Robbie,
> Why don't they just place a number of static mics, say in a grid, and average them for the mid frequencies, but use static results for the low frequencies? <
It's not that simple. But you knew that already!
Acoustic labs determine absorption by measuring the reverb time in a large "echo chamber" type room with and without the absorbing material present. They do this by playing pink noise loudly through a loudspeaker, and measuring for how long the sound lingers after the noise stops. The more the reverb time is reduced at a given frequency or range, the more the material absorbs at that frequency or range.
A moving microphone is a good way to avoid the effects of standing waves at mid and high frequencies. Most people think of standing waves as occuring only at low frequencies, but in fact they occur anywhere waves arriving from opposing directions collide in the air. So the reverb time measured at one place in the room might be very different from another place, even a few inches away, because the levels can vary so much.
With a moving microphone, the tests are repeated
many times in succession, and all the results are averaged together. At IBM's lab we use each test is run 100 times. But as I already pointed out, this doesn't work well at low frequencies, partly because a room has no real reverb at low frequencies. If these labs could be made with dimensions of 50 feet, then there would be enough "real" reverb to measure.
So for low frequencies it's better to put the loudspeaker in a tri-corner, and the measuring microphone in an opposing tri-corner. This placement excites and "reads" all of the room's modes the best, which yields the most information. The downside is the only frequencies you can then assess accurately are the room's own modes. If there are modes at 50 Hz and 60 Hz but nothing in between, then you can measure an absorber's effectiveness at only 50 Hz and 60 Hz but not in between. There are standard 1/3 octave frequencies, but I don't know if it's even possible to design a room shape having modes that align with those standard frequencies. And even if you could build such a room, it would be so large that it would cost too much to build.
--Ethan