ON THE NATURE AND SOURCES OF SOUND.

Nature inanimate employs sweet sounds,
But animated Nature sweeter still,

To soothe and satisfy the human ear.-CowPER.

INTRODUCTION.

"If the atmosphere be considered as a vast machine, it is difficult to form any just conception of the profound skill and comprehensiveness of design which it displays. It diffuses and tempers the heat of different climates; for this purpose it performs a circulation, occupying the whole range from the pole to the equator, and while it is doing this, it executes many smaller circuits between the sea and the land. At the same time, it is the means of forming clouds and rain, and for this purpose, a perpetual circulation of the watery part of the atmosphere goes on between its lower and upper regions. Besides this complication of circuits, it exercises a more irregular agency, in the occasional winds which blow from all quarters, tending perpetually to restore the equilibrium of heat and moisture. But this incessant and multiplied activity discharges only a part of the functions of the air. It is, moreover, the most important and universal material of the growth and sustenance of plants and animals, and is for this purpose everywhere present and almost uniform in its quantity. With all its local motion, it has also the office of a medium of communication between intelligent creatures, which office it performs by another set of motions, entirely different both from the circulation and the occasional movements already mentioned; these different kinds of motions not interfering materially with each other; and this last purpose, so remote from the others in its nature, it answers in a manner so perfect and so easy, that we cannot imagine that the object could have been more completely attained, if this had been the sole purpose for which the atmosphere had been created. With all these qualities, this VOL. XX.

extraordinary part of our terrestrial system is scarcely ever in the way: and when we have occasion to do so, we put forth our hand and push it aside without being aware of its being near us."-WHEWELL, Bridgewater Treatise.

The above eloquent passage forcibly reminds us that a large amount of knowledge is necessary to a due appreciation of the many blessings we enjoy from the constitution of the physical world, maintained as it is so constantly by an Almighty hand. Health, and strength, and reason, are indeed precious gifts vouchsafed to the majority of mankind, and these are sufficient to impress us with gratitude: but when by a careful examination of our earthly dwelling-place, we see the thousands of wise and beautiful adaptations whereby the world has been prepared for living creatures, or they for the world, we feel how natural was the exclamation of the inspired Psalmist, "Lord, what is man that thou regardest him, or the son of man that thou visitest him."

If we attend but to one of those minor offices of the airthe production and propagation of certain pulses which, falling upon the ear, produce sound,-abundant material may be offered for instruction and admiration. How many delightful associations do we connect with sound! how many of the beauties and the sublimities of nature! how much of the business and the pleasures of social life! The murmuring of waters, the whispering of winds, the sweeping of the blast through the forest, the rush of the cataract, the roaring of ocean and the voice of the thunder, these are a few of the distinctive characters of different objects which the atmosphere presents to us in so perfect a manner that we can distinguish any one of them amid a multiplicity of minor sounds. And then, how beautiful is that combination which makes up many a rural concert! the woodman's axe, the lowing of cattle, the cawing of rooks, the hum of insects, the distant village bells, the evening song of the thrush, the bleating of sheep, sounds apparently unconnected, and some of them inharmonious, yet, taken with their poetical

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associations, can scarcely be heard without emotion. But "the articulate character of sounds is for us one of the most important arrangements which exist in the world; for it is by this, that sounds become the interpreters of thought, will, and feeling, the means by which a person can convey his wants, his instructions, his promises, his kindness, to others: by which one man can regulate the actions and influence the convictions and judgments of another. It is in virtue of the possibility of shaping air into words, that the imperceptible vibrations which a man produces in the atmosphere become some of his most important actions, the foundations of the highest moral and social relations, and the condition and instrument of all the advancement and improvement of which he is susceptible."

SECTION I. ON THE NATURE OF SOUND.

Ir we listen to a sound, and at the same time observe the cause which produces it, it will be remarked that the cause has ceased to act before the sound has reached our ear. When, for example, a gun is fired, the flash is seen before the report is heard, that is, provided the observer be at the distance of 40 or 50 yards from the gun; for at a less distance the flash and the report seem to occur simultaneously. In proportion as the distance is increased, the interval between the two is more marked. A similar result is obtained during a thunder-storm: the lightning's flash is seen before the thunder is heard, and the time which elapses between the two gives a measure of the distance between us and the thunder cloud. A number of persons placed on the same line, at the distance of one hundred yards from each other, would not at the same instant hear a sudden sound, such as an explosion, produced at one of the extremities of this line the first person would hear the sound before the second, the second would hear it before the third, the third before the fourth, and so on; and it is important to remark, that at the moment when the third person, for example, heard the sound, the first and the second would have ceased to hear it, while the fourth and those beyond him would not yet have heard it. It appears then that an abrupt sound, such as an explosion, travels successively from one place to another; that it is heard in one place only at the same instant, and consequently that it must be a rapid motion capable of affecting our organ of hearing.

The invention of the air-pump enabled natural philosophers to explain many phenomena which had hitherto been involved in some degree of mystery; among which was the following:-In the year 1705 Hauksbee contrived an apparatus by means of which a bell might be rung in the receiver of an air-pump. On removing a portion of the air from the receiver, the sound of the bell was perceptibly diminished, and became feeble in proportion as the air was removed. A curious objection occurrel to him respecting the results of this experiment:-" Whether the sonorous body in such a medium might not so suffer, or undergo such a change in its parts, as to be rendered incapable of being put into such a motion as is requisite for the action or production of sound?" He therefore instituted another experiment. A strong receiver, inclosing a large bell, was firmly screwed to the table of the air-pump: this was inclosed within another receiver, and the air between the two removed. On causing the inclosed bell to vibrate, no sound was heard, although the bell itself was surrounded by air; the existence of a vacuum between the two receivers as completely prevented the transmission of sound as if the bell itself were in vacuo. It will be seen therefore that sound cannot be propagated from empty space; for although the sound-producing body, under such circumstances, is thrown into a vibratory state, yet there is no path to convey these vibrations to the ear, and consequently there is no sound.

Sounds excited in the atmosphere diminish in intensity as they are elevated, not only because the distance from which we hear them is increased, but also because the air becomes more and more thin, or rarefied, in ascending from the surface of the earth, and at the height of about forty-five miles, at which the atmosphere most probably ceases to exist, and where is placed the boundary line between the air and the wide fields of space, sound also must cease. Thus the most violent terrestrial noises cannot escape the limits of the atmosphere: they become weaker and weaker as they ascend, and are soon altogether extinguished. So also no sound can reach this earth from the regions of space. The light of many a meteor may strike the eye, and we may in some measure be aware of terrific volcanic eruptions in the moon, but they are incapable of affecting our planet,

because between us and them the Almighty has indeed fixed a great gulf, over which it is impossible to pass. We need not ascend far from the earth's surface to become painfully aware of the thinness of the air, and the diminished intensity of sounds. On the summit of Mont Blanc a pistol produces less noise than would a small cracker in the valley below, and at great heights in balloons the sound of the voice of the aeronauts is scarcely appreciable.

The experiments which our countryman, Hauksbee, had the honour first to perform, are very valuable, and still retain their place in the science of sound; but they led him to an incautious conclusion. Speaking of his last experiment, he says that it "plainly shows, and seems positively to confirm, that air is the only medium im for the propagation of sound." Now it was soon discovered that all elastic fluids, and even solids, and indeed all substances to which we generally apply the term elastic, were capable of transmitting sounds, more or less perfectly according to their varying degrees of elasticity. The air-pump furnishes the means for producing sound in various gases and vapours, by first pumping out the air from any convenient vessel in which a bell is suspended, and then allowing a gas to flow in to occupy the place of the air; or a liquid, such as ether, which the moment it falls into vacuo is converted into vapour, and fills the whole of the vessel. If the bell be rung in these various media the sound is always produced, accompanied, however, by many curious modifications which we cannot here consider

Water transmits sound with great facility. A diver can hear words spoken above water, and those above water can hear the sound produced by the diver when he strikes two pebbles together.

That solids transmit sound may be familiar to most persons who have performed the curious experiment with a long piece of wood, such as a felled tree by the road side. If one person place his ear close to one extremity of the tree, he will hear distinctly, even so slight a sound as that produced by another person scratching the other extremity with his finger nail, a sound so faint as not to be heard even by himself.

Sound therefore may be considered as a very complex phenomenon, in which no less than six distinct processes seem to be necessary. 1st, the excitement of a motion in the sounding body; 2nd, the communication of this motion to the air, or other substance placed between the sounding body and our ears; 3rd, the propagation of such motion from particle to particle of the air, or other intermediate body, in due succession; 4th, its communication from the particles of the air, or other intermediate body, adjacent to the ear, to the ear itself; 5th, its conveyance in the ear, by a certain mechanism which we have already described, to the auditory nerves; 6th, the excitement of sensation. Sound therefore must be considered as a sensation within us, and nothing but a series of motions exterior to us. The ear is therefore as necessary to sound as are the vibrations of matter. Without the ear there is probably no such thing as sound in nature-the mighty Niagara has no voice of thunder when no ear is present to participate in the disturbance it excites the ocean lashing the shingles on the beach -the artillery of the sky, and the fearful blast of the tempest, these have all their peculiar expressions for us, because we participate in the stupendous motions they produce in the air, and in surrounding matter; but in the absence of the animal ear, they consist of motions merely, not sounds. They are the beginnings of perceptions, but not the perceptions themselves, in the same way we may consider perception to be necessary to sensation, but altogether distinct from it.

The most accurate experiments which have yet been made render it probable, that when a body performs about sixteen vibrations in a second the lowest musical note is produced which can in general be appreciated. We must distinguish between musical sounds and noises, because our means of ascertaining what rapidity of vibration produces a noise or mere sound are uncertain. Musical tones can be compared with some fixed standard, and the number of vibrations within a given time calculated with ease and certainty; whereas a noise is due to impulses so irregular that it cannot be brought in unison with a musical note and therefore its value cannot be calculated.

Every continued sound is composed of frequently recur ring vibrations, from sixteen up to many thousand, during a second of time. The effect on the ear, for any give

a

repose be great or small, the vibrations are performed in | equal times, depending on the proportion existing between the length, breadth, and thickness of the glass. But if a square piece of glass be fixed at the centre and a fiddlebow be drawn against the edge, the stationary position of the point causes a remarkable break in the continuity of the vibration from one edge to another: the nature of this obstruction is best shown by previously sifting upon the glass a thin layer of dry powder; on drawing the bow across the edge at a, fig. 5, the powder will be thrown on the diagonals Fig. 5. of the glass, while scarcely any will remain on the four triangular spaces included between those lines. From this we learn that the diagonals of the plate are almost entirely stationary; that the points a a' a" a"" are in active vibration, which vibrations decrease in extent as we proceed from those points to the centre a, or to the corners b. It also follows that at the moment the section a is below the plane of repose, the opposite section a" is also below the same plane, but the other two portions a' a" are above that plane.

We will endeavour to show why this alternation of position is necessarily brought about: let fig. 6 represent a Fig. 6.

horizontal section of the plate, of which the middle point a, is one of the diagonals or corner lines: if by the impulse of the bow, the part a b be depressed below its natural level, its under, or convex surface is necessarily greater in extent than the upper, or concave surface, as it forms a similar portion of a larger concentric curve. The particles of the under side of the glass, therefore, must be somewhat strained, or drawn farther asunder, to admit of that extension of surface: but such is the tendency to an equalization of pressure among all bodies, that in order to compensate for the expansion of the lower side of the glass, in the portion a b, the portion a c takes a curvature upwards, that is, it becomes convex on the upper, and concave on the lower surface, while the other portion a b is the reverse of this.

In fig. 5 the powder is collected on the diagonals of the plate; but if the bow be applied near one corner, the powder assumes a rectangular figure, as shown in fig. 7: a similar explanation will apply Fig. 7. here: the corner of the plate to a which the bow is applied, is drawn down from its original position, and induces a similar displacement in all the particles around it: this displacement, by making the under surface at and near the point a convex, while the upper surface becomes concave, causes an unequal expansion of the two surfaces, which continues to the points b; the maximum of vibration is at a, and it decreases towards b, where it attains its minimum, but at those points a tendency to an opposite curvature of the adjoining portion commences, for the reasons before stated; and the portions ba" band bab become convex upwards: these two again act on the fourth division (b a b") which becomes convex on the under, and concave on the upper surface, the same as the first portion.

a"

These remarkable phenomena have been traced through a very extensive range of modifications. By holding the plate at the centre, and applying the bow to various parts of the edge; or by fixing the plate in the middle of one side, and applying the bow to different parts of the other three sides; or by holding the plate at one corner, and exciting vibration at different positions with regard to it, an almost endless variety of figures have been produced. A few examples are given at the head of this article. In these and similar examples the lines occupied by the accumulated trains of powder are called nodal lines: they represent the parts of the glass plate which remain still while the other parts are in a state of active vibration.

By varying the forms and dimensions of flat surfaces,

whether of glass or any other material, as also the modes of vibrating them, a variety of beautiful results has been obtained. These experiments are very surprising to a person who witnesses them for the first time: the powder seems as if endowed with voluntary motion, and assumes these beautiful forms with a rapidity which the eye cannot follow. But the object of these inquiries is far higher than the gratification of curiosity: they throw considerable light upon the constitution of matter; the arrangement of its particles and the properties resulting therefrom, as elasticity, hardness, fragility, malleability, &c. A further discussion of the subject would lead us into a difficult department of science: we will therefore conclude this part of our subject with an easy and practical example.

When the points of support in a circular plane surface extend round the whole circumference, as in the parchment head of a drum, the whole plate or surface generally vibrates in one unbroken system; but the membrane may be struck or pressed in such a manner that an impulse communicated to one spot of the surface may not have time to extend itself over the whole surface before the retrogade motion of the disturbed point commences; in this case a nodal line will be formed at the limit of the sphere of the original impulse; thus, it has been found that in certain mining operations connected with military engineering, some sand has been strewed on the head of a drum, and the latter placed either over, or in near approximation to, a supposed excavation or subterranean gallery; any operations performed in the latter which are calculated to excite tremulous impulses in the air or the ground near it, will, when communicated to the drum, cause the dust or sand to assume certain forms, according to the nature of the impulse communicated to it, and engineers accustomed to those operations have been enabled to determine as to the nature of the operations going on beneath, and in what direction the locality was disturbed, by observing the forms into which the sand is thrown on the drum. In these cases, as in the former, the nodal lines are indicated by the form assumed by the sand on the vibrating surface.

In the cases which we have been considering, the surfaces are supposed to vibrate transversely, i.e., in the direction of the thickness; but in some important experiments which have been instituted by Savart on the vibrations in a plane parallel to the surface, these he terms tangential vibrations, and they are most readily produced by rubbing the surfaces of bodies. His experiments were performed with square, circular, triangular, or longitudinal pieces of glass, with bars, with solid or hollow cylinders: these on being suspended lightly in the middle, and rubbed longitudinally with a wet cloth, will indicate nodal divisions of a complicated character; the nodes on the upper surface being vertically over the most actively vibrating points on the under surface and vice versa. In a cylinder the nodal .lines form a spiral, making four turns round it in its progress from end to end. On plane surfaces these nodes are detected by sprinkling dry lycopodium as before described; but with cylinders small rings of paper were hung upon it, and their state of agitation or rest indicated the presence or absence of vibrations.

3. The Vibration of Curved Surfaces.

If we draw a violin bow across the edge of a glass goblet, or any similar vessel, a musical note is produced, which depends for its existence on several remarkable changes in the form of the glass itself; so minute indeed that the unassisted eye can detect no motion. It is, however, easy to prove that when the glass receives its first impulse from the bow it is thrown into the form a a' a" a"" fig. 8, which the instant afterwards is changed to the position bbb" b the dotted circle being the position of the rim of the glass in a state of repose.

If we hang four little hooks upon the rim of the glass we shall find that they will be greatly agitated by the vibration of the glass, excepting at four points of its edge, at which points they will be at rest, or nearly so: these four points are equidistant from each other, and it will be seen that the point to which the bow is applied is equidistant between two of them: if the hooks be placed at those positions at first, they will remain there, but if at other points, they will travel round to the resting points.

The existence of these four points is very pleasingly shown by the use of lycopodium, the seed of the Lycoperdon bovista, which possesses a degree of fineness greatly exceeding the generality of powders, each grain being, according to Wollaston, less than the 85,000th of an inch in diameter.

For the use of this powder, a conical-shaped vessel is better than the shape of a goblet, but the latter will do. Fig. 8. B'

a

By sprinkling the lycopodium dust on the interior surface of the glass (to which a small quantity will adhere), and then vibrating the glass with a bow, a considerable portion of the powder will be shaken from off the surface, with the exception of four narrow lines of powder reaching from the top of the glass a considerable way down: in these lines there is very frequently not only the original portion of dust remaining, but an additional modicum derived from the other portions of the glass; and it will be always found that the point to which the bow is applied is midway between two of the lines.

To these modes of detecting the existence of vertical lines in the glass, having different properties from the remainder of the surface, we will now add another, which is, perhaps, more convenient in its application, and more appreciable; we mean, the presence of water, or any other liquid, in the glass. Water, coloured with litmus or ink to deaden the transparency, will answer very well.

If, when the glass is about half filled with water, it be vibrated by passing the moist finger round its edge, the liquid surface becomes broken up into a figure of four fans, which rotate in the direction and with the velocity of the finger, the latter being always midway between two of the fans, its pressure causing the point on which it rests at any given instant to assume the condition of a node; but if the glass be excited to vibration by means of a bow, the surface of the water is thrown into the form represented by fig. 9. From four equidistant points of the glass emanate four fans of liquid undulations, which proceed nearly to the centre of the liquid surface; and it is seen that, whatever part of the glass be chosen as the point of excitation, one of Fig. 9.

the fans emanates from

beneath that point. The oblique action of two contiguous fans raises a faint ridge which proceeds from each node to the centre; while the extreme ends of the four fans form, in meeting at the centre, a net-like figure, which is generally that of an imperfect square.

The last corroborative evidence of the existence of these four remarkable points in the circle of the ass which we shall mention, is obtained by the use of any oily or viscid fluid, such as is calculated to adhere to glass more than water does. If the vessel be half filled with such a liquid, (care being taken to preserve the inner surface of the glass, between the oil and the rim quite dry,) and vibrated by one rather decided stroke of the bow, it will be seen, on viewing the glass horizontally, that four vertical curves are formed by an upward starting or motion of the oil in four places, by which a small stratum is left adhering to the surface of the glass, and, in analogy with previous instances, the point of excitation occupies a position immediately over the highest point of one of these curves.

There are many other methods of proving the existence of four equidistant and quiescent points round the surface of the glass; but these instances will suffice. Let us now attend to the explanation of the phenomena. As in the stretched cord, so in the goblet; the action of the bow

throws the vibrating body into a new curve, which, in the present case, is an ellipse.

When the impulse has produced the greatest displacement of which it is susceptible, a momentary state of rest occurs, in which the glass is elliptical; but its elasticity will not permit a continuance in that form: the depressed portions acquire an outward tendency, and the elongated portions a tendency towards the centre; there must therefore be points where these opposite tendencies neutralize each other, and those points must necessarily be the parts of the glass which were not originally disturbed from their position of repose.

By the time the segments have regained their original position, they acquire a momentum which carries them beyond the circle of repose, the two outer segments passing within, and the two inner segments passing without. Å moment's consideration will show that this action must generate an ellipse, of which the longer axis is at right angles to the longer axis of the former ellipse a a a a which it has just superseded: this we may represent by the ellipse bb bb, fig. 8.

It will now be well understood that the same causes which produced the destruction of the first ellipse will act with equal force on the second; elasticity will carry the displaced segments back to their original positions, and in so doing will generate a momentum sufficient to carry them beyond that boundary, and thus give rise to the formation of an ellipse similar to the first, and at right angles to the second. Thus these reciprocations succeed each other until the resistance of the air and other circumstances finally, but gradually, subdue them; for it should be understood that each successive ellipse is less elongated than the preceding. The description of these changes necessarily takes a considerable time, but the changes themselves occur with almost inconceivable rapidity, being several hundred times in a second; and as our visual powers are quite inadequate to detect the individual members of such a rapidly-recurring series, whatever effect either ellipse considered separately is calculated to produce, we estimate the result as if both ellipses were co-existent; and this will now enable us to explain the quadripartite phenomena before described. If water be contained in the glass, the transformation of the latter from a circular to an oval form necessarily occasions a flow of water from the flatter towards the smaller ends of the ellipse: when the latter is reversed, a flow occurs in the opposite direction, and as the eye cannot detect any interval of rest between the two, an impression of their simultaneous existence is left upon the mind. Thus the form of fig. 9 is presented to us, and thus shall we be enabled to apply the same mode of reasoning to the points of rest indicated by the hooks, powder, &c. While the four segments of the glass are rapidly vibrating to and fro, the four intermediate points, being urged as it were, between two equal forces, do not move at all, and any bodies placed against those points will be nearly as quiescent as if the glass were not vibrating: thus if the little hooks be symmetrically placed equidistant from each other, and the bow be applied midway between two of them, the two resulting ellipses will cut each other at the points on which the hooks are placed, and then those points become nodes or quiescent points which are not likely to disturb the hooks placed upon them; but if the latter be placed at other points, or if the bow be applied other than midway between two of them, the hooks partake of the vibratory action of the parts of the edge on which they are resting, and are gradually shaken to those points where the agitation is less vigorous, and finally attain the nodal points.

With respect to the lycopodium dust, it is evidently shaken from those parts which are actively vibrating, because its adhesion to the glass is very slight; but as there is no motion occurring at the nodes, there is no reason why it should be removed from thence, and we consequently find that a line of powder remains on the quiescent points. It must here be remarked that although, for convenience, we have spoken of the glass as a vibrating circle, the effect is obviously carried a considerable distance towards the bottom, and instead of nodal points, we have nodal lines, down which the powder remains undisturbed. Thus may these interesting phenomena be analyzed, and the rationale of their production traced step by step; but the inquiry by no means stops here: we have treated of that combination of circumstances which will induce a system of four vibrating segments in the glass, but we shall find that the same principle, modified in its individual application, is discernible under other conditions, into the consideration of which we will now enter