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William,> Is there an exact science approach possible as to where one should place traps? <Yes, and it's not really that complicated. As JLM said, you put mid/high frequency absorption at the first reflection points, and bass traps in the corners. Then you can assess if more mid/high frequency absorption is still needed. For example, if the room has large areas of bare wall you'll want a few additional panels there to prevent flutter echo between those parallel surfaces. Likewise for the ceili ...
John,> the lower frequency bass waves spread out "omnidirectionally" until they encounter a room boundary ... <Good explanation, thanks.> Another type of treatment, that is not discussed as often is wall obstructive devices <I'm not sure how that would work. You can't diffuse bass frequencies very well in a smallish room, and even if you could that won't solve the ringing which is fully half of the problem. Or do you mean something else?> do you have any type of "on wall" ...