A hall has a volume of 12,500 m and reverberation time of 1.5 sec.If 200 cushioned chairs are additionally placed in the hall what will be the new reverberation time of the hall? The absorption of each chair is 1 O.W.U.
Answers
hall had a volume of 12500 m3 and reverberation time of 1.5 sec. if 200 cushioned chairs are additionally placed in the hall, what will be the new reverberation time of the hall ? the absorption of each chair is 1.0 o.w.u
Expert Answer
The new reverberation time of the hall with the additional 200 cushioned chairs is 1.31 seconds.
To calculate the new reverberation time of the hall, we need to use Sabine's formula which relates the volume, absorption coefficient and reverberation time of a room:
RT = (0.161 x V) / A
where RT is the reverberation time in seconds,
V is the volume of the room in cubic meters,
and A is the total absorption coefficient of the surfaces in the room.
Since we know the volume and the initial reverberation time of the hall, we can calculate the initial absorption coefficient A1 using the formula above:
A1 = (0.161 x V) / RT1
= (0.161 x 12500) / 1.5
= 1341.33 m²
Now that we have the initial absorption coefficient A1,
We can calculate the absorption coefficient A2 of the hall with the additional 200 cushioned chairs:
A2 = A1 + (N x S x α)
= 1341.33 + (200 x 1 x 1)
= 1541.33 m²
where N is the number of chairs,
S is the surface area of each chair,
and α is the absorption coefficient of each chair in O.W.U. (which is given to be 1).
The new reverberation time RT2 of the hall can now be calculated using Sabine's formula:
RT2 = (0.161 x V) / A2
= (0.161 x 12500) / 1541.33
= 1.31 seconds
Therefore, the new reverberation time of the hall with the additional 200 cushioned chairs is 1.31 seconds.
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