GENERAL THEORY OF SOUND WAVES 219 



75. Refraction by Wind. 



Another interesting question is that of refraction by wind. 

 A uniform motion of the medium introduces of course no 

 complication, the relative motion of the sound waves being 

 exactly the same as if the medium were at rest. Usually, 

 however, the wind- velocity near the ground is less than above, 

 the motion of the lower layers of air being obstructed. Hence 

 when a wave-front travels with the wind, the upper portions 

 are propagated (in space) somewhat faster than the lower, the 

 velocity of the wind being superposed on that of sound. The 

 front is therefore continually being tilted downwards. For a 

 similar reason a wave-front travelling against the wind gets 

 tilted upwards, so that the sound tends to pass over the 

 head of an observer at a distance. This explanation of the 

 familiar fact that sound can be heard better, and further from 

 the source, when this lies to windward than when it is to 

 leeward of the observer, was first given by Stokes (1857). 

 The only previous suggestion had been that a sound which 

 has travelled a certain distance with the wind has really 

 traversed a shorter length of air. and has consequently become 

 less attenuated by spherical divergence, than if the wind had 

 been absent. Owing to the smallness of wind- velocities in 

 comparison with that of sound, this cause is quite inadequate 

 to explain the very marked effects which are observed. The 

 true theory was discovered independently by Reynolds (1874), 

 and confirmed by a number of interesting experiments. 



If we proceed to apply optical methods to the question, 

 it is necessary to dis- 

 tinguish, as in the theory 

 of aberration, between the 

 direction of a ray and that 

 of a wave-normal. Let S l 

 represent the position of a 

 wave-front at time t, S' 

 the position at time t + 8t 

 of those particles which 

 were on S l} and 8 2 the 

 new position of the wave- 



