I'm just trying to understand what Paul was saying. So horns have more a focused beam of intensity directly in front and the sensitivity is extremely high but the efficiency, as I understand it now, is based on intensity from all angles. So if horns are the most efficient designs possible then they must focus well at all angles...
If a speaker does not radiate sound at other angles well then it's efficiency won't be as high. I could be completely off-base with my interpretation of all of this. I just figured that if horn-loaded speakers were the most sensitive speakers with the best efficiency that would imply that their on-axis sound intensity is very high as well as off-axis results...
Does any of that make sense ?
Think of a point source speaker as if it were a small, bare light bulb and a horn as a very focused flashlight. The intensity is higher because all of the light is going in a narrow direction, even though the bulb may be rated as lower Wattage than the bare bulb. Also, in a free field, sound diminishes at a rate that's covered by the Inverse Square rule, which means that, as the distance doubles, the output becomes 1/4 of what it is at the original spot. If the space is highly reverberant, some of the sound/light reflects back and is still useful.
The sound from a horn can't be heard very well from the sides, unless it was designed for wide dispersion.
Volume, in dB, is how loud it's measured to be but intensity is how the sound or light is perceived.