WAVES (AS. wafian, to wave, fluctuate, waver, 5111G. to wave. Bavarian Ger. waiben, to waver, totter). Wave-motions are of two kinds: one is the advance of a disturbance into a medium, and the other is its advance along a surface. Illustrations of the former kind are given by waves produced in air or in the interior of water by a vibrating body such as a bell, and those produced in the ether by an electrical or 'atomic vibration; illustrations of the latter kind are given by waves on the surface of a lake or ocean. The former class of waves are due to the elasticity and inertia of the medium; and the velocity with which the disturbance spreads out from the vibrating centre depends upon these two properties of the fluid alone. Elastic waves in homogeneous media have a velocity given by the formula velocity = where E is the coefficient of elasticity and d is the density. See AcousTics; ETHER; ELECTRICITY.
Waves on the surface of a liquid are due to the action of gravitation, which tends to make the surface of a liquid horizontal (to the sur face-tension if the waves are nothing but ripples), and to the inertia of the liquid. (For a discus sion of these 'water-waves,' see HYamOsT-\Tics.) The 'wave-front' of a train of waves is the sur face which at any instant includes all those points of the medium which the disturbances have just reached ; or, more generally, it is a surface in the medium including those points where the motion is in the same 'phase.' The wave-front from a point source is a sphere in the ease of an elastic wave in an isotropic medium: it is a circle for waves on the surface of water.
Since all waves consist in the motion of por tions of matter, and since the medium carrying the waves is not in its natural position or condi tion, there is both kinetic and potential energy associated with wave-motion. This energy is lost by the vibrating source and gained by the body absorbing the waves. The 'intensity' of the waves is defined to be the energy carried in unit time through an area of one square centimeter of surface at right angles to the direction of ad vance of the waves. Thus, if the source of waves is a point and if the energy emitted per unit time is E, the intensity of the waves at a dis tance r is — , because the area of the surface of a sphere of radius r„ inclosing the point-source as a centre, is 4r/.2. Similarly, the intensity at a distance is L.= --. Therefore I, or the intensity of the waves from a point-source varies inversely as the square of the distance.
Since waves are due to some vibrating centre, the simplest type of train of waves will be one prodneed by the simplest vibration, that is a simple harmonic vibration, such as that of a tuning fork in the case of aiIrial waves. A train
of waves produced by a simple harmonic vibra tion is called a simple harmonic train. It is characterized by its 'amplitude' and its 'wave length' or 'wave-number.' The amplitude is the extent of the vibration of any individual particle of the medium owing to the passage of the waves. The wave-length is the distance from any one point in the medium to the next point, in the direction of advance of the waves, where the conditions are at any instant exactly the same— both in displacement of the particle of the me dium and in its velocity. The wave-number is the number of complete vibrations which each particle of the medium makes in one second; or, what is the same thing, it is the number of waves which pass any one point of the medium in one second. The velocity of the train of waves is, then, obviously the product of the wave-length and the wave-number. Moreover, since, in the case of waves due to the elasticity of a homo geneous medium, their velocity depends upon the elasticity and inertia alone, it is the same for waves of all lengths. Therefore, for a given me dium, if the wavelength is known, the wave number may be at once calculated. If the me dium is not homogeneous, waves of different length have different velocities. (See LIGHT and DiseEnstox.) It is not difficult to prove that the energy carried by a train of waves varies as the square of the amplitude; and, since in the ease of waves emitted by a point-source the in tensity of the waves varies inversely as the square of the distance from the source. the ampli tude of the waves must 'vary inversely as the dis tance itself.
A complex vibration, made up of several simple harmonic vibrations, will produce a com plex train of waves which is equivalent to the superposition of several trains of simple har monic waves. The characteristics of such a com plex train of waves are, first. the number of the component trains, and. secondly, their a 111 pl tildes, wave-numbers, and relative 'phases.' By relative phases is simply meant their relative po sitions in the medium. (See AcousTics.) As trains of waves pass through any medium some energy is always absorbed, as is shown by the gradual' decrease in amplitude. This is called `attenuation ;' and it is found that long waves are less attenuated than short ones in general. Consequently, as a complex train of waves ad vances, its different component trains arc at tenuated to different degrees, and the 'shape' of the wave changes. This is called 'distortion.' if the inertia of the medium is very great, the at tenuation is diminished, and the distortion al most vanishes. Waves along stretched cords are special cases of elastic waves. See ACOUSTICS.