Waves and ripples in water, air, and æther

by Sir J. A. Fleming

In addition to various material substances we find that we have to recognize different forms of something called Energy, associated with Matter. Thus an iron ball may be more or less hot, more or less electrified or magnetized, or moving with more or less speed. The production of these states of heat, electrification, magnetization, or movement, involves the transfer to the iron of Energy, and they are themselves forms of Energy. This Energy in all its various forms can be evaluated or measured in terms of Energy of movement. Thus the Energy required to heat a ball of iron weighing one imperial pound from a temperature of the melting point of ice to that of boiling water, is nearly equal to the Energy required to impart to it a speed of 1000 feet a second.

In the same way, every definite state of electrification or magnetization can be expressed in its mechanical equivalent, as it is called. Moreover, it is found that we can never create any amount of heat or mechanical motion or other form of energy without putting out of existence an equivalent of energy in some other form. We are therefore compelled to consider that Energy stands on the same footing as Matter in regard to our inability to create or destroy it, and its constancy in total amount, as far as we can ascertain, gives it the same character of permanence. The difference, however, is that we cannot, so to speak, ear-mark any given quantity of energy and follow it through all its transformations in the same manner in which we can mark and identify a certain portion of Matter. The moment, however, that we pass beyond these merely quantitative ideas and proceed to ask further questions about the nature of Energy and Matter, we find ourselves in the presence of inscrutable mysteries. We are not able as yet to analyze into anything simpler this “something” we call Energy which presents itself in the guise of heat or light, electricity or magnetism, movement or chemical action. It is protean in form, intangible, yet measurable in magnitude, and all its changes are by definite equivalent amount and value. There is a most rigid system of book-keeping in the transactions of the physical universe. You may have anything you like in the way of Energy served out to you, but the amount of it is debited to your account immediately, and the bill has to be discharged by paying an equivalent in some other form of Energy before you can remove the goods from the counter.

Matter in its various forms serves as the vehicle of Energy. We have no experience of Energy apart from Matter of some kind, nor of Matter altogether devoid of Energy. We do not even know whether these two things can exist separately, and we can give no definition of the one which does not in some way presuppose the existence of the other. Returning, then, to the subject of waves, we may say that a true wave can only exist when Energy is capable of being associated with a medium in two forms, and the wave is a means by which that Energy is transferred from place to place.

It has already been explained that a true wave can only be created in a medium which elastically resists some kind of deformation, and persists in motion in virtue of inertia. When any material possesses such a quality of resistance to some kind of strain or deformation of such a character that the deformation disappears when the force creating it is withdrawn, it is called an elastic material. This elasticity may arise from various causes. Thus air resists being compressed, and if the compressing force is removed the air expands again. It possesses so-called elasticity of bulk. In the case of water having a free surface there is, as we have seen, a resistance to any change of level in the surface. This may be called an elasticity of surface form. Whenever an elastic material is strained or deformed, energy has to be expended on it to create the deformation. Thus to wind up a watch-spring, stretch a piece of indiarubber, compress some air, or bend a bow, requires an energy expenditure.

As long as the material is kept strained, it is said to have potential energy associated with it. This term is not a very expressive one, and it would be better to call it Energy of strain, or deformation. If, however, we relax the bent bow or release the compressed air, the Energy of Strain disappears, and we have it replaced by Energy of Motion. The arrow which flies from a bow carries with it, as energy of motion, some part of the energy of strain associated with the bent bow.

A little examination of wave-motion shows us, therefore, that we always have at any instant associated with the material in which the wave is being propagated, both Energy of Strain and Energy of Motion. It can be shown that in a true wave of permanent type, the whole energy at any one moment is half energy of strain and half energy of motion, or, as it is called, half potential and half kinetic.

Thus if we consider a wave being propagated along a line of balls elastically connected, at any one moment some of the balls are moving with their greatest velocity, and some are at the extremity of their swing. The former have energy of motion, and the latter energy of strain.

Or, look at a train of sea waves. Some parts of the water are at any moment lifted high above the average level of the sea, or are much below it, but are otherwise nearly at rest. These portions possess what is called potential energy, or energy of position. Other parts of the water are at the average level of the sea, but are moving with considerable velocity, and these portions possess energy of motion. Every other part of the wave has in some degree both energy of motion and energy of position, and it can be shown that the energy of the whole wave is half of one kind and half of the other.

As a wave progresses over the surface, wave-energy is continually being imparted to portions of the water in front, and it is transferred away from others in the rear. In the very act of setting a fresh particle of water in oscillation, the portions already vibrating must diminish their own motion. They may hand on the whole of their energy or only a part of it to their neighbours. This distinction is a very important one, and it determines whether a single act of disturbance shall create a solitary wave or wave-train in a medium.