Page:Elementary Text-book of Physics (Anthony, 1897).djvu/169

§132] due to the systems taken separately. If the curve of displacements be drawn for each system, the algebraic sum of the ordinates will give the ordinates of the curve representing the actual displacements. In Fig. 47 the dotted line and the light full line represent respectively the displacements due to two wave systems of the same period and amplitude. The heavy line represents the actual displacement. In I the two systems are in the same phase; in II the phases differ by $$\tfrac{1}{4}$$, and in III by $$\tfrac{1}{2}$$, of a period. If both wave systems move in the same direction, it is evident that the conditions of the body will be continuously shown by supposing the heavy line to move in the same direction with the same velocity. The condition represented in III is of special interest. It shows that two wave systems may completely annul each other. Fig. 48 represents the resultant wave when the periods, and consequently the wave lengths, of the two systems are