Lecture Theatre Acoustics: Design for Occupied, Not Empty
A 20 m × 15 m × 4.0 m hall (volume 1200 m³) is being converted into a 250-seat lecture theatre. The measured unoccupied reverberation time at 500 Hz is 1.8 s. The acoustician's target for speech is 0.9–1.0 s at 500 Hz when the room is 70% occupied. The available budget allows about 110 m² of perforated acoustic panel with absorption coefficient α = 0.80 at 500 Hz, or 200 m² of heavy curtain with α = 0.40. The rear wall is 75 m², each side wall is 60 m², and the ceiling is 300 m². The fire officer will not allow combustible curtains on the rear wall. The architect proposes covering all four walls with curtain to make the room 'as absorbent as possible'. A junior designer checks only the empty-room condition and concludes that 108 m² of panel is needed. The client wants good speech intelligibility without a dead-sounding room.
1. Using the Sabine formula A = 0.161V/T, calculate the current absorption and the extra absorption needed for a 1.0 s empty-room target. Compare the panel and curtain options.
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Current absorption A₀ = 0.161 × 1200/1.8 = 107.3 m² sabins. For T = 1.0 s, required A = 0.161 × 1200/1.0 = 193.2 m². Extra absorption needed = 193.2 − 107.3 = 85.9 m² sabins. With panels, area = 85.9/0.80 = 107.4 m², just inside the 110 m² budget. With curtains, area = 85.9/0.40 = 214.8 m², which exceeds the 200 m² budget and would put combustible material on the rear wall. So on the empty-room criterion alone, panels are the only compliant option, and about 108 m² would be required.
2. The target is actually 0.9–1.0 s at 70% occupancy. Recompute the treatment needed, taking 0.35 m² sabins per occupant at 500 Hz. Which design should be adopted?
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70% of 250 seats = 175 occupants. Audience absorption = 175 × 0.35 = 61.3 m² sabins. Occupied absorption without treatment = 107.3 + 61.3 = 168.6 m², giving T = 0.161 × 1200/168.6 = 1.15 s. To reach 1.0 s, total A must be 193.2 m², so the extra needed is 193.2 − 168.6 = 24.6 m². At α = 0.80, panel area = 24.6/0.80 = 30.8 m². Adopt about 35–40 m² to allow for uncertainty, not 108 m². Designing for the empty room would over-treat the occupied room: 108 m² of panel gives occupied A = 107.3 + 61.3 + 86.4 = 255.0 m² and T = 0.76 s, below the speech target. The occupied design is both cheaper and more appropriate.
3. Evaluate the proposal to cover all four walls with curtain, and suggest a better placement strategy.
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All four walls total 280 m². At α = 0.40 that adds 112 m² sabins; with the existing 107.3 m² the empty-room T falls to 0.88 s, and with an audience it falls to about 0.69 s. That is over-absorbed for speech: the room sounds dead, performers feel they must strain, and the budget is wasted. Curtains also absorb high frequencies more than low frequencies, producing a dull imbalance, and the fire officer forbids them on the rear wall. A better strategy is targeted: treat the rear wall (75 m²) and part of one side wall with about 35–40 m² of perforated panel, leaving the ceiling and opposite wall reflective for useful early reflections and loudness. Break up parallel reflective surfaces to avoid flutter echo, and keep the treatment distributed rather than concentrated in one patch.