Question

A small cubical room 5.0 m on a side has all six surfaces of poured concrete. One wall has a wooden door 2.25 m × 0.75 m.

(a) What is the reverberation time of this room at 2048 Hz?

(b) Six wooden chairs are put into the room and the reverberation time at 2048 Hz changes to 5.0 s. What is the absorption, a, of one chair?

(c) What the total absorption, a, of the whole room should be in order to achieve a reverberation time of 2.0 s?

absorption coeficient for concrete 0.3

for wood 0.6

Answer 1

Answer :

Given data :

Side of room a= 5 m

Dimension of wooden door = 2.25 m x 0.75 m

Frequency = 2048 Hz

Absorption coefficient for concrete = 0.3

Absorption coefficient for wood = 0.6

So,

Volume of the room V= a³ = 5x 5x 5 = 125 m³

Total surface area of room S = 6a² = 6x 5x5 = 150 m²

Area of room without door = 148.3125 m²

Area of wooden door = 2.25 x 0.75 = 1.6875 m²

Formula for Reverberation time

   (equation 1)

where

 (equation 2)

where Total absorption = = Sum of absorption of each element.

Putting equation 2 in equation 1, we get

(equation 3)

putting the given values, we get

Solving this, we get

T = 0.4395 s

(b)

6 wooden chairs are added in this room,

Absorption coefficient of one chair =

Area of one chair =

Then, Reverberation time = 5 s

Then, we have to find absorption of 1 chair

Total absorption is the sum of absorption of each element in a room,

in our case total absorption is the sum of absorption by wall , door and 6 chairs,

So now updating equation 3, we get

(equation 4)

So, absorption by one chair =

So, By equation 4, we get

(equation 5)

putting values in equation 5, we get

Solving above equation we get

Absorption by 1 chair = -6.92 sabins

(c)

T = 2s

To find the Absorption of whole room

putting in equation 1 ,

we get

putting the values, we get

So,

Total absorption of room in this case = 10 sabins

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