Room Acoustics
Carpet buys you about a third of a second of reverberation in a classroom. The underlay under it buys nearly as much again.
— α
Noise reduction coefficient the construction is expected to reach
The NRC half is a regression, not physics: it was fitted over ordinary cut-pile carpet between roughly 4 and 15 mm and will mislead outside that, and it says nothing about the frequency shape — carpet absorbs the top of the band well and does almost nothing below 250 Hz, which is exactly where most room complaints live. Sabine also assumes a diffuse field and breaks down in rooms that are very dead or very long. Specify from measured ASTM C423 data when the number has to hold up; use this to decide whether a test is worth running.
Carpet Pile Density to Acoustic Absorption & Reverberation — free, with the formula and a worked example, at Textile School.