The time of reverberation of an empty hall is 1.5sec with 500 audience present in the hall,the time of reverberation falls to 1.4sec.Find the number of persons in the hall if the reverberations time falls to 1.312sec....Plsss answer this question...
Answer (1)
30th Oct, 2020
Hello Adithya
According to Sabine formula, time of reverberation t = (0.16*V)/(A*α)
Thus, For an empty room, 1.5 = (0.16*V)/(S*α)………………..[1]
Lets assume the volume of 1 person to be 1m 3
With 500 persons, 1.4 = 0.16(V – 500)/S α…………….[2]
From eq[1], S* α = 0.16V/ 1.5
Thus, on solving eq[2] , we get 1.4 = 1.5 – (500* 0.16/S α)
- 1.5 -1.4 = 500* 1.5 / V
- 0.1 = 750/V
- V = 7500
For t = 1.312, let the number of people be n
=> 1.312 = 0.16(V – n)/S α
=> 1.312 = 1.5 – (n* 1.5/7500)
=> n/5000 = 1.5- 1.312
=> n = 5000 * 0.188
=> n = 940
Hence, there are 940 persons.
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