Explanation:
To find the reverberation time of the hall, we can use the Sabine's Formula:
RT = 0.049 (V / A)
Where:
RT = Reverberation Time (seconds)
V = Volume of the hall (ft³)
A = Total absorption (ft²)
First, let's calculate the volume of the hall:
V = Length × Width × Height = 70 ft × 40 ft × 15 ft = 42,000 ft³
Next, let's calculate the total absorption:
A = (Plastered surface area × Absorption coefficient) + (Number of adults × Absorption per adult)
Plastered surface area = 2 × (Length × Width + Width × Height + Height × Length) = 2 × (2800 + 600 + 1050) = 2 × 4450 = 8900 ft²
A = (8900 ft² × 0.1) + (100 adults × 4.7 ft²) = 890 ft² + 470 ft² = 1360 ft²
Now, we can plug in the values to Sabine's Formula:
RT = 0.049 (42,000 ft³ / 1360 ft²) ≈ 1.53 seconds
So, the reverberation time of the hall is approximately 1.53 seconds.
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