6
Light Waves and Their Uses
moving more slowly the smaller the wire and the heavier the blocks, so that, by varying these two factors, any desired speed may be obtained.
The wave form which is propagated in any of the various possible cases is, in general, very complicated. It can be shown, however, that it is always possible to express such forms, however complex, by a series of simple sine curves such as that represented in Fig. 4. The study of wave motion may be much simplified by this device. Accordingly, in all that follows, except where the contrary is expressly stated, it will be assumed that we are dealing with waves of this simple type.
There are certain characteristics of wave motion of which we shall have to speak frequently in what follows, and which therefore need definition. In the first place, the shape of the wave illustrated in Fig. 4 is important. It is the curve which would be drawn by a pendulum, carrying a marker, upon a piece of smoked glass moving uniformly^at right angles to the motion of the pendulum. Since the pendulum moves in what is called simple harmonic motion, the curve is called a simple harmonic curve, or a sine curve. The amplitude of the wave is the maximum distance of a crest or a trough from the position of rest, i. e., from the straight line drawn through the middle of the curve. The period of the vibration is the time it takes one particle to execute one complete vibration; i. e., to revert to the pendulum, it is the time it takes the pendulum to execute
Wave Motion and Interference
7
one complete swing.1 The phase of any particle along the curve is the portion of a complete vibration which the particle has executed. The wave length is the distance between two particles in the same phase. Thus it is the distance
FIG. 4
between two consecutive crests or between two consecutive troughs. When all the particles vibrate in one plane, c> g the plane of the drawing, the wave is said to be polarized in a plane. The velocity of propagation of the wave is the distance traveled by any given crest in one second.
As has just been stated, the type of wave motion illus-strated in Fig. 4 may be approximately realized by imparting the motion of a pendulum or a tuning-fork to one end of a very long cord. It can be shown that after a time every particle of the cord will vibrate with precisely the
FIG. 5
same motion as that of the pendulum or tuning-fork from which the disturbance starts. Any particular phase of the motion occurs a little later in every succeeding particle; and it is this transmission of a given phase along the cord which constitutes the wave motion.
i In some works the half of this is taken, i. e., the time it takes a pendulum to move from the extreme left to the extreme right.