Refraction of Sound by Wind. 



161 



which itself makes the angle BAD = with the horizontal. 

 From C let fall CN perpendicular to the horizontal line AN. 

 Then, for the relation between c/> and 0, we have by con- 



struction 



or 



NA NA' 



tanNCA=^; = 



A'A 



CN CN CA' cos NO A' 

 tan<£ = tan 6+ - sec 0. . . . 



(i) 



Accordingly the ray, instead of making the angle 6 with the 

 vertical as it would if normal to the wave-front, makes the 

 angle 4>, which usually differs from 6 whenever there is a 

 wind in the region in question. An exception occurs when 

 e is 90°, <b being then 90° also. 



Refraction of Waves and Rays on crossing into a new Wind 

 Zone. — Consider now two wind zones divided by a horizontal 

 plane ; let the wind in the lower zone be everywhere horizontal 

 of speed u , and in the upper zone in the same direction but 

 of speed u x . Let a plane wave-front in the lower zone, 

 inclined 6 to the horizontal, assume the inclination Q x after 

 refraction into the upper zone. It is required to determine 

 the relation between 6 X and O . 



Fig. 2. — Refraction of Sound by abrupt change of Wind Speed. 



In fig. 2 let AC represent the wave-front incident at A 

 upon the plane of separation AB of the two zones. Draw 

 CB' at right angles to AC, and lay off B'B, making 

 B'B : CB / = m : v > Then, by previous paragraph, CB is the 

 direction of propagation in the lower zone. And, if t be the 

 time occupied from C to B, we have CB ; = vt and B'B = u t. To 

 construct the new wave-front in the upper zone it is necessary 

 to consider A as the origin of a wavelet as in the first case. 



Phil Mag. S. 6. Vol. 1. No. 1. Jan, 1901. M 



