Respuesta :
Answer:
69db
Explanation:
For a single person the intensisty is [tex]I[/tex] and the sound intensity level in decibels [tex]b[/tex], to relate this two we use the equation:
[tex]b=10ln\frac{I}{I_{0}}[/tex]
where [tex]I_{0}[/tex] is a constant: [tex]I_{0}=1x10^{-12}W/m^2[/tex], and since [tex]b=60db[/tex]
[tex]60=10ln\frac{I}{I_{0}}[/tex]
We have 8 people, so the intensity now is 8 times the intensity of a single person: [tex]8I[/tex]
and the new sound intensity that I will call [tex]B[/tex] will be:
[tex]B=10log\frac{8I}{I_{0}}[/tex]
and due to the property of the logarithm of a product: [tex]log(a*c)=log(a)+log(c)[/tex]
[tex]B=10(log\frac{I}{I_{0}}+log8 )\\B=10log\frac{I}{I_{0}} +10log8[/tex]
The first part of the right side of the equation, is the equation we found at the beginning: [tex]10log\frac{I}{I_{0}}=60[/tex]
so we substitute this value and we have:
[tex]B=60+10log8[/tex]
[tex]B=60+10(0.9)[/tex]
[tex]B=60+9[/tex]
[tex]B=69[/tex]
The sound intensity level due to 8 people is 69db
