Very elementary considerations show that the length (l) of the wave is connected with the period (p) of vibration of the particles (the time of one complete cycle) and the velocity (v) of transmission by the simple relation l = pv. FIG. 6In 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 amplitude FIG. 7is 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-