Page 12 - Spring 2006

Refraction by wind gradients
In 1857, George Stokes suggested that the wind passing over the ground—its speed increasing naturally with height—might be the reason that sounds seemed louder downwind than upwind. Sound waves might be “bent” instead of scattered or absorbed. Stokes’ view was revolution- ary. Some conditions would bend the waves upward over the head of the observer; other conditions would bend the waves down toward the observer. The sound was not absorbed, just redirected. Initially unaware of Stokes’s suggestion, Osborne Reynolds had the same idea and he proposed to test the hypothesis.
By the middle of the 19th century, the banks of the river Medlock near Manchester had been replaced by walls. Here, in 1874, Reynolds tried an experiment. He released drops of water into the river near the Oxford Road Bridge: “A pipe sent a succession of drops into the water at a few inches from the wall, that, falling from a considerable height, made very definite waves...Had the water been at rest [the waves] would have been semicircular rings; as it was, the front of the waves up the stream...gradually died out, showing the effect of divergence. The waves proceeding down the stream were, on the other hand, inclined to the wall that they approached.”
Fig. 4. A reproduction of Osborne Reynolds’ sketch of the wave motion on the sur- face of flowing water. He let drops of water fall into the Medlock River in Manchester where the river flowed past a smooth wall. The flow of the river increases in speed with distance away from the wall and this causes the waves to weaken and lift away from the wall in the upstream (to the left) direction. Reynolds uses the thickness of the lines to indicate the strength of the wave – stronger downstream than upstream along the wall. The curved path would only be clear by watching the waves themselves. The breaks shown to the left of the source Reynolds attributes to interference but this is not fundamental to the process of refraction. (From Reynolds, 1873/4.)
Reynolds proposed that sound waves in the atmosphere behaved in the same way as the water waves on the river’s sur- face. The variation in flow speed of the water—slow at the wall, faster away from the wall—caused the water waves to bend from their normal circular arcs. The waves appeared to be lifting away from the wall as they advanced in the upstream direction while bending toward the wall and strengthening in the downstream direction. This bending of the waves is refraction. Refraction is not caused simply by the flow of the water but by the increase in flow speed with dis- tance from the wall.
Imagine dropping a stick into the river near the wall. The stick would rotate. The end farther from the wall is in faster flow while the end nearer the wall is in slower flow. If the stick was instead a portion of a moving wave front, this rotation would change the wave’s direction of travel. If that portion of the wave had been traveling initially upstream, the rotation would cause the wave to veer away from the wall toward the middle of the river. If that portion of the wave had been trav- eling initially downstream, the rotation would cause it to bend toward the wall. An observer at the wall would see the upstream wave weaken and eventually leave the wall altogeth- er while the downstream wave would seem to strengthen.
In still air, sound waves travel with a speed that depends on the temperature of the air. If the air is also moving, this motion adds to the wave speed if the wind is in the direction of travel and it subtracts from the wave speed if the wind is in the opposite direction. In fact, Reverend Derham had recog- nized this but he thought that the acceleration or retardation by the wind caused the difference in sound intensity. Stokes understood that a wind that increases in speed with altitude would bend wave fronts traveling in the upwind direction, lifting them away from the ground. This would produce a rapid decrease in audibility. In air, the effect can be so strong that a signal heard clearly at some distance downwind may, at the same distance upwind, be faint or inaudible.
This redirection or refraction of sound caused by varia- tion in wind speed was a new and revolutionary hypothesis. More importantly, Reynolds realized that the hypothesis could be verified with a simple test.
Reynolds wrote: “Thus the effect of wind is not to destroy the sound, but to raise the ends of the wave, that would other- wise move along the ground, to such a height that they pass over our heads...It will at once be perceived that by this action of the wind the distance to which sounds can be heard to windward must depend on the elevation of the observer and the sound-pro- ducing body...It is difficult to conceive how it can have been overlooked, except that, in nine cases out of ten, sounds are not continuous, and thus do not afford an opportunity of compar- ing their distinctness at different places...Elevation, however, clearly offered a crucial test whether such an action as that I have described was the cause of the effect of wind upon sound.” Reynolds also recognized the value of a continuous sound: “My apparatus consisted of an electrical bell, mounted on a case con- taining a battery. The bell was placed horizontally on the top of the case, so that it could be heard equally well in all directions...” Furthermore, he arranged to vary the elevation of the observer (or the source of sound).
Upwind of the source, “...at all distances greater than 20 yards from the bell the sound was much less at the ground than a few feet above it; and I was able to recover the sound after it had been lost in every direction by [climbing] a tree, and even more definitely by raising the bell on to a post 4 feet high, that had the effect of doubling the range of the sound...”
Reynolds distinguished himself by his approach to inves- tigation: he proposed a hypothesis that sound traveling into the wind would be refracted upward by the increasing wind speed (the wind speed “gradient”) with altitude; he made a critical, testable prediction—that the sound would increase
10 Acoustics Today, April 2006