I just wanted to point out that there's no real conflict between the 6dB loss per doubling of distance which Alan mentioned in his article and the 3dB loss per doubling which Dr. Toole describes(pp. 59-60). There's no question that a 6dB loss of sound intensity results when the distance is doubled with an omnidirectional sound source operating in an anechoic chamber or wide open area(e.g., top of the Axiom test tower)offering no sound reinforcement. This results because an omnidirectional source spreads out as a sphere, and the formula for the area of a sphere is 4pi x radius[squared], so when the radius of the sphere of sound is doubled, the surface area of the sphere is quadrupled since the doubled radius is squared. The intensity of the sound per unit of area is therefore only 1/4th what it was before the doubling of distance. Since 3dB gain is a doubling and 6dB is a quadrupling of sound intensity, conversely a 1/4th intensity represents a 6dB loss.
However, this number isn't applicable to home audio where the room boundaries add support to the sound and reduce the loss. This is the major reason why the Crown calculator doesn't give realistic results for home use, since its formula simply uses the 6dB per doubling figure. Only near the end in "other considerations" does it point out this key difference and suggest a 6dB adjustment(which would reduce the power number from the calculator to 1/4th of its previous value). Strangely, instead of suggesting that a much less powerful amplifier be bought, Crown suggests that the 6dB correction be applied to yet more headroom.
Dr. Toole, using previous research by Schulz, combined with his own work on the subject with speakers, finds that 3dB is the best number to use. Because of this research and earlier work I'd read about, I simply deduct 4dB from the 1 meter sensitivity number for a typical 9-10' listening distance and calculate the requirements at various dB levels from there, rather than using the Crown or other similar online calculators.
