Sound Waves An the Atmosphere. 



Ill 



partly reflected and partly transmitted. In fig. 5, (40) is 

 divergent; the sound is audible at all points on the ground, 



Fig. 5. 

 Total reflexion with unlimited range of audibility. 



but however far we go along Ox the rays always arrive with 

 a non-zero and the apparent elevation of the source 

 (judged by the sound) is the same at all sufficiently large 

 distances. 



§ 8. Envelopes and curves of vertices. 



The descending portions of rays can never intersect one 

 another ; in figs. 4 and 5 the ascending portions of totally 

 reflected rays have been drawn as non-intersecting also. 

 Under certain conditions, however, these latter may inter- 

 sect and have an envelope, analogous to the caustics of 

 optics. To investigate these, take axes through the source 



Fig- 6. 



o 



(T) 





2 





i / 



(fig. 6), and let Cf, £) be the co-ordinates of the vertex of 

 any ray (point of total reflexion). The locus of (f, J) for 

 different rays will be called the curve of vertices. It is 



