Waves and Ripples in Water, Air, and æther

CHAPTER I.. Water Waves and Water Ripples.

WATER WAVES AND WATER RIPPLES.

PAGE

A visit to the seaside—What is a wave?—Wave-motion on water—Definition of a wave—Sea waves—Various forms of wave-motion—Wave length, velocity, and frequency—Atlantic waves—Rules for speed of sea waves—Illustrations of wave-motion—A stone falling on water—Production of a wave-train—Wave-energy—Conditions for the production of wave-motion—Distinction between wave-velocity and wave-train velocity—Why a wave breaks—Waves in canals—Rule for speed of a canal wave—Falling bodies—A “bore”—Tidal waves—Ripples—Distinction between waves and ripples—Surface tension on liquids—A needle floating on water—Experimental production of ripples—Reflection and refraction of ripples and waves—Interference of waves and ripples—Photography of waves and ripples 1

CHAPTER II.. Waves and Ripples Made by Ships.

WAVES AND RIPPLES MADE BY SHIPS.

Ship-waves—The viscosity of liquids—How it is demonstrated—Rotational and irrotational motion in fluids—Eddies and whirls—Smoke rings—Vortex motion—Professor Hele-Shaw’s experiments—Irrotational or stream-line motion in water—The motion of water round a ship—The motion of water along a pipe—Flow in uniform pipes and non-uniform pipes—Relation between fluid velocity and pressure—Skin resistance and wave-making resistance—The movement of a fish—Motion through a perfect fluid—The waves made by moving objects—Waves made by ducks and swans—Echelon waves—Ship bow waves—The form of ship-waves—Mr. Froude’s experiments—Ship-models and experimental tanks—How a ship is designed—Froude’s laws—Testing ship-models—The design of a racing-yacht—Comparison of British and American yachts—The Cup race—Scott Russell’s experiments on canal-boats 57

CHAPTER III.. Waves and Ripples in the Air.

WAVES AND RIPPLES IN THE AIR.

Air necessary for the production of sound—A sounding body is in vibration—Harmonic motion—The difference between noise and music—The nature of an air wave—The physical qualities of air—Longitudinal or compressional waves—Wave-models to illustrate the nature of sound waves—Quality of a sound—Velocity of an air wave—An illustration on a gigantic scale—The voice of a volcano heard round the world—The effect of temperature on air-wave velocity—Comparison of theory and experiment—Circumstances affecting distance at which sounds can be heard—Funeral guns—Fog-signals and sirens—Effect of wind and density—Sensitive flames as sound-detectors—Inaudible sounds—The reflection and refraction of sound waves—A sound-lens and sound-prism—The interference of sounds—Two sounds producing silence—The phonograph—A soap-bubble film set in vibration by air waves 103

CHAPTER IV.. Sound and Music.

SOUND AND MUSIC.

The difference between sounds and musical tones—The natural period of vibration of an elastic body—The effect of accumulated impulses—Free and forced vibrations—Breaking down a bridge with a pea-shooter—The vibration of a stretched string—Stationary waves—A string vibrating in segments—Acoustic resonance—Nodes and anti-nodes—The musical scale or gamut—Musical intervals—The natural gamuts and the scale of equal temperament—Concords and discords—Musical beats—Helmholtz’s theory of discords—Musical instruments—Pipes—Strings and plates—A pan-pipe—An organ-pipe—Open and closed organ-pipes—The distribution of air pressure and velocity in a sounding organ-pipe—Singing flames—Stringed instruments—The violin—The Stroh violin—The structure of the ear—The ear a wonderful air-wave detector and analyzer 147

CHAPTER V.. Electric Oscillations and Electric Waves.

ELECTRIC OSCILLATIONS AND ELECTRIC WAVES.

The conception of an æther—The phenomena of light require the assumption of an æther—The velocity of light—Interference of light—Two rays of light can produce darkness—An electric current—The phenomena of electricity require the assumption of an electro-magnetic medium—Properties and powers of an electric current—Alternating and continuous electric currents—Electromotive force and electric strain—A Leyden jar—The oscillatory discharge of a condenser—Oscillatory sparks—Transformation of electric oscillations—Hertz oscillator—Production of a wave of electric displacement—Detection of electric waves—Metallic filings detectors—The coherer—Inductance and capacity of circuits—Electro-static and electro-magnetic energy—An induction coil—Electric oscillations give rise to electric waves—The electron theory of electricity 185

CHAPTER VI.. Waves and Ripples in the æther.

WAVES AND RIPPLES IN THE ÆTHER.

The experiments of Heinrich Hertz—Electric radiation—Lecture apparatus for producing and detecting electric radiation—Electric transparency and opacity—Why this difference—The reflection of electric radiation—The refraction of electric rays—An electric prism and an electric lens—The electric refractive index—Interference of electric rays—The velocity of electric radiations identical with that of light—Dark heat rays—Actinic or photographic rays—The cause of colour—The frequency of light waves—The classification of electric or æther waves—The gamut of æther waves—The eye an æther-wave detector of limited power—The electro-magnetic theory of light—Artificial production of light—Use of Hertz waves in wireless telegraphy—Marconi’s methods—Marconi’s aerial and wave-detector—The Morse alphabet—How a wireless message is sent—The tuning of wireless stations—Communication between ships and shore—The velocity of wireless waves—Conclusion 232

Appendix 287

INDEX 293

USEFUL MEMORANDA.

One statute mile is 5280 feet. One nautical mile is 6086 feet = 1¹⁄₆ statute mile. A knot is a speed of 1 nautical mile per hour.

Hence the following rules:—

To convert Knots to miles per hour—multiply by 1¹⁄₆. Miles per hour to knots—multiply by ⁶⁄₇. Feet per second to miles per hour—multiply by ²⁄₃. ⁄ Feet per second to knots—multiply by ⁶⁄₁₀. Knots to feet per minute—multiply by 100.

WAVES AND RIPPLES IN WATER, AIR, AND ÆTHER.

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CHAPTER I.. Water Waves and Water Ripples.

WATER WAVES AND WATER RIPPLES.

We have all stood many times by the seashore, watching the waves, crested with white foam, roll in and break upon the rocks or beach. Every one has more than once cast a stone upon still water in a lake or pond, and noticed the expanding rings of ripples; and some have voyaged over stormy seas, whereon great ships are tossed by mighty billows with no more seeming effort than the rocking of a cradle. In all these things we have been spectators of a wave-motion, as it is called, taking place upon a water surface. Perhaps it did not occur to us at the time that the sound of the splash or thunder of these breaking waves was conveyed to our ears as a wave-motion of another sort in the air we breathe, nay, even that the light by which we see these beautiful objects is also a wave-motion of a more recondite description, produced in a medium called the æther, which fills all space.

A progressive study of Nature has shown us that we are surrounded on all sides by wave-motions of various descriptions—waves in water, waves in air, and waves in æther—and that our most precious senses, our eyes and ears, are really wave-detectors of a very special form. The examination of these waves and their properties and powers has led us to see that waves in water, air, and æther, though differing greatly in detail, have much in common; and many things about them that are difficult to understand become more intelligible when we compare these various wave-motions together. In these lectures, therefore, I shall make use of your familiar experiences concerning sea and water waves to assist you to understand some of the properties of air waves to which we owe our sensations of sound and music; and, as far as possible, attempt an explanation of the nature of æther waves, created in the all-pervading æther, to which are due not only light and sight, but also many electrical effects, including such modern wonders as wireless telegraphy. 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.

Fastening our attention for the moment on surface water waves, the first question we shall ask ourselves is—What is a wave? If we take our station on a high cliff looking down on the sea, on some clear day, when the wind is fresh, we see the waves on its surface like green rounded ridges racing forward, and it appears at first sight as if these elevations were themselves moving masses of water. If, however, we look instead at some patch of seaweed, or floating cork, or seagull, as each wave passes over it, we shall notice that this object is merely lifted up and let down again, or, at most, has a small movement to and fro. 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 little more careful scrutiny will show us that, in the case of sea waves in deep water, the motion of the floating object as the wave passes over it is a circular one, that is to say, it is first lifted up, then pushed forward, next let down, and, lastly, pulled back; and so it repeats a round-and-round motion, with the plane of the circle in the direction in which the wave is progressing. This may be illustrated by the diagram in Fig. 1, where the circular dotted lines represent the paths described by corks floating on the sea-surface when waves are travelling over it.

Accordingly, we conclude that we have to distinguish clearly between the actual individual motion of each water particle and that general motion called the wave-motion. We may define the latter by saying that to produce a wave-motion, each separate particle of a medium, be it water, or air, or any other fluid, must execute a movement which is repeated again and again, and the several particles along any line must perform this same motion one after the other, that is, lagging behind each other, and not simultaneously. We might illustrate this performance by supposing a row of fifty boys to stand in a line in a play-ground, and each boy in turn to lift up his arm and let it down again, and to continue to perform this action. If all the boys lifted up their arms together, that would not produce a wave-motion; but if each boy did it one after the other in order, along the rank, it would constitute a wave-motion travelling along the line of boys. In more learned language, we may define a wave-motion by saying that a wave-motion exists in any medium when the separate portions of it along any line execute in order any kind of cyclical or repeated motion, the particles along this line performing the movement one after the other, and with a certain assigned delay between each adjacent particle as regards their stage in the movement.

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