Please explain in detail, the solution to this Physics problem regarding sounds

Question

Please explain in detail, the solution to this Physics problem regarding sounds (concepts and formula application if you will). I am not familiar with this topic that well. Thank you in advance!

Problem 16.11 Part A The sound level at 1.0 m from a certain talking person talking is 60 dB. You are surrounded by five such people, all 1.0 m from you and all talking equally loud at the same time. The threshold of hearing is 1.0 × 10-12 W/m2. What sound level are you being exposed to? You can neglect any absorption, reflection, or interference of the sound. The threshold of hearing is 1.0% 1012 W/m? ANSWER: 60 dB O 81 dB 74 dB 67 dB 300 dB Correct

Explanation / Answer

let I be the Intensity of sound wave due to each person,then

sound intensity level is beta = 10 dB*log(I/Io)

Io = 1*10^-12 W/m^2

then 60 dB = 10dB*log(I/10^-12)

I/10^-12 = 10^6

I = 10^-6

due to 5 persons it was 5*10^-6

then intensity level due to 5 persons is beta' = 10 dB*log*(5*10^-6/10^-12) = 67 dB

So the correct option is 67 dB

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