Sub-essay on the nature of hearing
The human ear is a marvel with regard to the range of sound that it can sense. A parent can hear the sleepy whisper of a child, the buzz of a fly or the chirp of a cricket (about 40dB). That same parent can detect the change in the pitch of a chainsaw or enjoy Tchaichovski's 1812 Overture (about 110dB).
In terms of power, that is a difference of 10^7, or ten million.
The downside of this huge range is that the human ear is very insensitive to modest changes in sound power. You could put ten people with healthy hearing in a room and play them two snippets of music. One snippet of music would have twice the power of the other. Half the people would vow that the two snippets were of equal loudness. (Key point: Loudness is different than Power). The tester will not get overwhelming agreement that one snippet is louder than the other until the louder piece has four times as much power as the other.
Aside: The poor mapping between power and apparent loudness is why it is mandatory to have good instrumentation. You cannot rely on your ears. They are incapable of discriminating with the precision required to incrementally improve systems.
Mapping that requirement into dB tells us that we need a minimum of a 6dB reduction for back-to-back comparisons. A minimum of a 10dB reduction (90% power reduction) is prudent for a session-to-session comparison.
Twenty dB reduction was chosen for the purpose of this "paper" study. Assumptions are made for ease of computations. One of those assumptions is typically 100% performance. Another reason for choosing 20dB reduction is that there is little point in going through much effort if the customers...the neighbors, for instance...can barely tell the difference.
To provide a frame of reference for my readers who shoot, an honest 20dB reduction would reduce the noise levels heard by a neighbor at 50 yards to a level similar to what a neighbor currently hears at a quarter mile of distance. When explaining it to your neighbor it is technically accurate to say that a 20dB reduction is the same as if you had picked up your shooting bench and moved it so it was ten times further away from your neighbor than before.
An earlier essay suggested the possibility of positioning a "doghouse" on the shooting bench. The doghouse would have openings in both the front and the back of the house. The shooter would sight through the doghouse with the muzzle of the gun positioned inside, near the middle of the house. A true example of a "shotgun" floor plan.
By the time you make the standard assumptions and do all of the mathematical pushups, it boils down to a relationship between the size of the openings and the distance between the openings. Smaller holes are better. More distance is better.
I chose two hole sizes for a first attempt.
One "model" really looks like a doghouse. It would be made of dimension lumber and would be lined with fiberglass insulation with the unfaced surface exposed. I chose a common hole size for both ends of 6" tall by 3.5" wide (150mm tall by 90mm wide). My hope is that I would be able to align the holes with the target (and chronograph 8-) ) and not shoot up the box or bang my gun too often.
The other model uses 4" diameter holes on both ends. If this model goes to physical evaluation it will be a length of corrugated, plastic drain-tile. The corrugations will act somewhat like anti-resonance panels and abate the sound. I may roll up some coarse, fiberglass furnace filters to line the inside of the drain tile to get broader acoustic attenuation.
|So far, the length of drain tile, aka sewer pipe, is the winner in the efficiency department.|
To be continued.....