Page:Elementary Text-book of Physics (Anthony, 1897).djvu/172

158 medium reaches the boundary, the bounding particles, instead of stopping with a displacement such as they would reach in the interior of the medium, move to a greater distance, and this movement is communicated back from particle to particle as a reflected wave, in which the motion has the same sign as in the direct wave. It is reflection without change of sign. The two latter cases are extremely important in the study of the formation of stationary waves in sounding bodies.

Let us suppose a system of spherical waves departing from the point $$C$$ (Fig. 50). Let $$mn$$ be the intersection of one of the waves with the plane of the paper. Let $$AB$$ be the trace of a plane smooth surface perpendicular to the plane of the paper, upon which the waves impinge. $$mo$$ shows the position which the wave of which $$mn$$ is a part would have occupied had it not been intercepted by the surface. From the last section it appears that reflection will take place as the wave $$mno$$ strikes the various points of $$AB$$. In § 130 it was seen that any point of a wave may be considered as the centre of a wave system, and we may therefore take $$n', n,$$ etc., the points of intersection of the surface $$AB$$ with the wave mn when it occupied the positions $$m'n', mn'',$$ etc., as the centres of systems of spherical waves, the resultant of which would be the actual wave proceeding from $$AB$$. With $$n'$$ as a centre describe a sphere tangent to $$mno$$ at $$o$$. It is evident that this will represent the elementary spherical wave of which the centre is $$n'$$ when the main wave is at $$mn$$. Describe similar spheres with $$n, n',$$ etc., as centres. The surface $$np$$, which envelops and is tangent to all these spheres, represents the wave reflected from $$AB$$. If that part of the plane of the paper below $$AB$$ be revolved about $$AB$$ as an axis until it coincides with