Question

If the volume of a room is doubled and the total absorption is halved, the reverberation time will

• A. Remain unchanged
• B. Be doubled
• C. Become four times
• D. Be halved

Hint:

Reverberation time is directly proportional to volume and inversely proportional to absorption.

Answer 1

The Correct Option is C

Concept: According to Sabine's formula: \[ T=\frac{0.161V}{A} \] where \(T\) is reverberation time, \(V\) is volume of the room, and \(A\) is total absorption.

Step 1: Original reverberation time: \[ T=\frac{0.161V}{A} \]

Step 2: New volume is doubled: \[ V'=2V \] Total absorption is halved: \[ A'=\frac{A}{2} \]

Step 3: New reverberation time: \[ T'=\frac{0.161V'}{A'} \] \[ T'=\frac{0.161(2V)}{\frac{A}{2}} \] \[ T'=0.161(2V)\cdot \frac{2}{A} \] \[ T'=4\left(\frac{0.161V}{A}\right) \] \[ T'=4T \] Therefore, reverberation time becomes four times: \[ \boxed{\text{Become four times}} \]