Waves and ripples in water, air, and æther

WAVES AND RIPPLES IN THE AIR.

LEAVING the consideration of waves and ripples on a water-surface, we pass on to discuss the subject of waves and ripples in the air. Nearly every one is aware, in a general way, that sound is due to a disturbance created in the atmosphere. Few, however, are fully acquainted with the nature of the movements in the air which excite our sense of hearing, and to which we owe, not only the pleasures of conversation and the enjoyment of all the sounds in nature, but those delights of music which are amongst the purest forms of pleasure we possess.

In the first place, it is necessary to demonstrate the fact that in a place where there is no air there can be no sound. Before you on the table is a brass plate covered with a glass dome. Under the dome is a piece of clockwork, which, when set in action, strikes a gong. This clockwork is suspended by silk strings from a frame to keep it out of contact with the plate. The plate is in connection, by a pipe, with an air-pump downstairs, and from the space under the dome we can at pleasure remove the air. Before so doing, however, the clockwork shall be set in motion, so that you will then see the hammer striking the gong, and you also hear the sound. If now we exhaust the air, the sound rapidly dies away, and when a fairly perfect vacuum has been made, whilst you see the hammer continuing to pound the bell, you notice that no sound at all reaches your ears. Turning a tap, I let in the air, and once more the ring of the bell peals forth. The experiment shows conclusively that sound is conveyed to us through the air, and that if we isolate a sounding body by removing the air around it, all transmission of sound is stopped. Even rarefying the air greatly weakens the sound, for it is noticed that an exploding pistol or cracker does not create the same intensity of sensation in the ear at the top of a very high mountain as it does in the valley below.

We have then to show, in the next place, that a substance which is emitting sound is in a rapid state of vibration, or to-and-fro movement. Taking a tuning-fork in my hand, I strike its prongs against the table, and you hear it faintly sounding. Your unassisted vision will not, however, enable you to see that the prongs are in rapid motion. If, however, I hold it against a pith-ball suspended by a silk fibre, you see by the violent bouncing of the ball that the prongs must be in energetic vibration.

Another experiment of the same kind, which you can yourselves repeat, is to elicit a sound from a small table-gong by striking it with the hammer. Then hold near the surface of the metal a small ball of wood or cork, to which a suspending thread has been tied. The ball will keep jumping from the gong-surface in a manner which will convince you that the latter is in a state of violent agitation. The mode and extent of this movement in a sound-emitting body must next be more thoroughly examined. Let me explain the means by which I shall make this analysis. On the prong of a tuning-fork, T (see Fig. 44), is fixed a small mirror, M, and a ray of light is reflected from an electric lantern on to this mirror. The ray is then reflected back again on to a sort of cubical box, C, the sides of which are covered with looking-glass, and finally it falls upon the screen. The mirrors are so arranged that if the cubical mirror is at rest and the fork also, a bright spot of light is seen upon the screen. If the fork is set in vibration, then the spot of light moves up and down so rapidly that it forms a vertical bar or line of light upon the screen. The cubical mirror is carried upon an axis, and can be set in rotation. If the fork is at rest and the cubical mirror revolves, then the spot of light marches horizontally across the screen, and when the motion of the mirror is sufficiently rapid it forms a horizontal and brilliant band of light. If, then, these two motions are performed at the same time, the tuning-fork being set in vibration and the cubical mirror in rotation, we find that the spot of light on the screen executes a wavy motion, and we see in consequence a sinuous bright line upon the wall.

We have here two principles involved, which it may be better to explain a little more in detail. An impression made upon the eye lasts for about the tenth part of a second. Hence, if a luminous point or bright object moves sufficiently rapidly, we cease to be able to follow its movement, and we receive on our eyes merely the effect of a luminous line of light. Every boy sees this when he whirls round a lighted squib or stick with a flaming end. In the next place, notice that two independent movements at right angles combine into what is called a resultant motion. Thus the vertical up-and-down motion of the spot of light in our experiment, combined with its uniform horizontal movement, results in the production of a wavy motion. For the sake of those who wish to repeat the experiment, a few little hints may be given. The revolving cubical mirror is a somewhat expensive piece of apparatus, but found in every well-appointed physical laboratory. A cheap substitute, however, may be made by firmly sticking on to the sides of a wooden box pieces of thin looking-glass. The box is then to be suspended by a string. If the string is twisted, the box may be set spinning like a joint of meat roasting before the fire. An ordinary magic lantern may be used to provide a parallel beam of light. In lecture demonstrations it is necessary to employ the electric arc lamp, and to make use of an arrangement of lenses to create the required powerful parallel beam of light. Then as regards the fork. We are employing here a rather elaborate contrivance called an electrically driven tuning-fork, but for home demonstration it is sufficient to make use of a single piece of stout steel clock-spring, or any other flexible and highly tempered piece of steel. This must be fixed to a block of wood as a support, and to its end must be fastened with care a small piece of lead, to which is attached a fragment of thin silvered glass of the kind called a galvanometer mirror, which may be procured of any scientific instrument maker. The position of this vibrating spring must be such that, if the spring vibrates alone, it will reflect the ray of light on to one face of the cubical mirror, and thence on to a white wall, and create a vertical bar of light, which becomes a spot of light when the spring is at rest. It is possible to purchase very small concave mirrors about half an inch in diameter, made of glass silvered at the back. If one of these can be procured, then there is no need to employ an optical lantern; with an ordinary table-lamp, or even a candle as a source of light, it is easy to focus a bright spot of light upon the screen, which effects the desired purpose of making evident the motion of the spring.

Before we dismiss the experiment, let me say one or two more words about it. You notice when it is proceeding that the luminous wavy line is a regular and symmetrical one. This shows us that the motion of the prong of the fork is similarly regular. This kind of backwards-and-forwards motion is called an harmonic motion, or a simple periodic motion. It is very similar to the kind of movement executed by the piston of a steam-engine as it oscillates to and fro. The exact nature of the wavy line of light you see upon the screen can be delineated by a line drawn as follows: On a sheet of paper describe a circle, and divide its circumference into twelve equal parts (see Fig. 45). Through the centre and through each of these points on the circumference draw parallel lines. Divide up a length of the line drawn through the centre into twelve equal parts, and number these divisions 1 to 12. Number also the points on the circumference of the circle. Through the twelve points on the horizontal line erect perpendiculars. Make a dot at the intersection of the perpendicular, or ordinate, as it is called, drawn through point 1 on the horizontal line, and the horizontal through point 1 on the circumference of the circle. Do this for all the twelve intersections, and then carefully draw a smooth curve through all these points. We obtain a wavy curve, which is called a sine curve, or simple harmonic curve, and is the same form of curve as that exhibited on the screen in the experiment with the tuning-fork and spot of light. The piece of the curve drawn as above is called one wave-length of the harmonic curve.

In our case the tuning-fork is making one hundred complete vibrations (to and fro) per second. Hence the periodic time, or time occupied by one complete wave, is the hundredth part of a second. To realize what this small interval of time means, it is sufficient to remember that the hundredth part of a second is to one second as the duration of this lecture (one hour) is to four days and nights.

The prongs of a sounding tuning-fork or the surface of a gong or a bell, when struck, are therefore in rapid motion. We can then proceed to an experiment fitted to indicate the difference between those motions in sounding bodies which create musical tones, and those which create mere noises or vocal sounds.

I have on the table before me a bent brass tube provided with a mouthpiece at one end, and the other end of the tube is covered over with a very thin piece of sheet indiarubber tied on like the cover of a jam-pot. To the outer surface of this indiarubber is cemented a very small, light silvered-glass mirror. The same arrangements are made as in the case of the previous experiment, and the ray of light from a lantern is reflected from the little mirror on to the revolving cubical mirror, and thence on to the screen. Setting the cubical mirror in rotation, we have a line of bright light upon the screen. If, then, my assistant sings or speaks into the mouthpiece, the motion of the indiarubber sets in vibration the little attached mirror. This mirror is not attached to the centre of the membrane, but a little to one side. Hence you can easily understand that when the indiarubber is bulged in or out, the attached mirror is more or less tilted, and the spot of light is displaced up or down on the screen. In this manner the movements of the spot imitate those of the diaphragm. Hence the form of the bright line on the screen is an indication of the kind of movement the diaphragm is making. Let us then, in the first place, sing into the tube whilst the cubical mirror is uniformly rotated. If my assistant sounds a full pure note, you will see that the straight line of light instantly casts itself into a wavy form, which is not, however, quite of the same shape as in the case of the tuning-fork. Here the zigzag line resembles the outline of saw-teeth (see Frontispiece).

If he varies the loudness of his sound, you see the height of the teeth alter, being greater the louder his note. If he changes the tone, singing a bass or a treble note, you observe that, corresponding to a high or treble note, the waves are short, and corresponding to a deep or bass note, the waves are long. Accordingly, the shape of the line of light upon the screen gives us exact information as to the nature of the movement of the indiarubber diaphragm, viz. whether it is moving in and out, slowly or quickly, much or little.

Again, suppose, instead of singing into the tube, my assistant speaks a few words. If, for instance, he repeats in a loud tone the simple but familiar narrative of “Old Mother Hubbard,” you will see that, corresponding to each word of the sentence, the line of light upon the screen bends itself into a peculiar irregular form, and each particular word is as it were written in lines of fire upon the wall.

Notice how certain sounds, such as b and p and also t are represented by very high notches or teeth in this line of light. These sounds are called explosive consonants, and if you examine the manner in which they are made by your mouth, you will notice that it consists in closing the mouth by the lips or tongue placed between the teeth, and then suddenly withdrawing the obstruction so as to allow the air from the lungs to rush forcibly out. Hence the air outside, and in this case the diaphragm, receives a sudden blow, which is represented by this tall tooth or notch in the luminous band. The experiment teaches us that whereas musical tones are caused by certain very regular and uniform vibrations of the sounding body, vocal sounds and noises are caused by very irregular movements. Also that loud sounds are created by large motions, and feeble ones by small motions. Again, that the difference between tones in music is a difference in the rate of vibration of the sounding body. We may infer also that the difference between the quality of sounds is connected with the form of the wave-motion made by them.

Having established these facts, we must, in the next place, proceed to notice a little more closely the nature of an air wave. It will be necessary to remind you of certain qualities possessed not only by the air we breathe, but by all gases as well. Here is a cylinder with a closely fitting piston, and a tap at the bottom of the tube. If I close the tap and try to force down the piston, I feel some resistance, which increases as the piston is pushed forward. If the pressure is removed, the piston flies back to its old position, as if there were a spring underneath it. The air in the tube is an elastic substance, and it resists compression. At constant temperature the volume into which the air is squeezed is inversely as the pressure applied.

The air, therefore, possesses elasticity of bulk, as it is called, and it resists being made to occupy a smaller volume. Again, the air possesses inertia, and when it is set in motion it continues to move like any other heavy body, after the moving force is withdrawn. We have, therefore, present in it the two essential qualities for the production of a wave-motion, as explained in the first lecture. The air resists compression in virtue of elasticity, and when it is allowed to expand again back, it persists in motion in virtue of inertia.

Let us consider next the process of production of a very simple sound, such as an explosion. Suppose a small quantity of gun-cotton to be detonated. It causes a sound, and therefore an air wave. The process by which this wave is made is as follows: The explosion of the gun-cotton suddenly creates a large quantity of gas, which administers to the air a very violent outward push or blow. In consequence of the inertia of the air, it cannot respond everywhere instantly to this force. Hence a certain spherical layer of air is compressed into a smaller volume. This layer, however, almost immediately expands again, and in so doing it compresses the next outer layer of air and rarefies itself. Then, again, the second layer in expanding compresses a third, and so on.

Accordingly, a state of compression is handed on from layer to layer, and each state of compression is followed by one of rarefaction. The individual air-particles are caused to move to and fro in the direction of the radii of the sphere of which the source of explosion is the centre. Hence we have what is called a spherical longitudinal wave produced.

Each air-particle swings backwards and forwards in the line of propagation of the wave. The actual motion of each air-particle is exceedingly small.

The speed with which this zone of compression travels outwards, is called the velocity of the sound wave, and the extent to which each air-particle moves backwards and forwards is called the amplitude of the wave.

Suppose, in the next place, that instead of a merely transitory sound like an explosion, we have a continuous musical sound, we have to inquire what then will be the description of air-movement executed. The experiments shown already will have convinced you that, in the case of a musical sound, each air-particle must repeat the same kind of motion again and again.

The precise nature of the displacement can be best illustrated by the use of two models. Before you is placed a frame to which are slung a series of golf-balls suspended by threads (see Fig. 4, Chapter I.). Between each pair of balls there is a spiral brass spring, which elastically resists both compression and extension. You will see that the row of balls and springs, therefore, has similar properties to the air. In virtue of the springs it resists compression and expansion, and in virtue of the mass or inertia of the balls any ball, if displaced and allowed to move back, overshoots its position of equilibrium because it persists in motion. The row of balls, therefore, resists extension and compression in consequence of the elasticity of the springs, and each ball persists in movement in consequence of the inertia of the ball.

If we then administer a little pat to the first ball, you will see a wave-motion run along the line of balls. Each ball in turn moves to and fro a little way, and its movement is handed on to its neighbours. We have here an example of a longitudinal wave-motion which resembles that of the air when it is traversed by a sound wave.

Another model which is of a more elaborate character shows us the sort of motion made in a tube when a sound wave due to a continuous musical sound is passing along it. It consists of a glass disc which is blackened, and has the paint removed along certain excentric circular lines. This disc is made to revolve in front of a wide slit in a piece of metal. By means of an optical lantern we project on to the screen an image of the slit, which you see is crossed by certain bright bars of light, crowded together at some places and more spaced apart at others. When the disc revolves, these bars of light each move to and fro successively, and the result is that the crowded place moves along, or is displaced.

A wave of compression is propagated along the slit, and the localities where the bars of light are compressed or expanded continually change their place. If we imagine the air in a tube to be divided into slices, represented by these bars of light, the motion of the model exactly represents the motion of the air in the tube when it is traversed by a series of sound waves.

The distance from one place of greatest compression to the next is called the wave-length of the sound wave. Hence, although a sound such as that of an explosion may consist in the propagation of a single layer of compression, the production of a continuous musical note involves the transference of a series of equidistant compressional zones, or waves.

These models will have assisted you, I trust, to form a clear idea of the nature of a sound wave in air. It is something very different, in fact, from a wave on the surface of water, but it is characterized by the same general qualities of wave-motion. It is a state of longitudinal periodic motion in a row of particles, which is handed on from one to another. Each particle of air oscillates in the line of propagation of the wave, and moves a little way backwards and forwards on either side of its undisturbed position.

It will be seen, therefore, that a solitary sound wave is a state of air-compression which travels along in the otherwise stationary air. The air is squeezed more tightly together in a certain region, and successive layers of air take up this condition. In the case of water-surface waves the wave is a region of elevation at which the water is raised above the general or average level, and this elevated region is transferred from place to place on otherwise stationary water. In the case of an air-wave train we have similar regions of compression following each other at distances, it may be, of a fraction of an inch or of several feet.

Thus in the case of ordinary speech or song, the waves are from 2 to 8 feet in length, that is, from one compressed region to the next. In the case of a whistle, the wave-length may be 1 or 2 inches, whilst the deepest note of an organ produces a sound of which the wave-length is about 32 feet.

As in every other instance of wave-motion, air waves may differ from each other in three respects. First, in wave-length; secondly, in amplitude; and thirdly, in wave-form. The first determines what we call the tone, i.e. whether the sound is high or low, treble or bass; the second determines the intensity of the sound, whether faint or loud; and the third determines its quality, or, as the Germans expressively call it, the sound-colour (Klangfarbe).

We recognize at once a difference between the sound of a vowel, say ah, sung by different persons to the same note of the piano and with the same loudness. There is a personal element, an individuality, about voices which at once arrests our attention, apart altogether from the tone or loudness. This sound-quality is determined by the form of the wave-motion, that is, by the nature of the movement of the air-particle during its little excursion to and fro in which it takes part in producing a zone of compression or rarefaction in the air and so forms a sound wave.

We have next to discuss the speed with which this air-compression is propagated through the air. Every one knows that it is not instantaneous. We see the flash of a gun at a distance, and a second or so afterwards we hear the bang. We notice that the thunder is heard often long after the lightning flash is seen. It would take too long to describe the experiments which have been made to determine precisely the speed of sound waves. Suffice it to say that all the best experiments show that the velocity of a sound wave in air, at the temperature of melting ice, or at 0° C. = 32° Fahr., is very nearly 1087 feet per second, or 33,136 centimetres per second. This is equivalent to 741 miles per hour, or more than ten times the speed of an express train. At this rate a sound wave would take 4 hours to cross the Atlantic Ocean, 16 hours to go half round the world or to the antipodes, and some 2 minutes to cross from Dover to Calais.

An opportunity of observing this speed of sound waves on a gigantic scale occurred about 20 years ago on the occasion of a great volcanic eruption near Java. If you open the map of Asia and look for Java and Sumatra in the Asiatic Archipelago, you will easily find the Sunda Strait, and on a good map you will see a small island marked called Krakatoa. This island possesses, or rather did possess, a volcano which, until the year 1883, had not been known to be in eruption. In that year, however, it again burst into activity, and after preliminary warnings a final stupendous outburst occurred on August 27, 1883. The roar of this volcanic explosion was probably the loudest noise ever heard upon this earth. The pent-up volcanic gases and vapours burst forth from some subterranean prison with such appalling power that they created an air wave which not only encircled the earth, but reverberated to and fro seven times before it finally faded away. The zone of compressed air forming the mighty air wave as it passed from point to point on the earth’s surface, caused an increase of atmospheric pressure which left its record on all the self-registering barometers, and thus enabled its steps to be traced. A diligent examination of these records, as collected in a celebrated Report of the Royal Society upon the Eruption of Krakatoa, showed exactly the manner in which this great air wave expanded. Starting from Krakatoa at 10 a.m. on the 27th of August, 1883, the air wave sped outwards in a circle of ever-increasing diameter until, by 7 p.m. on the same day, or 9 hours later, it formed a girdle embracing the whole world. This stupendous circular air wave, 24,000 miles in circumference, then contracted again, and in 9 hours more had condensed itself at a point in the northern region of South America, which is the antipodes of Krakatoa. It then rebounded, and, expanding once more, just like a water wave reflected from the side of a circular trough, returned on its own steps, so that 36 hours afterwards it had again reached the point from whence it set out. Again and again it performed the same double journey, but each time weaker than before, until, after seven times, the echoes of this mighty air wave had completely died away. This is no fancy picture, but a sober record of fact obtained from the infallible records of self-registering air-pressure-measuring instruments. But we have evidence that the actual sound of the explosion was heard, 4 hours after it happened, on the other side of the Indian Ocean, by human ears, and we have in this an instance of the measurement of the velocity of sound on the largest scale on which it was ever made.

There are many curious and interesting facts connected with the transmission of a sound wave through air, affecting the distance at which sounds can be heard. The speed of sound in air is much influenced by the temperature of the air and by wind.

The speed of sound increases with the temperature. For every degree Fahrenheit above the melting-point of ice (32° Fahr.) the speed is increased by one foot per second. A more accurate rule is as follows: Take the temperature of the air in degrees Centigrade, and add to this number 273. In other words, obtain the value of 273 + t° where t° is the temperature of the air. Then the velocity of sound in feet per second at this temperature is equal to the value of the expression⁠—

There is one point in connection with the velocity of propagation of a sound wave which should not be left without elucidation. It has been explained that the velocity of a wave in any medium is numerically given by the number obtained by dividing the square root of the elasticity of the medium by the square root of its density. The number representing the elasticity of a gas is numerically the same as that representing its absolute pressure per square unit of surface. The volume elasticity of the air may therefore be measured by the absolute pressure it exerts on a unit of area such as 1 square foot. At the earth’s surface the pressure of the air at 0° C. is equal to about 2116·4 lbs. per square foot. The absolute unit of force in mechanics is that force which communicates a velocity of 1 foot per second to a mass of 1 lb. after acting upon it for 1 second. If we allow a mass of 1 lb. to fall from rest under the action of gravity at the earth’s surface, it acquires after 1 second a velocity of 32·2 feet per second. Hence the force usually called “a pressure of 1 lb.” is equal to 32·2 absolute units of force. Accordingly, the atmospheric pressure at the earth’s surface is 2116·4 × 32·2 = 68,148 absolute units of force in that system of measurement in which the foot, pound, and second are the fundamental units.

The absolute density of the air is the mass of 1 cubic foot: 13 cubic feet of air at the freezing-point, and when the barometer stands at 30 inches, weigh nearly 1 lb. More exactly, 1 cubic foot of air under these conditions weighs 0·080728 lb. avoirdupois. If, then, we divide the number representing the absolute pressure of the air by the number representing the absolute density of air, we obtain the quotient 844,168; and if we take the square root of this, we obtain the number 912·6.

The above calculation was made first by Newton; and he was unable to explain how it was that the velocity of the air wave, calculated in the above manner from the general formula for wave-speed, gave a value for the velocity, viz. 912·6, which was so much less than the observed velocity of sound, viz. 1090 feet per second at 0° C. The true explanation of this difference was first given by the celebrated French mathematician Laplace. He pointed out that in air, as in all other gases, the elasticity, when it is compressed slowly, is less than that when it is compressed quickly. A gas, when compressed, is heated, and if we give this heat time to escape, the gas resists the compression less than if the heat stays in it. Hence air is a little more resilient to a very sudden compression than to a slow one. Laplace showed that the ratio of the elasticity under sudden compression was to that under slow compression in the same ratio as the quantities of heat required to raise a unit mass of air 1° C. under constant pressure and under constant volume. This ratio is called “the ratio of the two specific heats,” and is a number close to 1·41. Hence the velocity, as calculated above, must be corrected by multiplying the number 844,168 by the number 1·41, and then taking the square root of the product. When this calculation is made, we obtain, as a result, the number 1091, which is exactly the observed value of the velocity of sound in feet per second at 0° C. and under atmospheric pressure. The velocity of sound is much affected by wind or movement of the air. Sound travels faster with the wind than against it. Hence the presence of wind distorts the shape of the sound wave by making portions of it travel faster or slower than the rest.

These two facts explain how it happens that loud sounds are sometimes heard at great distances from the source, but not heard at places close by.

Consider the case of a loud sound made near the surface of the earth. If the air were all at rest, and everywhere at the same temperature, the sound waves should spread out in hemispherical form. But if, as is generally the case, the temperature near the ground is higher than it is up above, then the part of the wave near the earth travels more quickly than that in the higher regions of the air. It follows that the sound wave will have its direction altered, and instead of proceeding near the earth in a direction parallel to the ground, it will be elevated, so as to strike in an upward direction. Again, it may be brought down by meeting with a current of air which blows against the lower portion and so retards that to a greater extent than it does the upper part. So it comes to pass that a sound wave may, as it were, “play leap-frog” over a certain district, being lifted up and then let down again; and persons in that region will not hear the sound, although others further off will do so.

A very striking instance of this occurred on the occasion of the funeral procession of our late beloved Queen Victoria of blessed memory. The body was conveyed across the Solent on February 1, 1901, between lines of battleships which fired salutes with big guns. Arrangements were made to determine the greatest distance the sound of these guns was heard. In a very interesting article in Knowledge for June, 1901, Dr. C. Davison has collected the results of observation from eighty-four places, some of which are indicated in the map (see Fig. 47), taken, by kind permission of the editor of Knowledge, from that journal. Observations were received from places as far distant as Alderton (Suffolk), 139 miles from the Solent. At several places the sound of the guns was loud enough to make windows shake. This occurred at Longfield (56 miles), Sutton (58 miles), and Richmond Hill (61 miles). But whilst there is clear evidence that the sound of the guns was heard even at Peterborough (125 miles), most curious to say, the sound was hardly heard at all in the neighbourhood of the Solent. The nearest place from which any record was received was Horley, in Surrey (50 miles). Hence it appears evident that the sound was lifted up soon after leaving the Solent, and passed right over the heads of observers near, travelling in the higher air for a considerable distance, probably 40 or 50 miles, and was then deflected down again, and reached observers on the earth’s surface at much greater distances. An examination of the wind-charts for that day makes it tolerably clear that this was due to the manner in which the wind was blowing at the time. Dr. Davison, loc. cit., says⁠—

The same explanation has been given of the extraordinary differences that are found at various times in the distance at which lighthouse fog-horns are heard by ships at sea. There is in this case, however, another possible explanation, due to what is called interference of sound waves, the explanation of which will be given presently. The late Professor Tyndall, who was an authority on this subject, was of opinion that in some states of the atmosphere there existed what he called “acoustic opacity,” the air being non-uniform in temperature and moisture; and through this very irregular medium, sound waves, when passing, lost a great deal of their intensity by internal reflection, or eclipses, just as light is stopped when passing through a non-homogeneous medium like crushed ice or glass. At each surface a little of the light is wasted by irregular reflection, and so the medium, though composed of fragments of a transparent substance, is more or less opaque in the mass.

On the subject of sound-signals as coast-warnings, some exceedingly interesting information has recently been supplied by Mr. E. Price-Edwards (see Journal of the Society of Arts, vol. 50, p. 315, 1902). The Lighthouse Boards of different countries provide the means for making loud warning sounds at various lighthouses, as a substitute for the light when fog comes on. The distance at which these sounds can be heard, and the distance-traversing power of various kinds of sounds, have been the subject of elaborate investigations.

The instrument which has been found to be the most effective in producing very powerful sound waves is called a siren. It consists of a tube or horn, having at the bottom a fixed disc with slits in it. Outside this disc is another movable one which revolves against the first, and which also has slits in it. When the second disc revolves, the passage way into the horn is opened and closed intermittently and suddenly, as the slits in the discs coincide or not. Air or steam under a pressure of 10 to 40 lbs. on the square inch is blown into the horn, and the rapid interruption of this blast by the revolving slits causes it to be cut up into puffs which, when sufficiently frequent, give rise to a very loud sound. The air under pressure is admitted to a back chamber and awaits an opportunity to escape, and this is given to it when the revolving disc moves into such a position that the slits in the fixed and moving disc come opposite each other. In comparative trials of different sound-producing instruments, nothing has yet been found to surpass this siren as a producer of penetrating sounds.

It has been found very important that the frequency of the note given by the siren should coincide with the fundamental tone of the trumpet or horn. As will be explained in the next lecture, every column of air in a tube has a particular natural time-period of oscillation. Suppose, for instance, that for a certain length of trumpet-tube this is ¹⁄₁₀₀ second. Then the siren with that trumpet will be most effective if the interruptions of the air-blast are 100 per second.

Lord Rayleigh has also shown that the shape of the mouth of the trumpet is important, and that this should not be circular as usual, but elliptical or oval, the shortest diameter of the ellipse being one quarter of the longest one. Also that the mouth should occupy such a position that the longer axis is vertical. Moreover, he considers that the short axis of the oval should not exceed half the wave-length of the sound being emitted. With a trumpet-mouth of such a shape, the sound is prevented to some extent from being projected up and down, but diffused better laterally—a result which is desired in coast sound-signals.

The information accumulated as regards the distances at which sounds can be heard is very briefly as follows:⁠—

First as regards wind. The direction of the wind has a most remarkable influence on the distance at which a given loud sound can be heard. In one instance, the noise of a siren was heard 20 miles in calm weather; whereas, with an opposing wind, it was not heard more than 1¹⁄₄ mile away.

It has been found that for calm weather a low-pitched note is better in carrying power than a high note, but in rough weather the opposite is the case.

One thing that has been noticed by all who have experimented with this subject is the curious occurrence of “areas of silence.” That is to say, a certain siren will be well heard close to its position. Then a little farther off the sound will be lost, but on going farther away still it is heard again.

Many theories have been advanced to account for this, but none are completely satisfactory. It is, however, a well-established effect, and one with which it behoves all mariners to be acquainted.

One curious fact is the very great power that can be absorbed in creating a loud siren note. Thus in one case, a siren giving a high note was found to absorb as much as 600 horse-power when the note was sounded continuously. The most striking and in one sense the most disappointing thing about these loud sounds is the small distance which they travel in certain states of the wind. As a general result, it has been found that the most effective sound for coast-warnings is one having a frequency of 100, or a wave-length of about 10 feet. When dealing with the subject of waves in general, it was pointed out that the velocity of a wave depended upon the elasticity and the density of the medium in which it was being propagated. In the case of a sound wave in air or any other gas, the speed of wave-transmission is proportional to the square root of the elasticity of the gas, and inversely proportional to the square root of the density.

At the same temperature the elasticity of a gas may be taken to be the same as its pressure. Hence, at the same pressure, the speed of sound-wave transmission through different gases varies inversely as the square root of their densities. An example will make this clear. If we take the density of hydrogen gas to be unity (= 1), then the density of oxygen is 16. The ratio of the densities is therefore 1 to 16, and the square roots of the densities are as √1 to √16, or as 1 to 4. Accordingly, the velocity of sound waves in hydrogen gas is to that in oxygen gas as 1 is to ¹⁄₄. In other words, sound travels four times faster in hydrogen than it does in oxygen at the same temperature and pressure. The following table shows the velocity of sound in different gases at the melting-point of ice (= 0° C.) and atmospheric pressure (= 760 mm. barometer).

Accordingly, we see that the lighter the gas the faster sound travels in it, pressure and temperature being the same. If the atmosphere we breathe consisted of hydrogen instead of a mixture of oxygen, nitrogen, and many other gases, a clap of thunder would follow a flash of lightning much more quickly than it does in our present air, supposing the storms to be at the same distance. Under present circumstances, if 20 seconds elapse between the flash and the peal, it indicates that the storm is about 4 miles away, but if the atmosphere were of hydrogen, for a storm at the same distance the thunder would follow the lightning in about 5 seconds.

Furnished with these facts about the propagation of air waves, it is now possible to point out some interesting consequences. It will be in your recollection that in the first chapter it was pointed out that a wave on water could be reflected by a hard surface, and that it could be refracted, or bent, when it passed from a region where it was moving quickly to one where it was moving more slowly. It will be necessary now to prove experimentally that the same things can be done with sound, in order that a body of proof may be built up in your minds convincing you that the external cause of sound-sensation must be a wave-motion in the air.

In the first place, I must describe to you, somewhat in detail, the nature of the arrangements we shall employ for producing and detecting the sound waves which will be used in these experiments.

It would not do to rely upon the ear as a detector because you cannot all be so placed as to hear the sounds which will be produced, and we shall, therefore, employ a peculiar kind of flame, called a sensitive flame, to act as a detector.

If ordinary coal-gas stored in a gasometer is burnt at a small jet under considerable pressure, we are able to produce a tall flame about 18 to 24 inches in height. The jet used is one with a steatite top and small pin-hole gas exit about ¹⁄₂₅ inch in diameter. The pressure of gas must be equal to about 10 inches of water, and it cannot be drawn straight off the house gas-pipes, but must be supplied from a special gasometer or gasbag under a pressure sufficient to make a flame 18 inches or so in height. If the pressure is too great, the flame roars; if the pressure is slightly reduced, the flame can be made to burn quietly and form a tall reed-like flame (A, Fig. 48). This flame, when properly adjusted, is curiously sensitive to shrill, chirping sounds. You may shout or talk loudly near it, and it takes no notice of your voice, but if you chirrup or whistle in a shrill tone, or clink your keys or a few coins in your hand, the flame at once shortens itself to about 6 or 7 inches in height, and becomes possessed of a peculiarly ragged edge, whilst at the same time it roars (B, Fig. 48). When in adjustment, the clink of a couple of coins in the hand will affect this sensitive flame on the other side of the room.[22]

The flame is also very sensitive to a shrill whistle or bird-call. It will be clear to you, from previous explanations, that the flame responds, therefore, to very short air waves forming high notes. The particular flame I shall now use responds with great readiness to air waves of 1 inch to ¹⁄₂ inch in length.

It may be well to explain that the sensitive portion of the flame is the root, just where it emerges from the burner, and it is the action of the sound wave in throwing this portion of the flame into vibration which is the cause of its curious behaviour.

If you think what the action must be, you will easily see that the operation of the sound wave is to throw the particles of the gas, just as they escape from the hole in the jet, into vibration in a direction transverse or at right angles to the direction of their movement in the flame. The gas molecules are, when unacted upon by the sound wave, rushing out of the jet, in an upward direction. When the sound wave impinges on them they are, so to speak, caught, and caused to rock to and fro in a direction across the flame. The combination of these two motions results in a spreading action on the flame, so that instead of being a thin lance-like shape, it becomes more blunt, stumpy, and ragged at the sides. The flame acts, therefore, as a detector of certain sounds. It is a very sensitive kind of ear which listens and responds to the slightest whisper if only uttered in certain tones, but is deaf to all other sounds. Its great use to us is that it acknowledges the presence of air waves of short wave-length, and shows at once when it is immersed in a stream of air waves or ripples of very short wave-length.

In addition to this, I am provided with a whistle giving a very shrill or high note, which is blown steadily by a current of air supplied under constant pressure from a reservoir. If the whistle is set in action, you will at once see the sensitive flame dip down and acknowledge the presence of the air-waves sent out by the whistle.

The air waves sent out by this whistle proceed, of course, in all directions, but for our present purpose we require to create what I may call a beam of sound. You all know the action of a magnifying-glass, or lens, upon a ray of light. What boy is there who has not, at some time or other, amused himself by concentrating the rays of the sun by a burning-glass, and by bringing them to a focus set light to a piece of paper, or burnt his own or companion’s hand? In this case we use a piece of glass called a lens, which is thicker in the middle than at the edges, to converge parallel rays of light to a point or focus. We also use such a lens in our optical lantern to render the diverging rays from an electric lamp parallel, and so make a parallel beam of light. I shall defer for a moment an explanation of this action, and simply say here that it is possible to construct a sound-lens, which operates in the same manner on rays of sound. I have had such a sound-lens constructed for our present experiments, and it is made as follows:⁠—

It is possible to buy small balloons made of very thin material called collodion, this latter consisting of gun-cotton dissolved in ether and alcohol, and then poured out on a glass plate and allowed to dry. If one of these balloons is purchased, it is possible with great dexterity to cut from it two spherical segments or saucer-shaped pieces. These have then to be cemented with siccotine to a wooden ring having two small pipes opening into it (see Fig. 49). By means of these pipes we can inflate the lens-shaped bag so formed with a heavy gas called carbonic acid gas, made by pouring strong acid upon marble or chalk. The result of these operations, all of which require considerable skill of hand, is to furnish us with a sound-lens consisting of a collodion film in the shape of a magnifying-glass, or double convex lens, filled with carbonic acid gas heavier than the air.

The sound-lens so made is fixed up against a hole in a glass screen of the same size as the lens, and on one side of the lens is placed the whistle, and on the other side the sensitive flame. These have to be adjusted so that the whistle W, the centre of the lens L, and the jet of the flame F are in one straight horizontal line perpendicular to the glass plate.