Wave propagation

“ If the medium be crystalline the velocity of propagation of plane waves will depend also on the aspect of the wave-front. For any given direction of the wave-normal there are in the most general case three distinct velocities of wave-propagation, each with its own direction of particle-vibration. ”

“ To understand wave propagation, you must have at least a basic understanding of the earth's atmosphere. The earth's atmosphere is divided into three separate regions, or layers. They are the troposphere, the stratosphere, and the ionosphere. ”

“ Wind, air temperature, and water content of the atmosphere can combine either to extend radio communications or to greatly attenuate wave propagation. making normal communications extremely difficult. Precipitation in the atmosphere has its greatest effect on the higher frequency ranges. ”

“ In free space æther waves of various wave-lengths all travel, as far as we know, at the same rate. This [256] equality in speed is, however, disturbed the moment the waves enter a transparent material substance such as glass. The velocity of propagation is then reduced in all cases, but it is generally more reduced for the shorter waves than for the longer ones; and as a consequence the rays of shorter-wave lengths are more bent or refracted than the rays of longer wave-length. ”

“ Observe a sea-fowl, or, if you are a swimmer, abandon yourself to the action of the waves; you are not carried forward, but simply rocked up and down. The propagation of a wave is the propagation of a form, and not the transference of the substance which constitutes the wave.
The length of the wave is the distance from crest to crest, while the distance through which the individual particles oscillate is called the amplitude of the oscillation. You will notice that in this description the particles of water are made to vibrate across the line of propagation. ”

“ Thus in the wave method the actual motion of the string is considered as the resultant of two wave motions, neither of which is of itself, and without the other, consistent with the condition that the ends of the string are fixed. Each of the wave motions is periodic with a wave-length equal to twice the distance between the fixed points, and the one set of waves is the reverse of the other in respect of displacement and velocity and direction of propagation ”

“ The longer waves travel faster than the shorter, so that each wave is continually being drawn out in length, and its velocity of propagation therefore continually increases as it advances. If we fix our attention on a particular point of the surface, the level there will rise and fall with increasing rapidity and increasing amplitude. ”

“ At each oscillation some energy is frittered away into heat in the conductor, and if the conductor and condenser have a special form, energy may be rapidly removed from the system by the electric waves which are formed in the surrounding æther or dielectric. These waves consist in the propagation through the medium of lines of electric strain, just as an air wave consists in the propagation through the air of regions of air-compression, or a water wave consists in the propagation of an elevation on the surface. ”

“ REFLECTED WAVE— (1) The wave that reflects back from a medium; (2) Waves traveling from the load back to the generator on a transmission line; (3) The wave moving back to the sending end of a transmission line after reflection has occurred.
REFLECTION WAVES—Waves that are neither transmitted nor absorbed, but are reflected from the surface of the medium they encounter.
REFLECTOR—The parasitic element of an array that causes maximum energy radiation in a direction toward the driven element. ”

“ Now if the elastic constants of the media are such that the velocities of propagation of the longitudinal waves are of the same order of magnitude as those of the transverse waves, the direction-cosines of the longitudinal reflected and refracted rays will in general have real values, and these rays will carry away some of the energy which is brought to the interface by the incident wave. ”

“ Each oscillation in the transmitting aerial is accompanied by the detachment from it of semi-loops of electric strain, as already explained. The alterations of electric strain directed perpendicularly to the earth, and of the associated magnetic force parallel to the earth, constitute an electric wave in the ether, just as the alternations of pressure and motion of air molecules constitute an air wave. Associated with these physical actions above ground, there is a propagation through the earth of electric action, which may consist in a motion or atomic exchange of electrons. ”

“ We have already explained that, in a medium such as air, a wave of compression is propagated at a speed which is measured by the square root of the quotient of the air-pressure, or elasticity, by its density. In exactly the same way the hump that is formed on a rope by giving one end of it a jerk, runs along at a speed which is measured by the square root of the quotient of the stretching force, or tension, by the density. The propagation of a pulse or wave along a string is most easily shown for lecture purposes by filling a long indiarubber tube with sand, and then hanging it up by one end. ”

“ When the waves leave the generating area and continue as free waves, the wavelength and period continue to increase, while the height decreases. The rate of change gradually decreases. The speed (S) of a free wave in deep water is nearly independent of its height or steepness. ”

“ 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. ”

“ If two infinitely long sets of deep-sea waves, having slightly different wave-lengths, and therefore slightly different velocities, are superimposed, we obtain a resultant wave-train which exhibits a variation in wave-amplitude along its course periodically. ”

“ It has already been shown that when a single wave-disturbance is made upon water it gradually develops itself into a group of waves. The single wave when created causes a disturbance on water which extends both forwards and backwards. As the wave moves forward the wave-disturbance is always growing in front and dying away behind, and the wave-group therefore moves forward, but the centre or limits of the group move with only half the velocity of a single wave. ”

“ The sea-surface acts somewhat like an optical reflector or mirror, and the electric waves glide along its surface. The rotundity of the earth within certain limits hardly makes any perceptible effect upon the ease of communication. The waves sent out by the transmitter of a long-distance wireless station are from 3000 to 20,000 feet in length, and there is, therefore, a considerable amount of bending or diffraction. It is a familiar fact, as already explained, that a wave-motion, whether on water or in air, spreads round an obstacle to a certain extent. ”

“ We are led, therefore, to infer that, even when agitated by waves, each particle of water never moves far from its position when at rest, and that the real movement of the water is something very different from its apparent motion. If we place on the surface of water a number of corks or pieces of paper, and then watch them as a wave passes over them, we shall notice that the corks or bits of paper rise and fall successively, that is, one after the other, and not all together. ”

“ A good conception of the relative speeds of water waves, air waves, and æther waves can be gained by considering the time each of these would take to cross the Atlantic Ocean, travelling in its own medium. Suppose we could, at the same moment, create a splash in the sea near England sufficiently great to cause a wave which would travel over the surface of the Atlantic at the speed of many ocean waves, say at 30 miles an hour. ”

“ 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. ”

“ 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. ”

“ In all departments of natural science we find ourselves confronted by the phenomena of wave-motion. In the study of earthquakes and tides, telegraphs and telephones, as well as terrestrial temperature, no less than in the examination of water waves and ripples, sound, music, or light and heat, we are bound to consider waves of some particular kind. ”

“ Consequently, internal waves are much more easily formed than surface waves, and they are often much larger. The maximum height of wind waves on the surface is about 60 feet, but internal wave heights as great as 300 feet have been encountered. ”

“ They radiate from the aerial like the ripples from a pebble in a pool of water, in gradually enlarging circles. If a cross section of the aerial and atmosphere could be made in the same manner that an apple can be sliced with a knife, and the waves held stationary long enough to see them, they would appear as in Fig. 8. The curved lines represent the lines of strain induced by the oscillations. Each group of lines represents a wave. It will be noticed as they radiate farther from the aerial that they become larger and spread out. ”

“ The physical effect we call light, and that which we have up to the present moment merely called electric radiation, are really identical in nature, and both consist in waves propagated through the space-filling æther, the only difference between them is in wave-length and wave-amplitude. ”

“ The creation of the waves will bring it to rest in time, unless it is continually urged forward by some external and impressed force, and wave-generation is a reason for a part at least of the resistance we experience when we attempt to push it along. ”

“ In those places at which the pressure variation is greatest, the velocity changes are least, and vice versa. Outside the tube, as a result of these air motions in it, we have a hemispherical air wave produced, which travels out from the mouthpiece as a centre; and if we could examine the distribution of air pressure and velocity through all external space, we should find a distribution which is periodic in space as well as time, constituting the familiar phenomenon of an air wave. ”

“ An air-wave is made up of a compression and a rarefaction—a push and a stretch—the two being produced in one vibration of the prong, the compression by the motion from a to a', and the rarefaction by the reactive motion from a to a". On its way back to a, the prong lets up on the stretch, and goes on to a' with another push, and so on as long as it vibrates. These compressions and rarefactions, represented in the figure by its shadows and lights, correspond to the crests and hollows of water-waves. ”

“ If light is a substance, no possible explanation can be given which will enable us to account for the combination of two rays of light producing darkness at their meeting-point. If, on the other hand, rays of light consist of waves of some kind in a medium, then, as we have seen in the case of water ripples and air waves, it is quite possible for two wave-trains to annihilate each other’s effect at a certain point, if a hollow of one wave-train reaches [191] that place coincidently with a hump belonging to the other. ”

“ Since the incoming wave affects water which is at the same time under the influence of the undertow, it gives to that current a pulsating character, for the wave-motion sometimes supports and sometimes opposes the undertow, and thus endows it with a higher transporting power than belongs to its mean velocity. ”

“ We know how, as the circles widen, the height of the wave grows less and less, until, at no great distance from the centre of disturbance, the wave can no longer be discerned, so slight is the slope of its advancing and following faces. How tremendous, then, must have been the upheaval of the bed of ocean by which wave-circles were sent across the Pacific, retaining, after travelling 5000 miles from the centre of disturbance, the height of a two-storied house! ”

“ In calculating the velocity of a system of plane waves of homogeneous light, regarded as oscillating electrical fluxes, in transparent and sensibly homogeneous bodies, whether singly or doubly refracting, we may assume that such a body is a very fine-grained structure, so that it can be divided into parts having their dimensions very small in comparison with the wave-length, each of which may be regarded as entirely similar to every other, while in the interior of each there are wide differences in electrical as in other physical properties. ”

“ If the steepness gets very great our investigation ceases to apply, and neither experiment nor theory has yet shown what happens. Probably there is a breakdown of the wave somewhat like the breaking of a water-wave when the, crest gains on the next trough. In ordinary sound-waves the effect of the particle velocity in affecting the velocity of transmission must be very small. ”