewise unite with the result of longer depressions and elevations respectively; or it may very well be that elevation will meet depression, and then the so-called “interference” of waves will produce points of repose. These points are termed nodes. The waves of the string proceed in the plane of its axis; water waves extend in circles which increase in circumference.

The progression or propagation of sound may be said to begin when some tiny globule of matter expands in the air. The air particles strike one against the other, and so the motion is communicated to the air waves, which in time reach the ear. But the velocity of the sound is not equal in all substances. Air will convey it around our earth at the rate of 765 miles an hour, or 1,090 feet in a second. That is, we may accept such rate as correct at a temperature of 32° Fahr., and at a pressure of thirty inches, and the velocity increases almost exactly one foot per second for each degree of temperature above 32°. Therefore on an average, and speaking in “round numbers,” the estimate of 1,100 feet in a second may be accepted as correct. In hydrogen gas the rate is much higher. Through water again it is different, and still faster through iron, glass, and wood, as will be seen in the following table:—

TAKING AIR AS 1.
Whalebone	6⅔
Tin	7½
Silver	9
Walnut	10⅔
Brass	10⅔
Oak	10⅔
Earthen pipes	11
Copper	12
Pear-wood	12½
Ebony	14⅔
Cherry	15
Willow	16
Glass	16⅔
Iron or Steel	16⅔
Deal	18

So there is a considerable difference in the velocities of sound through the solid substances quoted, but these figures cannot be taken as exact, as different samples may give different results. In wires and bells the bodies themselves produce the sounds we hear. In wind instruments and the voice the air is the cause of the sound.

The very deepest notes are produced by the fewest vibrations. Fourteen or fifteen vibrations will give us a very low note, if not the very lowest. The pipe of sixteen feet, closed at its upper end, will produce sound waves of thirty-two feet. High notes can be formed from vibrations up to 48,000 in a second. Beyond these limits the ear cannot accept a musical sound.

Fig. 172.—The vibration of strings.

We will explain the phenomenon of the vibration of strings by means of the illustration. In the cut we find a string or wire, which can be lengthened or shortened at pleasure by a movable bridge, and stretched by weights attached to the end (fig. 172).

We can now easily perceive that the shorter and thinner the string is, and the tighter it is, the number of vibrations will be greater and greater. The density of it is also to be considered, and when these conditions are in the smallest proportion then the tone will be highest. The depth will naturally increase with the thickness, density, and length, and with a decreasing tension. But we have strings of same thickness stretched to different degrees of tension, and thus producing different notes. Some strings are covered with wire to increase their gravity, and thus to produce low notes.

When a number of separate sounds succeed each other in very rapid course they produce a sound, but to appear as one sound to the ear they must amount to fifteen or sixteen vibrations every second. The particles of matter in the air form a connected system, and till they are disturbed they remain in equilibrium; but the moment they are in any way thrown out of this state they vibrate as the pendulum vibrates. The particles thus strike each other, and impart a motion to the elastic medium air, so a sound comes to us.

The intensity of sounds gets less the farther it goes from us, or the loudness of sound is less the greater its distance. The law is, that in an unvarying medium the loudness varies inversely as the square of the distance. But Poisson has shown that when air-strata, differing in density, are existing between the ear and the source of the sound, the intensity or loudness with which it is heard depends only on the density of the air at the place the sound originated. This fact has been substantiated by balloonists who heard a railway whistle quite distinctly when they were nearly 20,000 feet above the ground. It therefore follows that sound can be heard in a balloon equally well as on the earth at certain given distances. But as the density of the air diminishes the sound becomes fainter, as has been proved by the bell rung in the receiver of an air-pump. The velocity of sound, to a certain extent, depends upon its intensity, as Earnshaw sought to prove; for he instanced a fact that in the Arctic regions, where sound can be heard for an immense distance, in consequence of the still and homogeneous air, the report of a cannon two miles and a half away was heard before the loud command to “fire,” which must have preceded the discharge. Another instance showing the difference in hearing through mixed and homogeneous media may be referred to. In the war with America, when the English and their foes were on opposite sides of a stream, an American was seen to beat his drum, but no sound came across. “A coating of soft snow and a thick atmosphere absorbed the noise.” Glazed, or hard snow, would have a contrary effect. Reynault also experimentally verified his theory, that sound when passing through a space of nearly 8,000 feet lost velocity as its intensity diminished, and in that distance between its arrival at 4,000 feet and at 7,500 feet, the sound velocity diminished by 2·2 feet per second. He also tried to demonstrate that sound velocity depended upon its pitch, and that lower notes travelled with the greater speed.

The reflection and refraction of sound follows the same fundamental laws as the reflection and refraction of light. The reflection of sound is termed an Echo, which is familiar to all tourists in Switzerland and Ireland particularly. There are several very remarkable echoes in the world: at Woodstock, and at the Sicilian cathedral of Gergenti, where the confessions poured forth near the door to priestly ears were heard by a man concealed behind the high altar at the opposite end. It is curious that such a spot should have been accidentally chosen for the Confessional. The whispering gallery in St. Paul’s is another instance of the echo.

Echoes are produced by the reflection of sound waves from a plane or even surface. A wall, or even a cloud, will produce echoes. Thunder is echoed from the clouds. (The celebrated echo of “Paddy Blake,” at Killarney, which, when you say “How do you do,” is reported to reply, “Very well, thank you,” can scarcely be quoted as a scientific illustration.) And the hills of Killarney contain an echo, and the bugle sounds are beautifully repeated. In the cases of ordinary echo, when the speaker waits for the answer, he must place himself opposite the rock. If he stand at the side the echo will reply to another person in a corresponding place on the farther side, for the voice then strikes the rock at an angle, and the angle of reflection is the same, as in the case of light.

But if it should happen that there are a number of reflecting surfaces the echo will be repeated over and over again, as at the Lakes of Killarney. The Woodstock Echo, already referred to, and mentioned by several writers, repeats seventeen syllables by day, and twenty by night. In Shipley there is even a greater repetition. Of course the echo is fainter, because the waves are weaker if the reflecting surface be flat. But, as in the case of the mirrors reflecting light, a circular or concave surface will increase the intensity. A watch placed in one mirror will be heard ticking in the other focus. Whispering galleries carry sound by means of the curved surface. Sir John Herschel mentions an echo in the Menai Suspension Bridge. The blow of a hammer on one of the main piers will produce the sound from each of the crossbeams supporting the roadway, and from the opposite pier 576 feet distant, as well as many other repetitions.

Refraction of sound is caused by a wave of sound meeting another medium of different density, just as a beam of light is refracted from water. One sound wave imparts its motion to the new medium, and the new wave travels in a different direction. This change is refraction. The sound waves are refracted in different directions, according to the velocity it can acquire in the medium. If a sound pass from water into air it will be bent towards the perpendicular, because sound can travel faster in water than in air. If it pass from air into water its force will cause it to assume a less perpendicular direction, there being greater velocity in water. The velocity in air is only 1,100 feet in a second in our atmosphere. In water sound travels 4,700 feet in the same time. When the wave of sound falls upon a medium parallel to the refracting surface there is, however, no refraction—only a change of velocity, not direction.

When sound waves are prevented from dispersing the voice can be carried a great distance. Speaking tubes and trumpets, as well as ear trumpets, are examples of this principle, and of the reflection of sound.

There are many very interesting experiments in connection with Acoustics, some of which we will now impart to our readers. We shall then find many ingenious inventions to examine—the Audiphone, Telephone, Megaphone, and Phonograph, which will occupy a separate chapter. We now resume.

Amongst the experiments usually included in the course of professors and lecturers who have a complete apparatus at their command, and which at first appear very complicated and difficult, there are some which can be performed with every-day articles at hand. There is no experiment in acoustics more interesting than that of M. Lissajons, which consists, as is well known to our scientists, of projecting upon a table or other surface, with the aid of oxy-hydrogen light, the vibratory curves traced by one of the prongs of a tuning-fork. We can perform without difficulty a very similar experiment with the humble assistance of the common knitting-needle.

Fix the flexible steel needle firmly in a cork, which will give it sufficient support; fasten then at the upper extremity a small ball of sealing wax, or a piece of paper about the size of a large pea. If the cork in which the needle is fixed be held firmly in one hand, and you cause the needle to vibrate by striking it, and then letting it sway of itself, or with a pretty strong blow with a piece of wood, you will perceive the little pellet of wax or paper describe an ellipse more or less elongated, or even a circle will be described if the vibrations be frequent. The effect is much enhanced if the experiment be performed beneath a lamp, so that plenty of light may fall upon the vibrating needle. In this case, the persistence of impressions upon the retina admits of one seeing the vibrating circle in successive positions, and we may almost fancy when the needle is struck with sufficient force, that an elongated conical glass, like the old form of champagne glass, is rising from the cork, as shown in the illustration annexed (fig. 173).

Fig. 173.—Experiment showing vibration of sound waves.

Acoustics may be studied in the same way as other branches of physical science. We will describe an interesting experiment, which gives a very good idea of the transmission of sounds through solid bodies. A silver spoon is fastened to a thread, the ends of which are thrust into both ears, as shown in fig. 174; we then slightly swing the spoon until we make it touch the edge of the table; the transmission of sound is in consequence so intense that we are ready to believe we are listening to the double diapason of an organ. This experiment explains perfectly the transmission of spoken words by means of the string of a telephone, another contrivance which any one may make for himself without any trouble whatever. Two round pieces of cardboard are fitted to two cylinders of tin-plate, as large round as a lamp-glass, and four-and-a-half inches in length. If the two rounds of cardboard are connected by a long string of sixteen to eighteen yards, we can transmit sounds from one end to the other of this long cord; the speaker pronouncing the words into the first cylinder, and the listener placing his ear against the other. It is easy to demonstrate that sound takes a certain time to pass from one point to another. When one sees in the distance a carpenter driving in a stake, we find that the sound produced by the blow of the hammer against the wood only reaches the ear a few seconds after the contact of the two objects. We see the flash at the firing of a gun, before hearing the sound of the report—of course on the condition that we are at a fairly considerable distance, as already remarked upon.

Fig. 174.—Conductibility of sound by solid bodies.

Fig. 175.—Musical glasses.

We can show the production of the Gamut by cutting little pieces of wood of different sizes, which one throws on to a table; the sounds produced vary according to the size of the different pieces. The same effect may be obtained much better by means of goblets more or less filled with water; they are struck with a short rod, and emit a sound which can be modified by pouring in a greater or less quantity of water; if the performer is gifted with a musical ear, he can obtain, by a little arrangement, a perfect Gamut by means of seven glasses which each give a note (fig. 175). A piece of music may be fairly rendered in this manner, for the musical glasses frequently produce a very pure silvery sound. We will complete the elementary principles of acoustics by describing a very curious apparatus invented by M. Tisley, the Harmonograph. This instrument, which we can easily describe, is a most interesting object of study. The Harmonograph belongs to mechanics in principle, and to the science of acoustics in application. We will first examine the apparatus itself. It is composed of two pendulums, A and B (fig. 176), fixed to suspensions. Pendulum B supports a circular plate, P, on which we may place a small sheet of paper, as shown in the illustration. This paper is fixed by means of small brass clips. Pendulum A supports a horizontal bar, at the extremity of which is a glass tube, T, terminating at its lower extremity with a capillary opening; this tube is filled with aniline ink, and just rests on the sheet of paper; the support and the tube are balanced by a counterpoise on the right. The two pendulums, A and B, are weighted with round pieces of lead, which can be moved at pleasure, so that various oscillations may be obtained. The ratio between the oscillations of the two pendulums may be exactly regulated by means of pendulum A carrying a small additional weight, the height of which may be regulated by means of a screw and a small windlass. If we give to pendulum A a slight movement of oscillation, the point of tube T traces a straight line on the paper placed in P; but if we move pendulum B, the paper also is displaced, and the point of tube T will trace curves, the shape of which varies with the nature of the movement of pendulum B, the relation between the oscillations of the two pendulums, etc. If the pendulums oscillate without any friction the curve will be clear, and the point will pass indefinitely over the same track, but when the oscillations diminish, the curve also diminishes in size, still preserving its form, and tending to a point corresponding with the position of repose of the two pendulums. The result is therefore that the curves traced by the apparatus, of which we produce three specimens (figs. 177, 178, 179), are traced in a continuous stroke, commencing with the part of the greatest amplitude.

Fig. 176.—M. Tisley’s Harmonograph.

By changing the relation and phases of the oscillations we obtain curves of infinitely varied aspect. M. Tisley has a collection of more than three thousand curves, which we have had occasion to glance over, in which we failed to meet with two corresponding figures. The ratio between these curves corresponds with some special class, of which the analyst may define the general characters, but which is outside our present subject. By giving the plate P a rotatory movement, we obtain spiral curves of a very curious effect, but the apparatus is more complicated. Considered from this point of view it constitutes an interesting mechanical apparatus, showing the combination of oscillations, and resolving certain questions of pure mechanics. From the point of view of acoustics it constitutes a less curious object of study. The experiments of M. Lissajons have proved that the vibrations of diapasons are oscillations similar to, though much more rapid than those of the pendulum. We can therefore with this apparatus reproduce all the experiments of M. Lissajons, with this difference, that the movements being slower are easier to study. When the ratio between the number of vibrations—we purposely use the term vibration instead of the term oscillation—is a whole number, we obtain figs. 177 and 178. If the ratio is not exact, we obtain fig. 179, which is rather irregular in appearance, corresponding to the distortions noticeable in M. Lissajon’s experiments. Fig. 178 has been traced in the exact ratio 2:3; fig. 177 in the ratio 1:2; and fig. 179 corresponds to the ratio 1:2 and a small fraction, which causes the irregularity of the figure.

Fig. 177.—Ratio 1:2. Fig. 178.—Ratio 2:3.

Fig. 179.—Ratio 1:2 and a fraction.

Fig. 180. Construction of the Harmonograph. Fig. 181.

Fig. 182.—Method of constructing an Harmonograph.

Fig. 183.—The apparatus completed.

In considering the harmony of figs. 177 and 178—the first of which corresponds to the octave, the second to the fifth, whilst fig. 179 corresponds to the disagreeable interval of the ninth—one is almost tempted to put a certain faith in the fundamental law of simple ratios as the basis of harmony. At first sight this appears beyond doubt, but perhaps musicians would be hardly content with the explanation. M. Tisley’s Harmonograph, it will be seen, is a rather complicated apparatus; and I will now explain how it may be constructed by means of a few pieces of wood. I endeavoured to construct as simple an apparatus as possible, and with the commonest materials, feeling that it is the best means of showing how it is possible for everybody to reproduce these charming curves of musical intervals. Also I completely excluded the employment of metals, and I constructed my apparatus entirely with pieces of wooden rulers, and old cigar boxes. I set to work in the following manner: on the two consecutive sides of a drawing board I fixed four small pieces of wood (fig. 180), side by side in twos, having at the end a small piece of tin-plate forming a groove (fig. 181). In these grooves nails are placed which support the pendulums. The piece of wood is placed on the corner of the table, so that the pendulums which oscillate in two planes at right angles, are in two planes that are sensibly parallel to the sides of the table. The pendulums are made of a thin lath, with two small pieces of wood fixed to them containing some very pointed nails, on which the pendulum oscillates. Fig. 182 gives an illustration. The pendulums have a pin fixed in vertically, which passes through a piece of wood, and by means of a hinge connects the upper ends of the two pendulums. This contrivance of the pin is very useful, and if care is taken to make the hole through the hinge in the form of a double cone, as shown in fig. 182, c, it makes a perfect joint, which allows the piece of wood to be freely moved.

Fig. 184.—Details of mechanism.

To complete the apparatus, the heads of the two pendulums are united by the hinge, at the bend of which a slender glass tube is fixed, which traces the curves. The hinge is given in fig. 184, and to its two extremities are adjusted the two pins of the pendulum (fig. 183). The pendulums are encircled with round pieces of lead, which can be fixed at any height by means of a screw.