Refraction of Sound by the Atmosphere. 533 



right angles to the wind are but little affected by it ; and in moderate 

 winds sounds can be heard further with the wind than when there is 

 none. 



The same may be said against theories which would explain the effect 

 of wind as causing a heterogeneous nature in the air so that it might 

 reflect the sound. All such effects must apply with equal force with and 

 against the wind. 



This question has baffled investigators for so long a time, because they 

 have looked for the cause in some direct effect of the motion of the air, 

 whereas it seems to be but incidentally due to this. The effect appears, 

 after all, not to be due simply to the wind, but to the difference in the 

 velocity with which the air travels at the surface of the ground and at a 

 height above it ; that is to say, if we could have a perfectly smooth 

 surface which would not retard the wind at all, then the wind would not 

 obstruct sound in the way it does, for it would all be moving with an 

 equal velocity ; but, owing to the roughness of the surface and the ob- 

 structions upon it, there is a gradual diminution in the velocity of the 

 wind as it approaches the surface. The rate of this diminution will 

 depend on the nature of the surface; for instance, in a meadow the 

 velocity at 1 foot above the surface is only half what it is at an ele- 

 vation of 8 feet, and smaller still compared with what it is at greater 

 heights. 



To understand the way in which this variation in the velocity affects 

 the sound, it is necessary to consider that the velocity of the waves of 

 sound does depend on the velocity of the wind, although not in a great 

 degree. To find the velocity of the sound with the wind we must add 

 that of the wind to the normal velocity of sound, and against the wind 

 we must subtract the velocity of the wind from the 1100 feet per second 

 (or whatever may be the normal velocity of the sound) to find the 

 actual velocity. Now if the wind is moving at 10 feet per second 

 at the surface of a meadow, and at 20 feet per second at a height of 

 8 feet, the velocity of the sound against the wind will be 1090 feet 

 per second at the surface and 1080 feet per second at 8 feet above 

 the surface ; so that in a second the same wave of sound will have 

 travelled 10 feet further at the surface than at a height of 8 feet. This 

 difference of velocity would cause the wave to tip up and proceed in an 

 upward direction instead of horizontally. For if we imagine the front 

 of a wave cf sound to be vertical to start with, it will, after proceeding 

 for one second against the wind, be inclined at an angle of more than 45, 

 or half a right angle ; and since sound-waves always move in a direction 

 perpendicular to the direction of the front (that is to say, if the waves 

 are vertical they will move horizontally and not otherwise), after one 

 second the wave would be moving upwards at an angle of 45 or more. 

 Of course, in reality, it would not have to proceed for one second before 

 it began to move upwards : the least forward motion would be followed 



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