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3: On Waves

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Author Topic: 3: On Waves  (Read 8 times)
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« on: April 10, 2024, 08:08:42 am »

   But that one ripple on the boundless deep
   Feels that the deep is boundless, and itself
   For ever changing form, but evermore
   One with the boundless motion of the deep.
       TENNYSON, The Ancient Sage.

AN immense amount is known about waves, and the mere fact that a medium is able to transmit waves tells us something about its properties. A wave is always the result of an oscillation or vibration; and for an oscillation to be possible two things are necessary,---those two things are the power of recoil and the power of overshooting the mark. The power of recoil is called elasticity; the power of overshooting the mark is called inertia. A bent or coiled-up spring possesses one: any kind of a load or mass possesses the other. Their conjunction may be most easily illustrated by a piece of elastic or a spiral spring, held at the top by a hand or a fixed support, and loaded at the bottom by a weight. When everything is quiet the weight is in a position of equilibrium; and if it is either pulled down or raised up a little and let go, it will dance up and down. Let us analyse that motion. It tends to return to its original position when let go, by reason of the recoil or elasticity of the spring, but it will not simply return and stay there; it will overshoot that position, and only recover it after several oscillations. The recoil or recovery is due to elasticity, the overshooting is due to inertia. If the load is a massive one, the oscillations are slow: if the spring is a stiff one, the oscillations are quick. The rate of oscillation depends simply and entirely on the ratio of the elasticity to the inertia.

If a string is tightly stretched and then plucked, the stretching of the string confers elasticity on it, and makes it recoil back to its old position; but the string has a certain momentum, and accordingly it overshoots that position and vibrates, giving a musical note if the vibrations are rapid enough. Stretch the string tighter, the note rises in pitch: elasticity is increased. Load the string, or otherwise make it more massive, the rapidity of vibration or pitch is lowered. It will be found that if the tension of the string is increased four-fold, the pitch rises an octave; that is the rate of vibration is doubled. Conversely, if the load is increased four-fold, the pitch falls an octave; the rate of vibration is halved. This is expressed by saying that the rate of vibration depends on the square root of the ratio of elasticity to inertia. In a continuous medium the inertia of any given volume is called its density: it is also sometimes called specific gravity. Mercury is thirteen times as dense as water: water is 800 times as dense as ordinary air: lead is denser, that is heavier bulk for bulk, than iron: iron is denser than aluminium: the densest substances known are platinum and gold, twenty times as heavy or massive as an equal bulk of water. The lightest gas known is hydrogen; air is about fourteen times as dense as hydrogen. All these things are familiar; but I remind you of them, because they are one of the causes that regulate the rate of propagation of waves through these different substances.

The other property is elasticity and in a gas that is equal to the pressure, it measures the incompressibility of the substance. The incompressibility of water is much greater than that of air, thousands of times greater: this more than compensates for the extra density, and accordingly sound waves travel in water four times as quickly as in air. But in the Ether, waves travel a million times as quickly: hence the ratio of elasticity to density in the Ether must be enormous. The important thing at present is to realise that the fact that the Ether can transmit waves tells us something about its properties, tells us that it must possess something akin to elasticity, giving it a power of recoil, and something akin to density or inertia, giving it momentum. We must not suppose that these properties are due to the same cause as those of matter, but they must have some analogy. The possession of those properties makes the Ether very real: and the fact that it can transmit waves at a definite and ascertained speed tells us already a good deal about it, and shows that it is a real substance, whose properties we mainly study under the heads Electricity and Magnetism.

Varieties of Elasticity
Elasticity may be possessed by a substance for various reasons. Gases and liquids shew it by their resistance to compression, i.e. their incompressibility,---a term which does not mean that they are incompressible, but that their incompressibility can be measured and specified; the incompressibility can have a figure attached to it, can be expressed numerically in terms of proper units. A solid has other kinds of elasticity; it can be bent, it can be twisted; and in both cases it will recoil or recover from the strain, unless it is inelastic, like clay or putty, which are not able to transmit waves.

Waves then are of various kinds: sound waves are the simplest. The best known waves are those on the surface of the sea. The surface of water is naturally level; but if you lay a board on the top of a lake, say a wooden disk a foot in diameter, and then either lift it or push it down and let it go, it will oscillate: waves will be generated, and will spread out from the oscillating centre of disturbance, in accordance with its rate of oscillation. However the surface of water is deformed, it will tend to recover: it therefore possesses the power of recoil, a power which in this case is due to gravity. It also possesses inertia, so that a hump let go becomes a depression, and then a smaller hump again, and then another depression, and so on alternately, until the disturbance is wiped out by the waves it has generated, or by friction, or both.

A great deal is known about water waves, but that must suffice for the present purpose; they are only mentioned to show that elasticity may have various causes: the only thing essential is power of recoil or recovery. The recovery of a bent spring is one thing; it is this which drives our watches, and which gives the musical note in a harmonium or concertina (where the spring is called a reed); and this elasticity may be called its stiffness. The recovery of a stretched harp or violin string is another thing; it is due to the stretching force, and is commonly called its tension. The recovery of a raised weight is another thing; it is this which drives many of our clocks, and it is this which enables waves to travel along the sea. The recovery of compressed air or gases is another thing; it can be used to drive engines; it is this which enables waves of sound to travel.

The recovery of the Ether is another thing, and we do not fully know to what it is due. All we know about it is that it is not mechanical like the other things: Clerk Maxwell taught us that it was electrical, that it is the same property as we use when we charge a Leyden jar. We have no means of getting hold of the Ether mechanically: we cannot grip it or move it in the ordinary way: we can only get at it electrically. We are straining the Ether when we charge a body with electricity: it tries to recover, it has the power of recoil: if we charge it enough, it will, so to speak, snap its moorings, smash the insulating air, and give a spark. But like all the other things, it will not settle down into equilibrium instantaneously: the rushing electric current has momentum and overshoots the mark: so the body which had been positive becomes negative, and then positive again,---after the same fashion as the surface of water rises and falls alternately for a time; or as a thin steel bar clamped by one end in a vice, if the other end is pulled to the right and then let go, will oscillate over to the left and back again, several times.

That is how we start the wireless waves, or at least that is the simplest way. You charge an aerial till it overflows or sparks to earth; oscillations instantly begin; the aerial charges itself negatively and then positively again. The power of recoil depends on the properties of electric charge: the elasticity of the Ether is thus displayed. It is not matter which is strained when you charge a body electrically, it is Ether. It is really the Ether again which is strained when you bend a spring. Particles of matter are moved or changed only in relative position: it is always the connecting or cementing substance which is strained.

But what about the second property? Elasticity alone is not sufficient, an electric discharge must have momentum also: it must be able to overshoot the mark, else it cannot oscillate. In all the other cases we have been speaking of, this second power is due to inertia, massiveness, the fundamental property of matter. Ether is not any form of matter, as we know it: it seems strange that it should have an analogous property, a power of persistence, a power of obeying the First Law of Motion, that is of continuing to move until it is stopped, the power of overshooting the mark and going on even against an opposition force until that force is able to check it and throw it back again. Whether strange or not, the Ether does possess this property, a property quite distinct from that of electric charge, a property distinct from anything that can be called elasticity, a property analogous to density or inertia. This property was studied long before its function in connexion with waves was known, that is long before the time of Clerk Maxwell; and it is commonly spoken of as Magnetism,---magnetism is the fundamental property of an electric current as distinct from an electric charge.

The Ether has two properties, an electric property and a magnetic property, the one corresponding to elasticity and the other to density. What either of them is due to, we do not fully know, we are trying to ascertain; but there they are, those two properties, and it is owing to their interaction that Ether waves exist: without them there would be no light, and of course there would be no radio telegraphy. You can excite one without the other, but for waves you must have both. A charged body emits no waves, a magnet emits no waves; but you can only discharge a body by means of a current, that is to say, the act of discharge is a current. Magnetism is then evoked; the second property makes itself manifest, oscillations occur, and waves spread out in all directions.

The pace at which waves travel depends on the ratio of elasticity to density, that is on the ratio of the electric property to the magnetic property of the Ether. We cannot specify these properties more completely in words: we have to use symbols,---symbols enable us to work out things we do not fully understand. When we fully understand a thing, we can express it in words: that time is not yet; and that constitutes one of the difficulties of the subject.

But it is really a difficulty which surrounds all subjects: we know nothing completely, and even our words are only symbols, though they are symbols we have got accustomed to; it may be doubted if they are really simpler or more expressive than algebraic symbols. Language is inadequate for dealing with the processes of nature in a complete and entirely satisfactory manner. We understand a certain amount, and try to express that; but we are aware of a mass of ignorance beyond. We know enough for practical purposes about matter and elasticity and inertia and other properties, but we do not know these things completely: so also we know enough for practical purposes about electricity and magnetism, but we do not know them completely: we realise that there is much more to be known. So it is about everything really, though in some cases to all appearance our knowledge is greater than our ignorance: the truth of that however is very doubtful.

We have grown accustomed to the properties of matter, and to gravitation and the like, and so we delude ourselves into thinking that we understand them: we really understand less about them than we do about electricity and magnetism; these properties of the Ether are more fundamental than any of the properties of matter. We used to try to explain the properties of the ether in terms of matter: Lord Kelvin made a life-long effort in that direction, and at the end of his life he announced failure. The failure was due to no defect of his; such an explanation is impossible, Ether is not to be explained in terms of matter. We have learnt that the problem lies in the opposite direction; and modern Physics, since Lord Kelvin's time, may be said to be devoting itself to the explanation of matter in terms of Ether.

The two phenomena with which the human race has only comparatively recently become acquainted, the phenomena of electricity and of magnetism, are the fundamental things. Matter itself is an electrical phenomenon, just as light is: not electrical only, but magnetic also,---electromagnetic, as it is called. Light is electromagnetic; so is matter. Gravitation is an etherial phenomenon, we cannot say definitely that it is electromagnetic.

Those two properties of the Ether are known, but it may have others,---must have others, one would think. Gravitation may be a finger-post to some of the others: cohesion however is probably electromagnetic; and nearly all of the properties of matter will ultimately be expressible in those terms. Great strides already have been made in that direction: they seem to lead into an impenetrable thicket: we are not yet out in the open, it is hard going, and there is much to clear away. We had thought that the way towards the light must lie in the open country of ordinary mechanics; we are now plunging into the wood to seek a new way, changing our direction altogether; but flashes of illumination have been caught through the branches, which have heartened the younger generations of Physicists with a great enthusiasm. Obstacles are plenty, but they will not be deterred; they have caught glimpses of the light beyond: it may be long before they have made a path by which others can follow, it may be some time before they make a path for themselves: some may be lost in the under-wood, and there will be confusion and controversy for a time. But those who have insight and intuition know that here, through this strangely unpromising country, lies the road to Reality.

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