How can I calculate the effects a smaller volume room will have on the SPL measured in a large room?

Question

I measured 94dB from an industrial sound source (4 ft away) in a very large room (guessing 200 x 400 ft with 20 ft ceilings). I am taking that same device and placing it in a 20 ft x 22 ft room with 10 ft ceilings. Most of that sound will come back as early reflections and that will increase the perceived sound by occupants of the room by some amount. I've looked into the physics books, and I seem to grasp the concept of the intensity varying 1/R^2. But I'm not sure exactly how to calculate the increase due to the volume of the room reduction. Not looking for a science project, just a quick & dirty guestimate! Please help!

Answer 1

Check out this website. They discuss both direct and reverb loudness. It seems the steady-state reverb level depends on surface area and absorption coefficient while direct is 1/R^2 dependent. Unfortunately the symbols in their equations are not always defined right below the equation but they will be somewhere on the page. If you see a symbol that looks like 2 vertical sides and the top of a square, it's pi. Also they're not too careful about parentheses. One eq. you'll notice says
Wreverb = Wsource * (1 - a / Sa) but I'm betting it should be (1 - a) / Sa. (Otherwise they're using the fraction a/Sa which reduces to 1/S with 'a' irrelevant). Good luck. Maybe you'll find a more readable site.
P.S. Of course one major effect you'll notice if your program material extends into the deep bass is a falloff of low-frequency response below about 22 Hz. From the ref., Fcutoff = c / 2 * longest dimension, should be c / (2 * longest dimension).