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.