the loudness, $l$, measured in decibels (db), of a sound intensity, $i$, measured in watts per square meter…

the loudness, $l$, measured in decibels (db), of a sound intensity, $i$, measured in watts per square meter, is defined as $l = 10\\log\\frac{i}{i_0}$, where $i_0=10^{- 12}$ and is the least intense sound a human ear can hear. what is the approximate loudness of a rock concert with a sound intensity of $10^{-1}$?\no 2 db\no 22 db\no 60 db\no 110 db

the loudness, $l$, measured in decibels (db), of a sound intensity, $i$, measured in watts per square meter, is defined as $l = 10\\log\\frac{i}{i_0}$, where $i_0=10^{- 12}$ and is the least intense sound a human ear can hear. what is the approximate loudness of a rock concert with a sound intensity of $10^{-1}$?\no 2 db\no 22 db\no 60 db\no 110 db

Answer

Answer:

D. 110 Db

Explanation:

Step1: Substitute values into formula

Given $L = 10\log\frac{I}{I_0}$, $I = 10^{-1}$, $I_0=10^{-12}$. Then $L = 10\log\frac{10^{-1}}{10^{-12}}$.

Step2: Simplify the fraction inside log

Using the rule $\frac{a^m}{a^n}=a^{m - n}$, we have $\frac{10^{-1}}{10^{-12}}=10^{-1-(-12)} = 10^{11}$. So $L = 10\log(10^{11})$.

Step3: Use log property

Since $\log(a^b)=b\log(a)$ and $\log(10) = 1$, then $\log(10^{11})=11$. So $L = 10\times11=110$ Db.