Waves Sentence Examples

The waves had pulled her under before darkness took her.

The moon was non-existent, and the waves sparkled in starlight.

Jenn cried out, her body bucking from waves of agony.

He has spoken to me in whispers, in the dark of the night, how waves of guilt over our relationship are with him every waking moment, and yet he loves me so as to risk all for my embrace.

He'd managed to miss the hurricane, though the waters were still rough and the waves high.

The other rider doffed her helmet, spilling waves of blond hair.

Rhyn rested back on the boulder and closed his eyes to the rhythmic sounds of waves and Gabriel trying to kill the practice dummy.

A breeze picked up at the shoreline, wrinkling the water as the waves slowly rolled toward him in silver lines.

They quickly melted into the heat waves again.

It was so close to the sea that those who lived in it could hear the waves forever beating against the shore.

The waves seemed to be playing a game with me, and tossed me from one to another in their wild frolic.

She was closer to the top than to the waves, but the cliff had too few hand and footholds for her to try to climb.

Waves of wind-driven rain pummeled the terminal with a fury.

The gully shimmered in heat waves.

The sound of the ocean was calming under the full moon, the steady ebb and flow of waves drawing him to sit on the beach.

The sound of waves rushing the shore and the firm sand beneath his feet indicated its location a few yards from them.

On her walks at Lover's Lane near Evelyn's row house, she'd often seen couples entranced by the rhythmic movement of waves stand at a railing, the man's arms wrapped around the woman in front of him, his chin on her head.

She baited the hook and threw it in the pond, watching as tiny waves rippled out from the bobber and gently lapped at the grassy shore.

The shores are covered with coral; earthquakes and tidal waves are frequent, the latter not taking the form of bores, but of a sudden steady rise and equally sudden fall in the level of the sea; the climate is rather tropical than temperate, but sickness is almost unknown among the residents.

The difficulty of connecting lightships and isolated lighthouses to the mainland by submarine cables, owing to the destructive action of the tides and waves on rocky coasts on the wll- shore ends, led many inventors to look for a way out of the difficulty by the adoption of some form of inductive Smith.

Owing to the rough seas sweeping over the Fastnet, the conditions are such that any ordinary submarine cable would be broken by the wearing action of the waves at the rock boundary in a very short time.

Such a sequence of decreasing electric oscillations and corresponding set of waves is called a damped train.

The process of reflection in the case of a wave motion involves the condition that the wave-length shall be small compared with the dimensions of the mirror, and hence the attempt to reflect and converge electric waves loon ft.

Enhanced waves in these regions could play a major role in electron acceleration to relativistic energies during periods of prolonged substorm activity.

He also made 100 by running a silent auction with his wonderful image of the two dolphins in the waves.

We saw towering tabular bergs around the ship being battered by the waves.

After I had learned a great many interesting things about the life and habits of the children of the sea--how in the midst of dashing waves the little polyps build the beautiful coral isles of the Pacific, and the foraminifera have made the chalk-hills of many a land--my teacher read me "The Chambered Nautilus," and showed me that the shell-building process of the mollusks is symbolical of the development of the mind.

I thrust out my hands to grasp some support, I clutched at the water and at the seaweed which the waves tossed in my face.

I had the same feeling once before when I first stood by the great ocean and felt its waves beating against the shore.

These small waves raised by the evening wind are as remote from storm as the smooth reflecting surface.

At length the wind rose, the mist increased, and the waves began to run, and the perch leaped much higher than before, half out of water, a hundred black points, three inches long, at once above the surface.

Moreover, the waves, I suspect, do not so much construct as wear down a material which has already acquired consistency.

Historic figures were not borne by the waves from one shore to another as before.

In whatever direction a ship moves, the flow of the waves it cuts will always be noticeable ahead of it.

The riders were a blur in the heat waves, but she was sure one was Pete.

Could the fact that Howie's brain waves are somehow different after his lengthy coma and all the operations he endured be effected by what you were doing?

Bianca took one cautious step onto the frozen waves.

She climbed frozen hills of waves through the raindrops, surprised when they popped like tiny water balloons.

Bianca moved away from Talon towards the violent waves and then sat with her back to a wave as high as her waist.

He took in the various scenes, to include the local news, which blasted photos of the black skies and mounting waves of the tropical-storm-turned-hurricane.

Dean pulled down the top on his Jeep and slowly drove uptown, giving off what he hoped were candidate smiles and waves to the locals, all of whom seemed to be walking the sun drenched street.

Gabriel sat in silent thought, comforted by the ebb and flow of the waves.

Fortunately, the curls were now loose waves.

Some of the gems had been carried by gentle waves to the edges of the lake and deposited away from the bulk of the jewels.

She followed, startled, only to see a massive black bird the size of a pterodactyl coasting along the tops of the waves.

She appeared to be in her early thirties, had chestnut brown hair that fell in soft waves around her shoulders with thin streaks of what looked like fire running through it.

The house looked so far away as it shimmered in heat waves.

Aside from the infrequent sound of a passing car on the avenue, only the murmur of unseen waves lapping at the sand broke the stillness.

The weather remained ominous with dark clouds rolling in, pushed by an ever-increasing wind that churned the sky in threatening waves.

There in the blur of a passing auto and mirrored in descending waves of rain was the huddled figure of Cynthia Byrne stumbling across the parking lot toward the road and the beach beyond.

The fragrant ocean breeze was chilly as it brushed his skin, and his movements fell into the rhythm of the ebb and flow of waves.

The third line gives the range of the regular diurnal inequality, the next four lines the amplitudes of the first four Fourier waves into which the regular diurnal inequality has been analysed.

Beginning with the Aptian and Albian the sea again gradually spread over the country and attained its maximum in the early part of the Senonian epoch, when once more the ancient massifs of the Central Plateau, Brittany and the Ardennes, alone rose above the waves.

Nothing is known about the relative importance of these two waves.

Its most extreme point is called Buddon Ness, off which are the dangerous shoals locally known as the Roaring Lion, in consequence of the deep boom of the waves.

The general principle on which the instruments for working long submarine cables are based is that of making the moving parts very light and perfectly free to follow the comparatively slow rise and fall of the electric impulses or waves.

All these older methods have, however, been thrown into the background and rendered antiquated by inventions which have grown out of Hertz's scientific investigations on the production of electric waves.

The peculiar action of electric sparks and waves in reducing the resistance of discontinuous conductors was rediscovered and investigated by Calzecchi Onesti,' by Branly, 2 Dawson Turner, 3 Minchin, Lodge, 4 and many others.

Lodge particularly studied the action of electric waves in reducing the resistance of the contact between two metallic surfaces such as a plate and a point, or two balls, and named the device a coherer."

The object which Marconi had in view was not merely the detection of electric waves, but their utilization in practical wireless telegraphy.

Marconi, however, made the important discovery that if his sensitive tube or coherer had one terminal attached to a metal plate lying on the earth, or buried in it, and the other to an insulated plate elevated at a height above the ground, it could detect the presence of very feeble electric waves of a certain kind originating at a great distance.

The magnetic and electric forces are directed alternately in one direction and the other, and at distances which are called multiples of a wave length the force is in the same direction at the same time, but in the case of damped waves h.as not quite the same intensity.

These trains are produced by pressing the key in the primary circuit of the induction coil for a longer or shorter time' and generating a long or short series of oscillatory electric sparks between the spark balls with a corresponding creation of trains of electric waves.

It was also recognized that what is required at the transmitting end is the establishment of powerful electric oscillations in the sending antenna, which create and radiate their energy in the form of electric waves having their magnetic force component parallel to the earth's surface and their electric component perpendicular to it.

These communicate their energy to the surrounding air, and this energy is conveyed away in the form of air waves.

In one of these ways the oscillations can be created or stopped at pleasure in the radiating antenna, and hence groups of electric waves thrown off at will.

In the case of transmitters constructed as above described, in which the effective agent in producing the electric waves radiated is the sudden discharge of a condenser, it should be noticed that what is really sent out is a train of damped or decadent electric waves.

If, however, the antenna is inductively or directly coupled to a condenser circuit of large capacity then the amount of energy which can be stored up before discharge takes place is very much greater, and hence can be drawn upon to create prolonged or slightly damped trains of waves.

Allusion is made below to recent work on the production of undamped trains of electric waves.

The electric waves coming through space from the sending station strike against the receiving antenna and set up in it high frequency alternating electromotive forces.

It was then found that when electric waves fell on the antenna a sound was heard in the telephone as each wave train passed over it, so that if the wave trains endured for a longer or shorter time the sound in the telephone was of corresponding duration.

When electric waves fell on the antenna they caused the mercury-steel junction to become conductive during the time they endured, and the siphon recorder therefore to write signals consisting of short or long deflexions of its pen and therefore notches of various length on the ink line drawn on the strip of telegraphic tape.

Rutherford examined it very carefully, and produced a magnetic detector for electric waves depending upon the power of electric oscillations in a coil to demagnetize a saturated bundle of steel wires placed in it.

Fleming, " A Note on a Form of Magnetic Detector for Hertzian Waves adapted for Quantitative Work," Proc. Roy.

If, however, one electrode of this cell is connected to the earth and the other to a receiving antenna and electric waves allowed to fall on the antenna, the oscillations passing through the electrolytic cell will remove the polarization and L temporarily decrease the resistance of the cell.

It was found that to achieve this result the transmitter must be so constructed as to send out prolonged trains of slightly damped waves.

When oscillations are excited in this last circuit they communicate them to the antenna provided this last circuit is tuned or syntonized to the closed circuit, and the radiating antenna has thus a large store of energy to draw upon and can therefore radiate prolonged trains of electric waves.

When this is done we have a syntonic system which is not easily affected by electric waves of other than the right period or approximating thereto.

Lodge was, however, fully aware that it was necessary for syntonic telegraphy to provide a radiator capable of emitting sustained trains of waves.

Marconi's success in bridging the English Channel at Easter in 1899 with electric waves and establishing practical wireless telegraphy between ships and the shore by this means drew public attention to the value of the new means of communication.

All of them couple the transmitting antenna directly or inductively to a capacity-inductive circuit serving as a storage of energy, and all of them create thereby electric waves of the same type moving over the earth's surface with the magnetic force of the wave parallel to it.

In January 1901 he telegraphed without difficulty by electric waves from the Isle of Wight to the Lizard, viz.

This transmitting plant was completed in December 1901, and Marconi then crossed the Atlantic to Newfoundland and began to make experiments to ascertain if he could detect the waves emitted by it.

He operated with electric waves two or three feet in wave-length.

Even if the proposal had been practicable with waves 1000 or 2000 ft.

He showed that if an antenna were constructed with a short part of its length vertical and the greater part horizontal, the lower end of the vertical part being earthed, and if oscillations were created in it, electric waves were sent out most powerfully in the plane of the antenna and in the direction opposite to that in which the free end pointed.

Thus, for instance, when using an induction coil or transformer to charge a condenser, it is not generally convenient to make more than 50 discharges per second, but each of these may create a train of oscillations consisting of, say, 20 to 50 waves.

Supposing, then, that these waves are moo ft.

Poulsen's method of producing continuous or undamped electrical waves has been applied by him in radio-telegraphy.

To send signals the continuous or nearly continuous train of waves must be cut up into Morse signals by a key, and these are then heard as audible signals in the telephone.

The velocity of propagation of electric waves is the same as that of light, viz., about moo million feet, or 300 million metres, per second.

Starting from an observation of Marconi's, a number of interesting facts have been accumulated on the absorbing effect of sunlight on the propagation of long Hertzian waves through space, and on the disturbing effects of atmospheric electricity as well as upon the influence of earth curvature and obstacles of various kinds interposed in the line between the sending and transmitting stations.4 Electric wave telegraphy has revolutionized our means of communication from place to place on the surface of the earth, making it possible to communicate instantly and certainly between places separated by several thousand miles, whilst The Electrician, 1904, 5 2, p. 407, or German Pat.

The banner of the church waves above the camp of those who aim at positive prosperity and republican equality.

Pieces of amber torn from the sea-floor are cast up by the waves, and collected at ebb-tide.

On the 16th of March 1889 the heavy tidal waves created havoc in the harbour of Apia.

As the waves of the sea are fancifully compared to horses, so a field of corn, waving in the breeze, may be said to represent the wedding of the sea-god and the corn-goddess.

The political changes involved in the Babylonian, Assyrian, Egyptian or Persian conquests surely affected it as little as the subsequent waves of Greek, Roman and other European invasions.

In the restoration of the outlines of ancient and medieval geography in Asia Sven Hedin's discoveries of the actual remains of cities which have long been buried under the advancing waves of sand in the Takla Makan desert, cities which flourished in the comparatively recent period of Buddhist ascendancy in High Asia, is of the very highest interest, filling up a blank in the identification of sites mentioned by early geographers and illustrating more fully the course of old pilgrim routes.

Newton was also the first to investigate the difficult subject of the motion of waves (q.v.).

His dad was leaving for work, and there was the usual kisses and waves and " say au revoir to Papa, S!

You cannot see the waves rolling up the beach or hear their roar.

I hope the great ocean will love the new Helen, and let her sail over its blue waves peacefully.

Though it is now dark, the wind still blows and roars in the wood, the waves still dash, and some creatures lull the rest with their notes.

It was worth the while, if only to feel the wind blow on your cheek freely, and see the waves run, and remember the life of mariners.

Gondwanaland, however, did not long survive, and the portion which lay between India and South Africa sank beneath the waves in Tertiary times.

To such fields may be added the yet more complicated problems of those reflex waves which flowed backwards from India into the border highlands.

The blade of a kris may either be wavy or straight, but if wavy the number of waves must always be uneven in number.

Caves occur in the slight cliffs, and protection against the attacks of the waves has been found necessary.

In the case of substances possessing anomalous dispersion, the direct measurement of the refractive index for Hertzian waves of very long wave-length may be employed.

The waves finally obliterated the site in 1288, and Edward I.

The Grind of the Navir ("Gate of the Giants") is a staircase carved by the waves out of the porphyry cliffs.

His contributions to the theories of Elasticity and of Waves rank high among modern developments of mathematical physics, although they are mere units among the 150 scientific papers attached to his name in the Royal Society's Catalogue.

It extends as a completely even plain of snow, with long, almost imperceptible, undulations or waves, at a height of 7000 to 10,000 ft., obliterating the features of the underlying land, the mountains and valleys of which are completely interred.

By the waves of contraction executed by the proboscis accompanied by inflation of the collar, progression is effected, sometimes with marvellous rapidity.

During the great migrations in Asia from east to west many populations were probably driven to the northern borders of the great plateau and thence compelled to descend into Siberia; succeeding waves of immigration forced them still farther towards the barren grounds of the north, where they melted away.

His powerful scientific imagination enabled him to realize that all the points of a wavefront originate partial waves, the aggregate effect of which is to reconstitute the primary disturbance at the subsequent stages of its advance, thus accomplishing its propagation; so that each primary undulation is the envelope of an indefinite number of secondary undulations.

If round the origin of waves an ideal closed surface be drawn, the whole action of the waves in the region beyond may be regarded as due to the motion continually propagated across the various elements of this surface.

We will now consider in detail the important case in which uniform plane waves are resolved at a surface coincident with a wave-front (OQ).

Now as to the phase of the secondary wave, it might appear natural to suppose that it starts from any point Q with the phase of the primary wave, so that on arrival at P, it is retarded by the amount corresponding to QP. But a little consideration will prove that in that case the series of secondary waves could not reconstitute the primary wave.

For the aggregate effect of the secondary waves is the half of that of the first Fresnel zone, and it is the central element only of that zone for which the distance to be travelled is equal to r.

It is accordingly necessary to suppose that the secondary waves start with a phase one-quarter of a period in advance of that of the primary wave at the surface of resolution.

The recomposition of the secondary waves may also be treated analytically.

When the primary wave is plane, the area of the first Fresnel zone is 7rXr, and, since the secondary waves vary as r 1, the intensity is independent of r, as of course it should be.

Since the distance to be travelled by the secondary waves is still r, we see how the effect of the first zone, and therefore of the whole series is proportional to al(a+r).

An interesting exception to the general rule that full brightness requires the existence of the first zone occurs when the obstacle assumes the form of a small circular disk parallel to the plane of the incident waves.

The amplitude of the light at any point in the axis, when plane waves are incident perpendicularly upon an annular aperture, is, as above, cos k(at-r 1)-cos k(at-r 2) =2 sin kat sin k(r1-r2), r2, r i being the distances of the outer and inner boundaries from the point in question.

Properly applied, the principle could not fail; but, as may readily be proved in the case of sonorous waves, it is not in strictness sufficient to assume the expression for FIG.

When the waves are convergent and the recipient screen is placed so as to contain the centre of convergency - the image of the original radiant point, the calculation assumes a less complicated form.

The incident waves are thus plane, and are limited to a plane aperture coincident with a wave-front.

At the focal point (E =o, n = o) all the secondary waves agree in phase, and the intensity is easily expressed, whatever be the form of the aperture.

From the general formula (2), if A be the area of aperture, 102 = A2 / x2 f (7) The formation of a sharp image of the radiant point requires that the illumination become insignificant when, n attain small values, and this insignificance can only arise as a consequence of discrepancies of phase among the secondary waves from various parts of the aperture.

In the direction (suppose horizontal) for which n=o, /f=sin 0, the phases of the secondary waves range over a complete period when sin 0 =X/a, and, since all parts of the horizontal aperture are equally effective, there is in this direction a complete compensation and consequent absence of illumination.

The obliquity, corresponding to u =7, is such that the phases of the secondary waves range over a complete period, i.e.

Since the limitation of the width of the central band in the image of a luminous line depends upon discrepancies of phase among the secondary waves, and since the discrepancy is greatest for the waves which come from the edges of the aperture, the question arises how far the operation of the central parts of the aperture is advantageous.

But, as will be evident, the bright bands bordering the central band are now not inferior to it in brightness; in fact, a band similar to the central band is reproduced an indefinite number of times, so long as there is no sensible discrepancy of phase in the secondary waves proceeding from the various parts of the same slit.

For a certain distance outwards this remains sensibly unimpaired and then gradually diminishes to zero, as the secondary waves become discrepant in phase.

Thus if A be selfluminous, the illumination is a maximum at B, where all the secondary waves agree in phase.

This is necessarily a question of degree; but it does not require detailed calculations in order to show that the discrepancy first becomes conspicuous when the phases corresponding to the various secondary waves which travel from P to B range over a complete period.

The extreme discrepancy is that between the waves which travel through the outermost parts of the object-glass at L and L'; so that if we adopt the above standard of resolution, the question is where must P be situated in order that the relative retardation of the rays PL and PL' may on their arrival at B amount to a wave-length (X).

In his experiments upon this subject Fraunhofer employed plates of glass dusted over with lycopodium, or studded with small metallic disks of uniform size; and he found that the diameters of the rings were proportional to the length of the waves and inversely as the diameter of the disks.

Thus in estimating the intensity at a focal point, where, in the absence of aberration, all the secondary waves would have exactly the same phase, we see that an aberration nowhere exceeding 4X can have but little effect.

The function of a lens in forming an image is to compensate by its variable thickness the differences of phase which would otherwise exist between secondary waves arriving at the focal point from various parts of the aperture.

If the source be a point or a line, and a collimating lens be used, the incident waves may be regarded as plane.

At the middle of this band there is complete agreement of phase among the secondary waves.

It is evident that the waves from both halves of the grating are accelerated in an increasing degree, as we pass from the centre outFIG.

In strictness this idea is appropriate only when the source is a luminous line, emitting cylindrical waves, such as might be obtained from a luminous point with the aid of a cylindrical lens.

The same method of representation is applicable to spherical waves, issuing from a point, if the radius of curvature be large; for, although there is variation of phase along the length of the infinitesimal strip, the whole effect depends practically upon that of the central parts where the phase is sensibly constant.'

To assume a cylindrical form of primary wave would be justifiable only when there is synchronism among the secondary waves issuing from the various centres.

But, without entering upon matters of this kind, we may inquire in what manner a primary wave may be resolved into elementary secondary waves, and in particular as to the law of intensity and polarization in a secondary wave as dependent upon its direction of propagation, and upon the character as regards polarization of the primary wave.

These equations simplify very much in their application to plane waves.

The question as to the law of the secondary waves is thus answered by Stokes.

At every point the motion of the lamina will be the same as would have occurred in its absence, the pressure of the waves impinging from behind being just what is required to generate the waves in front.

Here again, on integration over the entire lamina, the aggregate effect of the secondary waves is necessarily the same as that of the primary.

Thus, to refer again to the acoustical analogue in which plane waves are incident upon a perforated rigid screen, the circumstances of the case are best represented by the first method of resolution, leading to symmetrical secondary waves, in which the normal motion is supposed to be zero over the unperforated parts.

The land has hills and valleys, but the surface of water at rest is a horizontal plane; and if disturbed the surface moves in waves.

With v=o, the angular velocity of the cylinder is 2w; in this way the velocity may be calculated of the propagation of ripples and waves on the surface of a vertical whirlpool in a sink.

In the same century the flourishing walled town of Reimenswaal and the island of Borsele or Borssele disappeared beneath the waves; but the last-named was gradually recovered during the 17th century.

They bore the brunt of each of the great waves of Tatar conquests, and were eventually overwhelmed.

He was the author of numerous papers on light and in 1903 published Light Waves and Their Uses, being Lowell lectures for 1899.

On the 13th of August 1868 an earthquake nearly destroyed Arequipa, and great waves rolled in.

Accordingly, the vessel was built so low in the water that the waves glided easily over its deck except at the middle, where was constructed a revolving turret 1 for the guns, and though the vessel's iron armour had a thickness of 1 in.

Apparent proof has been obtained that the shocks occurring in the Pacific districts originate at the bottom of the sea the Tuscarora Deep is supposed to be the centre of seismic activity and they are accompanied in most cases by tidal waves.

If, on the one hand, huge stones are transported hundreds of miles from sea-shore or river-bed where, in the lapse of long centuries, waves and cataracts have hammered them into strange shapes, and if the harmonizing of their various colors and the adjustment of their forms to environment are studied with profound subtlety, so the training and tending of the trees and shrubs that keep them company require much taste and much toil.

At suitable localities of the coast which are sheltered from the waves and overgrown with seaweed, especially in rock-pools, one or two males establish themselves with their harems, and may be observed without difficulty, being quite as fearless as their freshwater cousins.

They are connected with the ocean by narrow straits, the salinity of the water contained in them differs in a marked degree from that of the ocean, and the tidal waves are of small amplitude.

Waves and tidal currents produce their full effects in that region, and in high latitudes the effect of transport of materials by ice is very important; while in the warm water of the tropics the reefbuilding animals and plants (corals and calcareous algae) carry on their work most effectively there.

The littoral deposits include those of the actual shore on the wash of the waves and of the surface of the continental shelf.

Similar effects are produced along the boulder-clay cliffs of the Baltic. Where the force of the waves on the beach produces its full effect the coarser material gets worn down to gravel, sand and silt, the finest particles remaining long suspended in the water to be finally deposited as mud in quiet bays.

Such a condition of things is only possible in very calm weather, the action of waves having the effect of mixing the water to a considerable depth.

By one of those waves of popular feeling to which the Japanese people are peculiarly liable, the nation which had supported him up to a certain point suddenly veered round and opposed him with heated violence.

There the gigantic cliffs, with their banded strata, have been broken into fantastic forms by the waves.

The pipes composing it were stopped at one end, so that the sound waves had to travel twice the length of the pipe, giving out a note nearly an octave lower than that produced by an open pipe of equal length.

The breath directed horizontally across the open end, impinged against the sharp inner edge of the pipes, creating the regular series of pulses which generate the sound waves within the tubes.

As sound arises in general from vibrating bodies, as it takes time to travel, and as the medium which carries it does not on the whole travel forward, but subsides into its original position when the sound has passed, we are forced to conclude that the disturbance is of the wave kind, We can at once gather some idea of the nature of sound waves in air by considering how they are produced by a bell.

We may obtain an excellent representation of the motion of the layers of air in a train of sound waves by means of a device due to Crova and known as " Crova's disk."

But transverse disturbances may be propagated as waves in solids.

In liquids sound waves are longitudinal as they are in air.

But the waves on the surface of a liquid, which are not of the sound kind, are both longitudinal and transverse, the compound nature being easily seen in watching the motion of a floating particle.

We can represent waves of longitudinal displacement by a curve, and this enables us to draw very important conclusions in a very simple way.

In ordinary sound waves the displacement is very minute, perhaps of the order 105 cm., so that we multiply it perhaps by ioo,000 in forming the displacement curve.

If the waves are continuous and each of the same shape they form a " train," and the displacement curve repeats itself.

It sends out n waves in each second.

If each wave travels out from the source with velocity U the n waves emitted in one second must occupy a length U and therefore U = nX.

Then do= I do dx The Characteristics of Sound Waves Corresponding to Loudness, Pitch and Quality.

The loudness of the sound brought by a train of waves of given wave-length depends on the extent of the to and fro excursion of the air particles.

Methods of measuring the amplitude in sound waves in air have been devised and will be described later.

The pitch of a sound, the note which we assign to it, depends on the number of waves received by the ear per second.

This is generally equal to the number of waves issuing from the source per second, and therefore equal to its frequency of vibration.

That for the air waves from a violin are probably nearly as in fig.

The waves from a source surrounded by a uniform medium at rest spread out as spheres with the source as centre.

The waves for some little distance on each side of the plane will be practically of the same size.

In fact, we may neglect the divergence, and may regard them as " plane waves."

The disturbance, or the train of waves, is then fixed in space, though fresh matter continually enters the disturbed region at one end, undergoes the disturbance, and then leaves it at the other end.

But a priori we are hardly justified in assuming that waves can be propagated at all, and certainly not justified in assuming that they go on unchanged by the action of the internal forces alone.

The amplitude in the pipe was certainly much greater than in the issuing waves.

Meanwhile the waves are spreading out and the value of u is falling in inverse proportion to the distance from the source, so that very soon its effect must become negligible.

If the train of waves is reflected, the value of p at AB will be the sum of the values for the two trains, and will, on the average, be doubled.

Experiments may be made with plane and curved mirrors to verify these laws, but it is necessary to use short waves, in order to diminish diffraction effects.

If an ear-trumpet is placed at the focus of the second mirror the ticking may be heard easily, though it is quite inaudible by direct waves.

In the first case the waves are more likely to reach and be perceived by an observer level with the source, while in the second case they may go over his head and not be heard at all.

Many of the well-known phenomena of optical diffraction may be imitated with sound waves, especially if the waves be short.

As these " secondary waves " return to S their distance apart is nearly equal to twice the distance between the rails, and the observer then hears a note of wave-length nearly 2EF.

But if an observer is stationed at S' the waves will be about half as far apart and will reach him with nearly twice the frequency, so that he hears a note about an octave higher.

A musical note always arises from a source which has some regularity of vibration, and which sends equally-spaced waves into the air.

A given note has always the same frequency, that is to say, the hearer receives the same number of waves per second whatever the source by which the note is produced.

Thus, if the one note be an octave higher than the other, it will give double the number of waves in the same distance.

If the fork has slightly greater frequency, then a white line will not quite reach the next place while the fork is making its swing ip and out, and the waves will travel against the motion of the cylinder.

If the fork has slightly less frequency the waves will travel in the opposite direction, and it is easily seen that the frequency of the fork is the number of white lines passing a point in a second t the number of waves passing the point per second.

His remarkable result that two waves give some sense of pitch, in fact a tone with wavelength equal to the interval between the waves, has been confirmed by other observers.

The engine follows up any wave that it has sent forward, and so crowds up the succeeding waves into a less distance than if it remained at rest.

It draws off from any wave it has sent backward and so spreads the succeeding waves over a longer distance than if it had remained at rest.

Hence the forward waves are shorter and the backward waves are longer.

Then the n waves occupy a space U + w - u.

Now turning to the receiver, let us consider what length is occupied by the waves which pass him in one second.

If he were at rest, it would be the waves in length U + w, for the wave passing him at the beginning of a second would be so far distant at the end of the second.

Since there are n waves in distance U + w - u the number he actually receives is n(U + w - v)/(U + w - u).

But if their velocities are different, the frequency of the waves received is affected both by these velocities and by that of the wind.

The chief experimental basis for supposing that a train of longitudinal waves with displacement curve of this kind arouses the sensation of a pure tone is that the more nearly a source is made to vibrate with a single simple harmonic motion, and therefore, presumably, the more nearly it sends out such a harmonic train, the more nearly does the note heard approximate to a single pure tone.

Each of them is supposed to have its own natural frequency, and to be set into vibration when the ear receives a train of waves of that frequency.

But the same resonator will be appreciably though less affected by waves of frequency differing slightly from its own.

The amount radiated out in the form of sound waves is deduced, and hence the energy of the stream at any distance is known.

In the other, the waves produce a measurable effect on a vibrating system of the same frequency, and the amplitude in the waves can be deduced.

The open orifice of the resonator was then exposed to the waves from a source of its own frequency.

As a preliminary to the investigation of the modes of vibration of certain sources of sound we shall consider the formation of " stationary waves."

These are not really waves in the ordinary sense, but the disturbance arising from the passage through the medium in opposite directions of two equal trains.

We can form stationary waves with ease by fixing one end of a rope - say 20 ft.

When the hand is moved to and fro transversely waves are sent along the rope and reflected at the fixed end.

The vibrations of certain sources of sound may be represented, at least as a first approximation, as consisting of stationary waves, and from a consideration of the rate of propagation of waves along these sources we can deduce their frequency when we know their length.

We shall deduce the modes of vibration of the air column in a cylindrical pipe from the consideration that the air in motion within the pipe forms some part of a system of stationary waves, one train being formed by the exciter of the disturbance, and the other being formed by the reflection of the train at the end of the pipe.

In order to justify the use of stationary waves we must show that two such trains can move in opposite directions over the same ground without modifying each other so long as the displacement in either is small.

Let us suppose that a system of stationary waves is formed in the air in a pipe of indefinite length, and let fig.

The open end is therefore a loop. It is to be noted that the exciter of the vibrations is in general at the open end, and that the two trains forming the stationary system consist of the direct waves from the exciter travelling into the tube, and the waves reflected back from the closed end.

The stationary wave method regards the vibration in the pipe as due to a series of waves travelling to the end and being there reflected back down the pipe.

But the reflection is not complete, for some of the energy comes out as waves; hence the direct and reflected trains are quite equal, and cannot neutralize each other at the loop.

Stationary waves are formed in the air in the dust-tube if the length is rightly adjusted by the closely-fitting piston, and the lycopodium dust collects at the nodes in little heaps, the first being at the fixed end and the last just in front of the piston on the sounder.

If U 4 is the velocity of longitudinal waves along the sounder, and 1 the length of the sounder, the frequency of vibration is U 8 /2l.

If U is the velocity of sound in a gas at pressure P with density p, and if waves of length X and frequency N are propagated through it, then the distanc?e l between the dust-heaps is 2 = N - zN Vyp' where y is the ratio of the two specific heats.

We shall then show that on certain limitations two trains of disturbance may be superposed so that stationary waves may be formed, and thence we shall deduce the modes of vibration as with pipes.

To form stationary waves two equal trains must be able to travel in opposite directions with equal velocities, and to be superposed.

Let two trains of equal waves moving in opposite directions along such a string of indefinite length form the stationary system of fig.

But keeping r/X small we may as before form stationary waves, and it is evident that the series of fundamental and overtones will be just as with the air in pipes, and we shall have the same three types - fixed at one end, free at both ends, fixed at both ends - with fundamental frequencies respectively 41, p ' 21 V p, and I velocity in rod =velocity in air X distance between dust heaps.

By similar methods, a circular plate may be made to exhibit nodal lines dividing the surface by diametral lines into four or a greater, but always even, number of sectors, an odd number being incompatible with the general law of stationary waves that the parts of a body adjoining a nodal line on either side must always vibrate oppositely to each other.

It is easy to deduce the modes of vibration from stationary waves as in the previous cases.

When a system is set vibrating and left to itself, the vibration gradually dies away as the energy leaks out either in the waves formed or through friction.

When two trains of sound waves travel through the same medium, each particle of the air, being simultaneously affected by the disturbances due to the different waves, moves in a different manner than it would if only acted on by each wave singly.

The waves are said mutually to interfere.

We shall exemplify this subject by considering the case of two waves travelling in the same direction through the air.

If the two interfering waves, being still of same length X, be in opposite phases, or sõ that one is in advance of the other by 2X, and consequently one produces in the air the opposite state of motion to the other, then the resultant wave is one of the same length X, but the excursions of the particles are decreased, being the difference between those due to the component waves as in fig.

The reason of this is, that the segments of the plate AOD, BOC always vibrate in the same direction, but oppo sitely to the segments AOB, DOC. Hence, when the pasteboard is in its place, there are two waves of same phase starting from the two former segments, and reaching the ear after equal distances of transmission through the air, are again in the same phase, and produce on the ear a conjunct impression.

But when the pasteboard is removed, then there is at the ear opposition of phase between the first and the second pair of waves, and consequently a minimum of sound.

On interposing the hand between the ear and either prong of the fork when in one of those positions, the sound becomes audible, because then one of the two interfering waves is cut off from the ear.

The two waves, therefore, being in opposite phases, neutralize one another, and the result is a faint sound.

Suppose the two notes to correspond to 200 and 203 vibrations per second; at some instant of time, the air particles, through which the waves are passing, will be similarly displaced by both, and consequently the joint effect will be a sound of some intensity.

The formation of beats may be illustrated by considering the disturbance at any point due to two trains of waves of equal amplitude a and of nearly equal frequencies n, n2.

If, instead of considering one point in a succession of instants, we consider a succession of points along the line of propagation at the same instant, we evidently have waves of amplitude varying from 2a down to o, and then up to 2a again in distance U/(ni - n2).

This want of proportionality will have a periodicity, that of the impinging waves, and so will produce vibrations just as does the variation of pressure in the case last investigated.

It must be very different from ordinary matter as we know it, for waves travelling in matter constitute sound, which is propagated hundreds of thousands of times slower than light.

It has to be competent to transmit the transverse waves of light and electricity, and the other known radiant and electric actions; the way in which this is done is now in the main known, though there are still questions as to the mode of expression and formulation of our knowledge, and also as regards points of detail.

If the surrounding aether is thereby disturbed, the waves of light arriving from the stars will partake of its movement; the ascertained phenomena of the astronomical aberration of light show that the rays travel to the observer, across this disturbed aether near the earth, in straight lines.

Trains of waves nearly but not quite homogeneous as regards wave-length will as usual be propagated as wave-groups travelling with the slightly different velocity d(VX-1)/dX-', the value of K occurring in V being a function of X determined by the law of optical dispersion of the medium.

Tristan causes himself to be placed in a boat with his harp, and committed to the waves, which carry him to the shores of Ireland.

Others see in him a personification of the waves rising to a height and then suddenly falling, or of the treacherous sea.

The prophets of the restoration are only the last waves beating on the shore after the storm which destroyed the old nation, but created in its room a fellowship of spiritual religion, had passed over; they resemble the old prophets in the same imperfect way in which the restored community of Jerusalem resembled a real nation.

Similarly secular elevations of temperature, either accompanied by moisture or desiccation, by increasing droughts or by disturbance of the balance of nature, have been followed by great waves of extinction of the Mammalia.

Great waves of extinction have followed the long periods of the slow evolution of relatively inadaptive types of tooth and foot structure, as first demonstrated by Waldemar Kowalevsky; thus mammals are repeatedly observed in a cul-de-sac of structure from which there is no escape in an adaptive direction.

One of the finest of the endemic flowering plants of the group is the boraginaceous "Chatham Island lily" (M y ousitidium nobile), a gigantic forget-me-not, which grows on the shingly shore in a few places only, and always just on the high-water mark, where it is daily deluged by the waves; while dracophyllums, leucopogons and arborescent ragworts are characteristic forms in the vegetation.

The hair rising from the forehead falls in thick waves on each side of the face and descends nearly to the shoulder; the beard is short and close, the face square and massive, the eyes deep set under overhanging brows, the mouth well formed with settled calm about the lips.

Nearly all the rest of the coast is fringed by off-shore reefs, built up by waves from the very shallow sea bottom; in virtue of weak tides, the reefs continue in long unbroken stretches between the few inlets.

Fogs occur during summer and early autumn, and furious gales may be expected four or five times in the year, when the crash of the Atlantic waves is audible for 20 m.

Often the word thus extruded is irrecoverable; Ginevra, 125 sqq., "The matin winds from the expanded flowers I Scatter their hoarded incense and awaken I The earth, until the dewy sleep is shaken From every living heart which it possesses I Through seas and winds, cities and wildernesses"; the second "winds" is a repetition of the first, but what should stand in its place, - "lands" or "strands" or "waves" or something else - no one can say.

By British seamen it is commonly called the " molly mawk "1 (corrupted fromMallemuck),and is extremely well known to them, its flight, as it skims over the waves, first with a few beats of the wings and then gliding for a long way, being very peculiar.

They may represent the gigantic forces of nature which appear in earthquakes and other convulsions, or the multitudinous motion of the sea waves (Mayer, Die Giganten and Titanen, 1887).

It is a lofty chalk headland, and the resistance it offers to the action of the waves may be well judged by contrast with the low coast of Holderness to the south.

We may say therefore that if the difference between the frequencies n 1 and n, of the two waves is such that in the combined image of the slit the intensity at the minimum between -the two maxima falls to 0.81, the lines are just resolved and n l /(n l n 2) may then be called the resolving power.

These systems may only be semi-stable, but they must last a sufficient length of time to give a train of waves having a length corresponding to the observed homogeneity of the line.

The eruptions of 1868, 1887 and 1907 were attended by earthquakes; in 1868 huge sea waves, 40 ft.

Here Claudius himself appeared - the one reigning emperor of the 1st century who crossed the waves of ocean, - and the army, crossing the Thames, moved forward through Essex and captured the native capital, Camulodunum, now Colchester.

None returns, and the onward march of the survivors never ceases until they reach the sea, into which they plunge, and swimming onwards in the same direction perish in the waves.

But in Germany, as also in France, the waves of anti-Infallibility were rolling so high, that the further development of events was viewed with no small concern.

These instances of the very early use of this metal, intrinsically at once so useful and so likely to disappear by rusting away, tell a story like that of the single foot-print of the savage which the waves left for Robinson Crusoe's warning.

The land forms of a desert are exceedingly characteristic. Surface erosion is chiefly due to rapid changes of temperature through a wide range, and to the action of wind transferring sand and dust, often in the form of "dunes" resembling the waves of the sea.

According to tradition an abbot of Aberbrothock (Arbroath) had ordered a bell - whence the name of the rock - to be fastened to the reef in such a way that it should respond to the movements of the waves, and thus always ring out a warning to mariners.

The velocity of propagation of temperature waves will be the same under similar conditions in two substances which possess the same diffusivity, although they may differ in conductivity.

As in the case of steady-flow methods, by far the simplest example to consider is that of the linear flow of heat in an infinite solid, which is most nearly realized in nature in the propagation of temperature waves in the surface of the soil.

This can be measured graphically without any knowledge of the law of variation of the surface temperature, or of the laws of propagation of heat waves.

As the waves were propagated downwards through the soil the amplitude rapidly i ??.?

For instance, the velocity of propagation of a wave having a period of a day is nearly twenty times as great as that of a wave with a period of one year; but on the other hand the penetration of the diurnal wave is nearly twenty times less, and the shorter waves die out more rapidly.

In treating mathematically the propagation of other kinds of waves, it is necessary to analyse them into their simple-harmonic components, which may be treated as being propagated independently.

The values obtained in this way for waves having a period of one second and a wave-length of half an inch agreed very well with those obtained in the same cast-iron by Angstrom's method (see below), with waves having a period of i hour and a length of 30 in.

A similar method has frequently been applied to the study of variations of soil-temperatures by harmonic analysis of the annual waves.

Angstrom's Method consists in observing the propagation of heat waves in a bar, and is probably the most accurate method for 4 4 thehi 's ' 'so ' d 60 measuring the diffusivity of a metal, since the conditions may be widely varied and the correction for external loss of heat can be made comparatively small.

If h = o, a = b = (urnc/k), as in the case of propagation of waves in the soil.

The amplitudes and phases of the temperature waves at different points are observed by taking readings of the thermometers at regular intervals.

With a view to more minute examination, the annual frequency can be expressed in Fourier series, whose terms represent waves, whose periods are 12, 6, 4, 3, &c. months.

It is not unusual for arcs and bands to look as if pulses or waves of light were travelling along them; also the direction in which these pulses travel does not seem to be wholly arbitrary.

If sound waves originate at the seat of auroral displays they seem hardly likely to be audible on the earth, unless the aurora comes very low and great stillness prevails.

Birkeland (19) supposes the ultimate cause to be cathode rays emanating from the sun; C. Nordmann (24) replaces the cathode rays by Hertzian waves; while Svante Arrhenius (25) believes that negatively charged particles are driven through the sun's atmosphere by the Maxwell-Bartoli repulsion of light and reach the earth's atmosphere.

Hertzian waves have the velocity of light itself.

It ran along the shore at first, just behind the line of villas which fronted upon the sea, and are now half a mile inland, or even upon its edge (for an inscription records its being damaged by the waves).

The land slopes gently to the sea or to the edge of cliffs that nave been cut back by the waves.

Among the most picturesque features of Scottish sea-cliffs are the numerous stacks or columns of rock which during the demolition and cuttingback of the precipices have been isolated and left standing amidst the waves.

He is generally naked; his right leg rests on a rock or the prow of a ship; he carries a trident in his hand, and is gazing in front of him, apparently out to sea; sometimes he is standing on the water, swinging his trident, or riding in his chariot over the waves, accompanied by his wife Amphitrite, the Nereids and other inhabitants of the sea.

It was a production thrown up by the waves of the sea, and was used by the inhabitants to burn instead of wood.

This has been the origin of the long succession of Semitic waves - Babylonian, Assyrian, Canaanite, Hebrew, Nabataean, Moslem - that have flowed over Mesopotamia and Palestine; there is every reason to suppose that they will be followed by others, and that the Arab will remain master at the end, as he was in the beginning.

There were 8 in the year 1897 alone, and one of these ruined the town of Zamboanga in west Mindanao and caused considerable loss of life by falling buildings and immense sea waves.

The brown race, which came from the south in successive waves of immigration beginning in prehistoric times, is composed of twenty-three distinct tribes varying widely in culture, language and appearance; their languages however belong to one common stock and there is a general resemblance in physical features and in quality of mind.

The occupation began with sanguinary conflicts between the two contending waves of intrusion.

In a vaulted chamber under the waves, he fights with Grendel's mother, and kills her.

Yet even before his encounter with Grendel, he had won renown by his swimming contest with another youth named Breca, when after battling for seven days and nights with the waves, and slaying many sea-monsters, he came to land in the country of the Finns.

The phenomena attendant on the passage of electricity through solids, through liquids and through gases, are described in the article Electric conduction, and also Electrolysis, and the propagation of electrical vibrations in Electric Waves.

An immediate deduction from Maxwell's theory was that in transparent dielectrics, the dielectric constant or specific inductive capacity should be numerically equal to the square of the refractive index for very long electric waves.

Fitzgerald (1851-1901) in 1883 as to a method of producing electric waves in space.

These effects, as Hertz showed, indicated the establishment of stationary electric waves in space and the propagation of electric and magnetic force through space with a finite velocity.

Branly of Paris devised an appliance for detecting these waves which subsequently proved to be of immense importance.

Electric waves are produced wherever electrons are accelerated or retarded, that is, whenever the velocity of an electron is changed or accelerated positively or negatively.

This led Clerk Maxwell to frame his theory of electro-dynamics, in which electrical impulses were assumed to be transmitted through the ether by waves.

Fitzgerald was the first to attempt to measure the length of electric waves; Helmholtz put the problem into the hands of his favourite pupil, Heinrich Hertz, and the latter finally gave an experimental demonstration of electromagnetic waves, the "Hertzian waves," on which wireless telegraphy depends, and the velocity of which is the same as that of light.

On finding his body next morning on the shore, Hero flung herself into the waves.

When the earthquake occurs on the coast, or beneath the sea in its vicinity, tidal waves are sometimes formed, which cause even greater damage than the earthquake itself.