ACOUSTICS.

SOUND.

(1.) Introduction.-A bell rung under water has been heard nine miles distant; a whisper can be heard through a small tube at the distance of half a mile or more.

A sound heard at a considerable distance is seldom heard singly. Thus a bell rung at one end of a long tube gives a double sound, as does the report of a gun, or a blow with a heavy hammer.

Here are two facts: One, that sounds can be heard at considerable distances through tubes; another, that sounds so heard at a distance are usually double.

What is a sound? We say that we hear with our ears; but what is hearing? What do we hear? How do we hear it? Just as we can see only when light comes in actual contact with our eyes, so we can hear only when the air, whose vibration causes what we call a sound, is in actual contact with our ears. A bell is rung-i. e., its clapper is set in motion and strikes the side of the bell. This vibrates and sets the air in motion; this motion is communicated from one particle of air to the next, and so on until some particle strikes upon the tympanum, or drum, of the ear, and so produces in the brain the sensation of a sound.

When a gun is fired, the great expansion of the gases generated by the combustion of the powder drives away the air, which immediately recovers its equilibrium and re-enters the barrel of the gun. This vibration of the air is communicated to the surrounding particles on all sides, and thus the sound is conveyed to the

ear.

Sound, then, is simply an impression conveyed to the brain by the action of vibrating air on the ear, just as sight is an impression conveyed to the brain by the action of light on the eye. There are, however, important differences between the two. Light acts across a vacuum-sound cannot; light travels with almost inconceivable rapidity-sound, in comparison, but slowly.

Sound is conveyed by any medium-solid, liquid, or gaseous;

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and by solids better than by either liquids or gases. This will explain the double sound just mentioned. Thus, if a long bar of iron be struck at one end loudly with a hammer, a person at the other extremity will hear two sounds-one carried to his ear by the vibration of the air, and the other carried by the vibration of the iron. Sound will pass along a solid iron bar, or the iron of a pipe, just as water would pass through the pipe. So also, when a gun is fired, the sound is heard twice by a person some distance off; being carried by the air, and also by the vapour contained in the air.

But even if the iron and the air, the air and the water, each carries its own sound, need there be two sounds? Will they not be heard together so as to make but one? No: for their rates of travel differ, and so the ear gets first one message and then the second. I have just mentioned that light travels rapidly, and sound, in comparison, but slowly. This is why we see the lightning before we hear the thunder, since the light takes so short a time in comparison with the sound to reach us. Whatever be

the distance of the storm, we see the lightning-flash almost at the very instant, but the sound of the thunder will take some time to reach us and we may, by measuring the time between the flash and the roll, tell how far away is the storm; for sound travels at the rate of 1100 feet every second, so that if we hear the thunder five seconds after we see the lightning, the sound has travelled five times 1100 feet. But light travels nearly 200,000 miles per second, so that however far away the storm, the distance causes no delay in our seeing the flash. Just in the same way, but at much smaller intervals, we hear the same sound twice-first by one medium, then by another. There is an exact parallel to this in the case of light. It is easy to see the same object double -i.e., to get two rays of light coming from it and reaching the eye, but in different directions; so it is possible to hear the same sound twice, if there be two mediums of vibration, in which the sound travels at different rates. In air, sound travels 1100 feet per second; in water, 4900 feet; in iron, 17,000 feet.

Light and heat may be reflected-. e., have their direction changed. So may sound, but not in such small compass. Once, in walking through a long arched passage, near one end of which an itinerant band was playing, I heard the sound of the music twice in almost equal power-once when passing the players, again when near the opposite end of the passage. Just at that spot the sound was almost as audible as close to the men, though between it was scarcely distinguishable.

This will explain what is called echo. A person looking at a light on a table, in a room having a mirror on the wall, might see two lights; or rather, see the same light twice-once in its place on the table, and again in the mirror, and apparently behind it. So with an echo: a sound striking against a large smooth surface is reflected and may be heard twice; once directly through the

SOURCES OF SOUND.

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air, and again through the vibration reflected from the surface, as from a rock or wall.

Sounds may be so shrill as to be inaudible; our ears being only capable of taking cognisance of vibration between certain limits of rapidity and slowness. In distinguishing between sounds, we speak of their pitch, their quality, their loudness. All sounds arise from vibration of the air. The more rapid this vibration, the higher the pitch; the greater the quantity of air set in motion, the louder the sound: the quality depends on the nature and form of the body set in motion.

If I take a piece of ordinary string and shake it loosely in the air, I get no sound; but if I put my foot on one end, and holding the other in one hand, stretching the string tightly, I strike it with my finger or a penholder, I get a buzzing noise from its vibrations. If I shorten the tightened part, by holding only a portion of it stretched, I get a sharper noise, and this sharpness, or shrillness, increases as I shorten the string. If I fasten a ball to the end of the string and swing it slowly round, I hear nothing; but as I increase the speed of the revolutions I also increase the sound, and it gradually becomes audible.

By shortening the string, or by increasing the speed, I increase the number of vibrations in any given time, and this increases the sharpness, or pitch, of the sound.

(2.) Sources of Sound.-Just as the eye is the only organ of sight, and the palate the only organ of taste, so the ear is the only organ of sound-i. e., the only means by which we can become cognisant of it. This perception arises from the air in the immediate vicinity of the ear being disturbed so as to impinge upon the tympanum-i. e., a membrane that closes the orifice of the ear, separating the air without from the air within. This tympanum (the action of which is exactly that of a drum-head) being struck, the air enclosed is set in corresponding motion, and the auditory nerve, being acted on by this motion, conveys to the brain the idea of sound. If this be done but once, the result is simply a sound; if it be continued irregularly and confusedly, the result is noise; if it be continuous at regular intervals, the result is a musical note.

Since sound thus depends upon the motion of air in the neighbourhood of the ear, anything which so sets the air in motion is a source of sound. Thus I strike the table with my hand, knock two books together, ring a bell, break a window-in fact, move any object rapidly and continuously—and I so set the air in motion. But the sound may be too low to be audible; not that it is not a sound, but that our organ of hearing is too imperfect to give us the perception of all sounds. Some are too low and some too high for our perceptive powers.

(3.) Limits of Sound.-It has been proved by experiment

that the vibrations of the air upon the ear must be at least at the rate of sixteen per second for the production of a continuous sound-i. e., the impression does not last more than of a second. On the other hand, the vibrations may succeed each other so rapidly that no sound is perceptible. Theoretically there is no limit to the gamut of sounds, but our sense of hearing is capable only of appreciating the middle of the scale, some sounds being too low and others too high for our perception.

A precise parallel exists in the case of light. A ray of refracted light produces a spectrum, only the middle portion of which is visible to our eyes.

(4.) Form of Sound-Waves.-Just as a lighted candle in the centre of a room radiates light to every part of the room, so a sound produced at the same point would be audible at every position which a person would take. It is common to speak of light, heat, and sound as travelling in straight lines, but it would be, I think, more theoretically true to describe the motion as spherical, the source of the light, heat, or sound being always at the centre of the sphere. Just as an onion is covered by several concentric coats, so we may imagine a lighted candle or a source of sound to be surrounded on all sides by concentric shells of air. We need not imagine these shells to be in any sense distinct or divided from each other except by the effect of the vibration during its existence. Each shell will be, of course, greater than any one within, and less than any one without it; and from this it follows that the sound will become feebler and feebler because of the greater amount of air to be set in vibration.

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Let a small collodion balloon be exploded at a given point. The "explosion means that by the action of light upon the contents of the balloon a chemical change takes place, and that the new substance requires more room than the old one did. In consequence, the air is forced back on all sides to make room for it. The extent of this compression depends upon the active force remaining after some portion of it has been counteracted by the resistance of the air. Suppose the globular space marked (1)-fig. 17-to be occupied by the contents of the balloon after the explosion, then the radius of this sphere (the sphere being represented in the diagram by a circle) will be the measure of the intensity of the produced sound and of the amplitude of the sound-wave.

The air that did occupy this space will be driven into the surrounding space (2), and in like manner will produce a compression there, and a consequent action upon the space (3). In this way each shell of air will be compressed by the intrusion of the air from within it, and will by its resistance drive back the inner shell of air, while it is itself driven into the space of the shell without, to be again driven back into its original position.

In this way there is a constant series of waves of condensation and expansion, the length of the waves being governed entirely

FORM OF SOUND-WAVES.

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by the original force, and the intensity of the sound (generally called "loudness") depending likewise upon the same cause.

It is sometimes said that the intensity of the sound depends upon the amount of this compression, but it might be more correct to say that the amount of compression and the intensity of sound are both results of the same cause, the force with which the compression is made.

Thus, this alternate compression and expansion continues through the air (the thickness of the shells, i. e., lengths of the waves, continuing the same, according to some theories), until its

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Fig. 17.

further progress is stopped by some obstacle. If this be a large flat surface the sound is reflected-if it be irregular, the small inlets will be filled up, just as the waves of the sea enter all the bays and inlets of a coast.

Supposing such a sphere of vibration to come in contact with my head, my ear is to it just as an inlet on the coast to the sea. The spherical contour is broken, and the vibrating air, entering the ear, impinges upon the tympanum. Supposing a number of persons to be arranged so as to form a sphere, or any portion of a sphere (at the centre of which the source of the sound is placed), they will all hear the same sound at the same instant, with the same intensity, supposing all the organs of hearing to be equally sensitive. This must necessarily be the case, since the same shell of vibrating air strikes upon all the ears.

But if two persons are at different distances from the source of the sound, neither the times nor the intensities of the sound will coincide. The more distant, auditor will have to wait until the vibration reaches the sphere of air in which his ear is situate, and since this sphere is larger than the sphere in which the nearer person is, the sound will be weaker-i. e., the vibration will be weaker. In the chapter on Radiation I have discussed the question, whether these spherical shells of air are really all of the same thickness, as is usually described to be the case.

(5.) Intensity of Sound.-This depends entirely upon the force with which the sound-wave impinges upon the ear, and this depends entirely upon the original force which caused the sound-wave. The greater this force, the greater the radius of the first, and of every succeeding, sphere of air set in motion.