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.
8
Light Waves and Their Uses
Very elementary considerations show that the length (I) of the wave is connected with the period (j>) of vibration of the particles (the time of one complete cycle) and the velocity (r) of transmission by the simple relation I = pv.
FIG. 6
In fact, if we could take instantaneous photographs of such a train of waves at equal intervals of time, say one-eighth of the period, they would appear as in Fig. 5. It will readily be seen that in the eight-eighths of a period the wave has advanced through just one wave length, while any particle has gone once through all its phases.
Let us next consider the superposition of two similar trains of waves of equal period and amplitude. If the phases of the two wave trains coincide, the resulting wave train will have twice the amplitude of the components, as shown in Fig. 6. If, on the other hand, the phase of one train is half a period ahead of that of the other, as in Fig. 7, the resulting ampli-
FIG. 7
iude is zero; that is, the two motions exactly neutralize each other. In the case of sound waves, the first case corresponds to fourfold intensity, the second to absolute silence.
The principle of which these two cases are illustrations is miscalled interference; in reality the result is that each wave motion occurs exactly as if the other were not there to inter