Originally Posted by naethoven
Can you please teach me about the critical distance where reverberant sound = direct, and what the importance of it is? What do I do with it?
Don't worry about critical distance in a small room like this, especially with the treatments likely to go into a studio control room build. You really don't get much of a reverberant field (or statistical sound field) in such a small, absorptive room. It's effectively direct field anywhere you are likely to put your ears.
If you really want to calculate it, the formula is rc=square root of R/16(pi)D.
The "c" is really a subscript, meaning critical, and r means distance. This is because point sources spread spherically; the source is at the center, and the sound expands like a balloon being blown up. This means that a radius on the sphere is equal to the distance from source to receiver (listener). So r, or radius, always refers to distance.
So, r(sub)c is the critical distance - where the direct field and reverberant field meet, and the direct sound and reverberant sound are equal. Beyond the critical distance from the source, you are in the reverberant field and hear a greater proportion of reverberant sound to direct sound. Closer to the source than the critical distance, you hear more direct than reverberant. The direct field is essentially a bubble around the source. The distance is like a sphere around the point source. It's not like it's a straight line across the floor.
Inside the square root you get R (capital R this time) which is the Room Constant, divided by 16 times pi (3.14 etc.) times D, which is the directivity factor of the source. Optionally you can use "Q" which goes in the numerator instead of the denominator. Q = 4 equates to D = 1/4. The accepted Directivity factor for human speech is 1/2, or in the case of the math, a decimal value of .5 because you can't have a fraction in a fraction. For your source, you would need to know the directivity of your speakers, and if it changes significantly with distance in case the relevant distances make a difference. You also need to consider that you have two speakers radiating rather than a single source.
Next, you'll need to calculate the Room constant. You can do this with the equation R=A(sum)s/(sum)s - A, where A is the total absorption in sabins, and (sum)s, or greek symbol "sigma" s is the sum of the surface areas. This is the total area of all 4 walls plus ceiling and floor, or in your case, sum of each angled surface since it's really more than 4 rectangular walls.
You will need to calculate A to get R to get rc. To get A, take the surface area of each element times its absorption coefficient to get the number of sabins for that element, and sum all elements' absorption in sabins to get A, or total absorption in sabins. This can be written as the equation A=(sum)sa. Absorption coefficient charts for common materials can be easily found online, and values should be available for any acoustical treatments from the manufacturer.
So... all that, and critical distance really doesn't matter in a room like this. I bet if you ran the numbers, it would come out to be close to or beyond the walls. Calculations like this, including traditional RT60, especially from the Sabine equation (RT60=.049V/A), are far more useful and reliable for large room acoustics.
By the way, these equations are for American feet. For metric or SI, figures like A and R will be for meters squared instead of feet squared, critical distance will be meters rather than feet, and the Sabine equation becomes T60 (or RT60) = .16V/A, where V is volume in cubic meters and A is metric sabins calculated for meters rather than feet.