Question

A person is talking in a small room and the sound intensity level is 60 dB everywhere within the room. If there are eight people talking simultaneously in the room, what is the sound intensity level?

Answer 1

69db

Step-by-step explanation:

For a single person the intensisty is
`I` and the sound intensity level in decibels
`b`, to relate this two we use the equation:

`b=10ln(I)/(I_(0))`

where
`I_(0)` is a constant:
`I_(0)=1x10^(-12)W/m^2`, and since
`b=60db`

`60=10ln(I)/(I_(0))`

We have 8 people, so the intensity now is 8 times the intensity of a single person:
`8I`

and the new sound intensity that I will call
`B` will be:

`B=10log(8I)/(I_(0))`

and due to the property of the logarithm of a product:
`log(a*c)=log(a)+log(c)`

`B=10(log(I)/(I_(0))+log8 )\\B=10log(I)/(I_(0)) +10log8`

The first part of the right side of the equation, is the equation we found at the beginning:
`10log(I)/(I_(0))=60`

so we substitute this value and we have:

`B=60+10log8`

`B=60+10(0.9)`

`B=60+9`

`B=69`

The sound intensity level due to 8 people is 69db