Step 1: Understanding the Concept:
The reverberation time is the time taken for the sound pressure level to decay by 60 dB. This is calculated using Sabine's formula, which relates the volume of the hall and the total absorption.
Step 2: Key Formula or Approach:
Sabine's Formula: \( T = \frac{0.16V}{A} \)
Where:
* \( V \) = Volume of the hall (in m³)
* \( A \) = Total absorption (in metric sabins)
Step 3: Detailed Explanation:
Given: \( V = 5000 \text{ m}^3 \) and \( A = 200 \text{ sabins} \).
Substitute the values into the formula:
\[ T = \frac{0.16 \times 5000}{200} \]
\[ T = \frac{16 \times 50}{200} \]
\[ T = \frac{800}{200} = 4 \text{ s} \]
Step 4: Final Answer:
The reverberation time is 4 s.