Classroom Reverberation Priced per Intelligible Seat: An Absorption Bound for a Bare-Walled Room

A bare-walled classroom of 180 cubic metres has a reverberation time well above the level at which a teacher's speech remains clear at the back row. Using the Sabine relation, this paper computes the absorption required to reach 0.6 seconds, prices woven fibre panels that supply it, and states the cost per seat. The design meets the target on paper; rooms with hard parallel walls and flutter echo will do worse than the diffuse-field model states, and that limit is printed. Computed results: RT_bare_s = 1.96, A_bare_sab = 14.8, A_req_sab = 48.3, panel_area_m2 = 44.7, cost_usd = 491.33, RT_design_s = 0.6, cost_per_seat_usd = 12.28. Every number in this paper is produced by the accompanying script `compute.py`. SIMULATED, NOT MEASURED.