Fig. 49.—A sound-lens focussing a divergent beam of air waves.

The distance of the whistle from the lens has then to be adjusted so as to produce on the other side a nearly parallel beam of sound. In other words, the whistle must be placed in the focus of the lens. A rule for doing this is as follows: If the balloon from which the segments of collodion were cut was nearly spherical, and had a diameter of 8 inches, then the whistle must be placed at slightly less than 8 inches from the side of the lens next to it.[23] The exact distance, however, will have to be found by trial, but it is somewhere near the point so determined. The sensitive flame should be about 4 or 5 feet away from the lens on the other side of the screen.

These arrangements having been made and the whistle set in action, it will be found that the flame responds vigorously when it is placed on the axis-line of the lens, but if moved a few inches to right or left of this line, it will cease to flare. This shows us that we have formed a beam of sound, and with some little care it is possible to make this a nearly parallel beam, so that when plunged in this stream of air waves the flame dips, but by removing it just outside the stream of sound it no longer flares. I have found it not difficult, when using a sound-lens 6 or 7 inches in diameter, to make a beam of sound from a whistle some 10 inches wide at about 4 feet from the lens.

Supposing the sound-lens and sensitive flame so adjusted, it is then necessary for our purpose to provide a sound-prism, made in the following manner: A zinc box is made in wedge form, and the two inclined sides are cut out, and these windows are covered with thin collodion film. The box has two pipes connected with it, by means of which it can be filled with carbonic acid gas.

Provided with this apparatus, it is now possible to show you a series of experiments which will leave no doubt in your minds that the external agency which creates in us the sensation of sound is a wave-motion in the air we breathe. Let me, in the first place, show you that a sound-beam can be reflected. We adjust our sensitive flame and set the whistle in action, and create, as described, by the lens, a beam of sound. At a little distance, say a couple of feet, outside the parallel beam we place the sensitive flame, and, being sheltered from the direct action of the whistle, it remains perfectly quiescent. Taking a sheet of glass in my hand, I hold it at an angle of 45° in the sound-beam, and you see the flame at once roars. The beam has been reflected on to the flame, but a very small angular movement of the glass is sufficient to reflect the sound-ray past the flame without touching it, and the flame then exhibits no agitation.

A few experiments of this kind with the flame in various positions are sufficient to show that the sound-beam is reflected by the glass in accordance with the law of reflection of wave-motion, viz. that the angle of incidence is equal to the angle of reflection. We can in the same way reflect the sound-beam by a wooden board, a piece of cardboard, a looking-glass, or a sheet of metal. We can reflect it from a wet duster, but not very well from a dry handkerchief. If we place the flame in the direct beam, it is easy to show that all the above good reflectors of sound are opaque to a sound-ray, and cast an acoustic shadow. In fact, I can prevent the flame from roaring by merely interposing my hand in front of it. A wet duster is found to be opaque to these sound waves, but a dry linen handkerchief is fairly transparent.

The collodion film used in making the lens and prism is also exceedingly transparent to these short air waves. We may then go one step further, and show that these air waves are capable of refraction. It will be in your remembrance that, in speaking of water ripples, it was shown by experiment that, when water ripples passed over a boundary between two regions, in one of which they travelled more quickly than in the other, a bending of the direction of ripple-motion took place. We can show precisely the same thing with these air waves.

The collodion prism has been filled with a heavy gas called carbonic acid. This gas is about half as heavy again as air, and it is this heavy and poisonous gas which, by accumulating in old wells or brewers’ vats or in coal-mines after an explosion, causes the death of any man or living animal immersed in it.

It has already been explained that the velocity of sound waves in different gases varies inversely as the square root of their density. Hence the speed of a sound wave in carbonic acid gas will be less than that in air in the ratio of the square roots of the densities of these gases. The density of carbonic acid gas is to that of air as 1·552 is to 1. The square root of 1·552 is 1·246, or nearly 1¹⁄₄. Accordingly, the speed of a sound wave in carbonic acid gas is to the speed in air as 4 is to 5. A sound wave in air will therefore travel 5 feet or 5 inches in the same time that it travels 4 feet or 4 inches in carbonic acid gas.

Let us now consider what must happen if a sound wave falls obliquely upon the face of our carbonic acid prism.

Fig. 50.—The refraction of a wave by a prism.

Let ABC be the prism (see Fig. 50) represented in plan, and let ab, ab, ab, be a train of sound waves advancing against the face AC. As soon as the left end b of the wave ab touches the face AC, and enters the carbonic acid gas, its speed will begin to be retarded, and in the time taken by the right end a to move in air from a to c, the left end will have moved in carbonic acid gas, by a less distance, bd, the distances ca and db, being in the ratio of 5 to 4. Hence it is clear that the wave-front ab will be swung round, and when the wave has wholly entered the prism, its direction of motion will have been bent round to the left.

The same thing will happen at emergence. The right end, e, of the wave ef gets out into the air whilst the left end, f, is still in carbonic acid. Accordingly, in the time taken for the end f to move to h, the end e will have moved a greater distance, in the ratio of 5 to 4, to g, and therefore we have again a bending round of the wave-direction. It is evident, therefore, that this unequal retarding of the two sides of the wave will result in a refraction, or bending, of the wave-direction, and that whereas the sound-ray was proceeding, before entering the prism, in the direction of the arrow on the right hand, it is altered, after passing through the prism, so as to be travelling in the direction of the arrow on the left-hand side. The double bending of the sound-ray is therefore caused by, and is evidence of the fact that, the sound wave travels more slowly in carbonic acid gas than it does in air.[24]

Let us, then, bring these statements to the test of experiment. We again start in action the whistle W, and place the sensitive flame in the line of the lens-axis, and notice how violently the flame flares (see Fig. 51). The flame is now at a distance of 4 feet from the lens. I move the flame 1 foot to the left hand, and it is now outside the beam of sound, and remains quiescent. The prism P, previously filled with carbonic acid gas, is then inserted between the sound-lens and the flame, and close to the former. When properly placed, the sensitive flame F immediately dips and roars. It will be abundantly evident to you that this can only arise because the prism has bent round the sound-beam, and deflected it on to the flame. But if the beam is bent round, then it follows that if the flame is now moved back to the central position F′, the prism remaining in front of the lens, that the flame will not now roar, and this we find to be the case. If, however, the prism is then removed, the flame at once bursts into a roar.

Fig. 51.—The refraction of a sound-ray.

This experiment proves to demonstration that we can refract waves of sound just as we can refract ripples on water.

Having regard to what we have now seen, I do not think you will have any difficulty in seeing how it is that the biconvex sound-lens, filled with carbonic acid gas, is able to render divergent sound-rays parallel; in other words, can convert a spherical sound wave into a plane sound wave.

Consider what the effect really must be. Let the sound-lens be represented in section by AB (see Fig. 49), and let W be the whistle sending out spherical sound waves, represented by the dotted lines.

When the spherical wave meets the lens, the central portion of the wave passes into a retarding medium, whilst the right and left wings of the wave are still in air. Hence, as before, the wings gain on the centre. Again, at emergence the wings emerge before the centre of the wave, and hence again the wings gain on the centre. After complete emergence the spherical wave-surface has been flattened out and made into a plane wave. Hence the sound-rays diverging from the whistle are rendered parallel or even convergent, provided that the whistle is properly placed with regard to the lens.

You will see, therefore, that we can use a gas denser than the air, contained in a transparent bag or vessel of collodion, as the means of changing the form and direction of sound waves. We can make lenses and prisms of carbonic acid gas which act on rays of sound just as do lenses and prisms of glass on rays of light. There is, however, one great difference between the operation of a carbonic acid prism on rays of sound, and that of a glass or other prism on rays of light. In the lectures on æther waves it will be made clear to you that what we call light really consists in waves in a medium known as the æther. But when such light waves are propagated through a transparent material like glass, the speed of transmission depends on the wave-length, just as in the case of water waves. But as regards sound waves there is no difference between the velocity of propagation or speed with which waves of different wave-lengths move. Hence a bass note travels just as fast as a treble note, and the sound waves from a flute have a speed of the same value as that from a trumpet or bassoon. If it were not so, it would be impossible for us to hear music or song at a distance, because the notes would arrive all in the wrong order, and the most familiar melody would be unrecognizable. It follows from this that air waves, no matter what their wave-length, are equally refracted on passing from one medium to another of different density. We shall see later on that this is not the case with waves of light and æther waves generally.

In the case of most transparent substances the æther waves which constitute light are transmitted with different velocities, the longer waves moving faster than the shorter ones. Hence we have the familiar result of the decomposition of a ray of white light into its different constituents by a glass prism. We cannot, however, perform a similar experiment on a complex series of waves of sound by means of a carbonic acid prism. In other words, a sound-prism refracts, but does not disperse sound waves of various wave-lengths.

One thing, however, should be pointed out before dismissing this experiment, and that is that to show successfully the experiment with the prism, the length of the sound waves used must be small compared with the dimensions of the prism. The reason for this is that otherwise there would be too much bending of the waves round the obstacle. When a train of waves, no matter whether waves in air or waves in water, meets with an impervious body, there is always a certain bending of the waves round it, which is technically called diffraction. We may see this effect on a large scale when sea waves, rolling in, pass by some large rock standing up like an island out of the water. The waves meet it, pass round it, and, so to speak, embrace it and continue on the other side. If there is to be any calm water on the leeward side, the island must be large compared with the length of the waves. The same thing holds good with regard to air waves.

In order that an object may form an acoustic or sound-shadow, it is necessary that the construction shall be large compared with the length of the wave.

Thus the hand held in front of the mouth does not much obstruct the waves of the speaking voice, because these waves are about 2 to 4 feet long. But as you have seen when using sound waves only 1 inch long, the hand will form a very well-marked sound-shadow, as shown by its effect when held between a whistle and a sensitive flame.

In order to complete our proof that the agency which affects our ears as sound is really due to air waves, it is necessary to be able to show that we can produce interference with air waves, as in the case of waves on water. The nature of the effect called interference by which one wave is made to annihilate another has been already fully explained. I will now endeavour to exhibit to you the interference of two sound-wave trains in an experiment due to Lord Rayleigh, the apparatus for which he has kindly lent to me.

It consists, as you see, of a stand, to which is fixed a jet, from which we form a tall sensitive flame. Behind the flame is placed a sheet of glass, which is held vertically, but can be slid towards or from the flame. At a little distance we place a bird-call, or sort of whistle, which produces, when blown with air, a note so shrill as to be inaudible to human ears.

The air-vibrations so generated are at the rate of 33,000 per second, which is beyond the limit of audition. Hence, even when blown strongly, you hear no sound from this appliance.

It produces, however, as you can see, a very violent effect upon the sensitive flame. Hence this flame hears a note which we cannot hear, and it suggests that perhaps some animals or insects may have a range of hearing quite beyond the limits fixed for our human ears.

Such being the case, you will see that if the glass plate is placed behind the flame at a certain distance, the flame at once stops flaring and becomes quiescent. If, however, the plate is moved to or from the flame by a very small distance equal to about the one-twelfth part of an inch, the tall flame at once drops in height and begins to flare. If we move the plate steadily backwards by equal small distances, we find the flame alternately quiescent and waving.

The explanation of this effect is that it is due to the interference between the direct and reflected sound-rays. The waves of air are turned back when they meet the glass in such a manner that the crests of the arriving waves are made to coincide with the hollows of the reflected waves, or, to speak more correctly, the zones of condensation of one are coincident with the places of rarefaction of the other. When the glass is adjusted so that this happens, all air-wave motion just in front of it is destroyed, and hence the sensitive detecting flame remains quiescent. If, however, the glass is moved nearer to or further from the flame, then the condensations of the reflected wave may be made to fall in the same places as the condensations of the arriving wave, and in that case the disturbance is doubled, and not destroyed.

Fig. 52.

A little model may be made which will help the reader to grasp this point. Cut out a piece of paper in the form shown in Fig. 52 to represent a wave. Bend back the paper on itself at the dotted line ab, and let one half represent the arriving wave, and the other the reflecting wave. It will be seen that in this case the crests of the incoming wave are obliterated by the hollows of the returning wave. If, however, the paper is bent back at cd, then the crests of the reflected and incident waves conspire, and there is no interference.

Whenever we can produce interference in this manner between two sets of sound-rays, or light-rays, or rays of any other kind, we have the strongest possible proof that we are concerned with a wave-motion; because in no other way that we can understand is it possible that a destruction of sound by sound can take place by, so to speak, superimposing two sound-rays, or a destruction of light by bringing together two rays of light.

We may, then, conclude our discussion of this part of our subject by examining the manner in which vibrating bodies communicate a different form of wave to the air. As already explained, we are by our ears enabled to appreciate the fact that the air is thrown into a wave-motion, and that this wave-motion may consist of waves of great or small wave-length, and great or small amplitude. But we are able to do something more—we are able to detect a difference between the form of two waves, so that if represented by a wavy line of light, as you have seen, the nature of the outline of that line impresses itself upon our consciousness. Nothing is more remarkable than the extraordinary delicacy of the ear in this respect. Amongst all our scores of friends and acquaintances we recognize each by a quality of voice which we speak of as harsh, melodious, sympathetic, rasping, penetrating, or clear. This is not altogether a matter of enunciation or vocalization, for if different persons pronounce correctly the same vowel-sound, we can detect a great difference between their voices. We have, then, to ask wherein this difference consists when considered with respect simply to what goes on outside of us in the air.

Great light was thrown on this by the invention and perfection of the phonograph and telephone, and also a more recent and wonderful invention, variously called the micro-phonograph or telegraphone. You have all heard a phonograph speak, or sing, or reproduce music. In its original form the Edison phonograph consisted of a cylinder covered with tinfoil, against which pressed lightly a steel point attached to the centre of a metal disc. In its modern form, as improved by Edison, Bell, Tainter, and others, it is a far more perfect instrument for recording and reproducing sound. It now consists of a cylinder covered with a composition similar to very hard soap. This cylinder is carried on a metal drum, and caused to revolve by clockwork slowly and very uniformly. A metal arm carries an elastic metal disc called a receiving diaphragm, and to the back of this is attached a very delicate cutting-tool like a small chisel. By means of a screw the chisel and diaphragm are made to travel along the cylinder, and if no vibration is given to the disc the tool cuts a spiral on the recording cylinder, which is a clean groove with smooth bottom ploughed out of the soft composition. If, however, we speak or sing to the diaphragm, the air waves cause it to vibrate, and this makes the tool cut a furrow, the bottom of which is irregular, the undulations corresponding exactly to the movements of the diaphragm. Thus, if we could look at the section of the furrow, we should see it undulating like a miniature switchback railway, each up-and-down corresponding with one vibration of the diaphragm. In this manner we store up a record of air waves on the hard-soap cylinder. In the next place, to reproduce the sound, another diaphragm with a trumpet mouthpiece has at its back a little pointed lever or set of levers, one extremity resting upon the bottom of the irregular furrow.

Then, if the cylinder is so set that this reproducing diaphragm travels over the record cut by the receiving diaphragm, we have a motion communicated to it which is the exact facsimile of that which produced the furrow. Accordingly, the reproducing diaphragm gives back to the air impulses which reproduce the same wave-trains, and therefore the same speech or song, as that which created the record.

We may in this manner record any human utterance and receive it again, word-perfect, months or years after it was made.[25]

The action of the phonograph leads us to inquire how a disc of metal or other elastic material responds to aerial vibrations which fall upon it, and I shall conclude this lecture by showing you one experiment of a kind to illustrate this point, which, though not very easy to perform, is certainly one of the most attractive that can be shown.

There is on the table a brass tube, of a shape somewhat like a square-shouldered funnel, and over the smaller end is loosely slipped a wide indiarubber tube with a mouthpiece. It is essential that the indiarubber tube shall not fit tightly, but shall be supported so that an air space exists all round between it and the brass funnel tube. The latter may be carried on a wooden stand. The wider end of the funnel must have a diameter of about 2¹⁄₂ inches, and the lip must be quite smooth. The interior of the funnel should be blackened. A soap solution has then to be prepared as for blowing soap-bubbles. A good formula for making this solution is given by Professor Vernon Boys, in his book, “Soap Bubbles and the Forces which mould them,” and is as follows: Fill a clean stoppered bottle three-quarters full of soft water. Add one-fortieth part of its weight of oleate of soda, which will probably float on the water. Leave it until it is dissolved. Then nearly fill up the bottle with Price’s glycerine, and shake well. Leave the bottle stoppered for a week in a dark place. Then syphon off the clear liquid from the scum at the top. Add one or two drops of strong ammonia to every pint of the liquid. Do not warm or filter the liquid, and keep it carefully from exposure to the air. Do not expose the liquid to the air more than necessary; but in blowing a bubble pour out a little of the liquid into a saucer.

In default of this good solution a substitute may be found by dissolving bits of clear yellow soap in soft water; but this soapy water does not yield films which last so long as those made with the Plateau solution above described.

By dipping the wide end of the funnel tube into some of the soap solution placed in a saucer, it is easy to cover the end with a flat soap film which will last a considerable time. This tube has then to be fixed in front of an electric arc or lime-light lantern, so that a powerful parallel beam of light can be directed on to the film by a small flat mirror or looking-glass. A lens is also placed so as to focus an image of the film on to a screen. In finding the right position for the lens, it is a great help to place a piece of white card with some bold black letters upon it over the brass funnel in the place which will be occupied with the soapy film, and to focus this so as to obtain a sharp image of the letters on the screen. When the soap film is then substituted for the card, we should have on the screen a reflection of the film surface, which at first will appear as a patch of white light upon the screen. If we allow the film to stand for a few seconds, it begins to get thinner at the upper part than at the bottom, and the image on the screen will exhibit gorgeous bands of red and green, called interference colours, which are due, like the colours on a soap-bubble, to the interference of the rays of light reflected from the inner and outer surfaces of the film. If the experiment is skilfully performed, the appearance on the screen will then be very beautiful. We shall have a patch of light which exhibits bands of colours, becoming more intense the longer the film stands, and towards the end having somewhat the appearance of an unusually lovely sunset.

Just before this condition of the film is reached, if we sing gently into the mouthpiece of the indiarubber tube, the soap film will be thrown into vibration. The image on the screen will exhibit a set of regularly arranged concentric stationary ripples, which will alter in appearance with every change in the note sung. The experiment requires some care and practice to perform it properly, and should not be attempted in public without many rehearsals; but when well shown it is a most effective and interesting experiment. We see, therefore, that so delicate an object as a stretched soap-film can take up the vibrations of the air and be itself thrown into vibration. The reason is that the soap-film, as already explained in the first lecture, resists stretching, and behaves like a sheet of elastic indiarubber. Hence, as each air wave falls upon it, the film is alternately pushed out and pulled in, but being held at the edges, it can only accommodate itself by stretching. We have, therefore, set up in the film a set of stationary waves similar to those set up on a rope fixed at one end when the loose end is regularly jerked up and down by the hand. The experiment shows us clearly the way in which an elastic disc is set in vibration when compressional waves fall upon it, and in the next lecture we shall proceed to discuss the vibrations of this kind which give rise to musical effects.