CHAPTER XVII. WAVE MOTION. OUR study of electricity leads us now to the general subject of wave motion, which up to the time of the laying of the Atlantic cable seemed to be very little in touch with practical life. It was a subject for mathematicians and the natural philosophers, and it seemed to have no commercial importance. In signalling, however, through the cable the practical man was speedily confronted with problems of wave motion, and with the invention of the telephone the study of wave motion became instantly of importance to the practical electrician. The progress of electricity is steadily in the direction of the economical production of wave motion. "By a wave is understood a state of disturbances which is propagated from one part of a medium to another." Energy pauses, and not matter. Waves are free or forced. An example of a free wave is afforded by that of the wave running into the Bay of Fundy, which is almost free from the influence of the sun or moon; while the ocean tide is a forced wave, since it depends upon the continued action of the moon and sun. It has been computed that waves on the ocean of about three hundred feet long travel at the rate of nearly forty feet per second, or twenty-seven miles per hour. Their disturbance, however, is merely superficial. Even if they are forty feet high, the disturbance of a water particle at a depth of three hundred feet is not quite half an inch from its mean position. The depths of the ocean are practically undisturbed by such waves on the surface (Prof. Tait). Although the study of wave motions of heavy fluids, like water, or even air, may provide us with analogies by means of which we can illustrate wave motions in an attenuated medium like the ether, we must bear constantly in mind the fact that the viscosity of water or that of the air greatly modifies the circumstances of wave motion. Our ideas, however, of waves in the ether of space, which are believed to convey the energy of the sun to FIG. 30. B us, are primarily obtained from contemplation of the wave motions which we perceive in water and the air. The electric spark has been used in an interesting manner to make manifest waves in air which otherwise would escape our senses. Prof. Boys by its aid has photographed the waves caused by the motion of a bullet. His method is substantially as follows: * C is a plate of window glass (Fig. 30) with a square foot of tin foil on both sides. This constitutes the con denser, and it is charged until its potential is not sufficient to make a spark at each of the gaps, E and E', * Nature, March 9, 1893. though it would, if either one of these were made to conduct, immediately cause a spark at the other; c is a Leyden jar of very small capacity connected with C by a wire-as shown by the continuous lines and by a string wetted with a solution of chloride of calcium, as shown by the dotted line. So long as the gap at B is open this little condenser, which is kept at the same potential as the large condenser by means of the wire and wet string, is similarly unable to make sparks both at B and E', but it could, if B was closed, at once discharge at E'. Now, suppose the bullet to join the wires at B, a minute spark is made at B and at E' by the discharge of c. Immediately C, finding one of its gaps, E', in a conducting state, discharges at E, making a brilliant spark which casts a shadow of the bullet upon the photographic plate, P. The wet string suffices to charge the jar c, but acts like an insulator when the discharge takes place at E' and B. The photograph is a silhouette, but it serves to define the wave of air caused by the bullet. Prof. Boys remarks that the wave revealed by the photograph shows just as in the case of waves produced by the motion of a ship, which become enormously more energetic as the velocity increases, and which at high velocities produce an effect of resistance to the motion of the ship far greater than that of skin friction, that the resistance which the bullet meets increases very rapidly when the velocity is raised beyond the point at which these waves begin to be formed. Scott Russell has shown by diagrams and experiments what happens when a solitary wave meets a vertical wall. As long as the wave makes an angle with the wall it is reflected perfectly, making an angle of incidence equal to the angle of reflection, and the reflected and incident waves are alike in all its parts. When the wave front nearly perpendicular to the wall runs along nearly parallel to it, it then ceases to be reflected at all. The part of the wave near the wall gathers strength; it gets higher, travels faster, and so causes the wave near the wall to run ahead of its proper position, producing a bend in the wave front, and this goes on until the wave near B FIG. 31. A the wall becomes a breaker. To see if a similar phenomenon could be traced in the air, Prof. Boys arranged three reflecting surfaces (as seen in Fig. 31). Below the bullet two waves strike a reflector at a low angle, and they are perfectly reflected. The left side of the V-shaped reflector was met at nearly grazing incidence. There is no reflection, but the wave near this reflector is of greater intensity; it has bent itself ahead of its proper position, just as the water wave was found to do. The stern wave has a piece cut out of it and bent up at the same angle. Prof. Boys points out that if the wave was a mere advancing thing the end of the bent-up piece would leave off suddenly, and the break in the direct wave would do the same. But according to Huyghens's hypothesis, the wave at any epoch is the resultant of all the disturbances which have started from all points of the wave front at any preceding epoch. The reflector, where it has cut this wave, may be considered as a series of points of disturbance arranged continuously on a line, each coming into operation just after the neighbour on one side and just before the neighbour on the other. The reflected wave is the envelope of a series of spheres beginning with a point at the place where the wave and the reflector cut, growing up to a finite sphere about the end of the reflector to a centre; beyond this there are no more centres of disturbance, the envelope of all the spheres projected upon the plate—that is, the photograph of the reflected wave-is not therefore a straight line, leaving off abruptly, but it curls round, dying gradually to nothing. In the nonreflection of the air wave by the V-shaped reflector we have optical evidence of what goes on in a whispering gallery. The sound is probably not reflected at all, but runs round almost on the surface of the wall from one part to another. A most interesting method of studying sound waves in air by means of the electric spark was devised by Töpler.* He succeeded in making visible the reflection and the refraction of sound waves, and also the interference of two sound waves. the eye An idea of Töpler's method of rendering visible to the waves of sound in the air can be obtained from a consideration of the phenomenon of mirage. A low-lying strata of air of suitable density enables us to see objects below the horizon, for the rays of light (Fig. 32) from these objects are bent or refracted to the eye by the strata of air. For instance, if A represents the position of the horizon, and S that of the sun, which is a little below the horizon, the strata of air lying above A can refract the ray S C to E, and looking along C E we shall see the sun apparently elevated * Annalen der Physik und Chemie, 131, 1867, p. 180. |