Dispersion refers to how a sound spreads out in the atmosphere. We all know that a sound's intensity decreases as we get further from its source, and this section attempts to explain the principles behind that. Because sound is necessarily studied in a real physical environment it becomes very complicated to describe all its behaviors. I'll stick to the major (sometimes perfect-world) points, as always focusing on what I think is important to understanding wind turbines' characteristics.

The intensity of any emission will dissipate as the distance from the source increases. The most common expression of this is that the intensity of sound (or light, for that matter) goes down as the square of the distance: in other words, if you double your distance the sound will decrease to a fourth of what it was. A slightly more accurate expression would be that sound goes down as one less power than the number of dimensions it is spread out over. In the above example the sound is presumed to originate at a point and spread out over 3 dimensions. Thus the decrease is calculated as a power of 2, or squared. If the sound spreads out evenly in all 3 dimensions this would be called "spherical". Here are some other examples.

• Example #1. A laser goes out in a straight line - only one dimension. Applying our rule, it dissipates not at all. This assumes a perfect vacuum and rod, never practical possibilities.
• Example #2. The sound is not a point source, but rather a line source - like a long violin string (or more commonly, a road). The long string takes away one of the dimensions, so the sound can only disperse over 2 dimensions. This leads to linear dispersion, where if you double your distance the sound decreases by half.
• Example #3. The sound can't spread in 3 dimensions - like there's a temperature inversion that prevents the sound from spreading upward, thus providing only 2 dimensions for the spreading. This is "cylindrical" dispersion and leads to linear decreases.
• Example #4. More familar to us is where the source is point on the ground. The sound still spreads in 3 dimensions, but only through half the sphere, so this would be called "hemispherical". The "dimensions minus one" rule still applies, so the sound would dissipate as the square of the distance. But ground absorbs (or doesn't) the sound as it spreads. Now everything gets trickier. If the ground absorbed all the sound, you'd be left with the distance-squared behavior of the perfect sphere. If it absorbed none of the sound, the sound would still dissipate as the square of the distance, but would be a constant 6 dB higher.

As example #4 starts to show, the behavior of sound in the real atmosphere with real grass and trees around is not so simple to calculate. In addition the atmosphere itself absorbs some of the sound energy as heat, so the dissipation is somewhat higher than my perfect-world examples have implied. And I haven't even gotten into reflections and obstructions. Generally speaking, there exist computer modeling programs that can take into account most of these factors.

As example #2 shows, where there is a sound that is not a point source (and in reality there is never a true point source) the sound will not dissipate as quickly as you might otherwise expect. The computational complexity of handling arbitrary non-point sources is so high that for most purposes point (or a somewhat-arbitrary almost-a-point) sources are assumed, and many times the results are good enough for government work. I'll get into more details in the Regulation Problems section, but for now just imagine what might result when the point source is really a disk almost 100m in diameter, and you are only 350m away from it.

• Abom Paper, 0.4mb, sound propagation from wind turbines
• Rogers NREL 2006 Paper, 0.8mb