The speed of sound varies with temperature. Since temperature and sound velocity normally decrease with increasing altitude, sound is refracted upward, away from listeners on the ground, creating an acoustic shadow at some distance from the source. Wind shear of 4 m/(s · km) can produce refraction equal to a typical temperature lapse rate of . Higher values of wind gradient will refract sound downward toward the surface in the downwind direction, eliminating the acoustic shadow on the downwind side. This will increase the audibility of sounds downwind. This downwind refraction effect occurs because there is a wind gradient; the fact that sound is carried along by the wind is not important.
For sound propagation, the exponential variation of wind speed with height can be defined as follows:
where
* U(h) is the speed of the wind at height h;
* ζ is the exponential coefficient based on ground surface roughness, typically between 0.08 and 0.52;
* dU/dH(h) is the expected wind gradient at height h.
In the 1862 American Civil War Battle of Iuka, an acoustic shadow, believed to have been enhanced by a northeast wind, kept two divisions of Union soldiers out of the battle, because they could not hear the sounds of battle only  (six miles) downwind.