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

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 dinner conversation with a sound intensity of $10^{-7}$?\n-58 db\n-50 db\n9 db\n50 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 dinner conversation with a sound intensity of $10^{-7}$?\n-58 db\n-50 db\n9 db\n50 db

Answer

Explanation:

Step1: Substitute values into formula

Given $L = 10\log\frac{I}{I_0}$, $I = 10^{-7}$, $I_0=10^{-12}$. Then $\frac{I}{I_0}=\frac{10^{-7}}{10^{-12}}$. Using the rule $\frac{a^m}{a^n}=a^{m - n}$, we have $\frac{10^{-7}}{10^{-12}}=10^{-7-(-12)} = 10^{5}$.

Step2: Calculate the logarithm

$L = 10\log(10^{5})$. Since $\log_{10}(a^b)=b\log_{10}(a)$ and for base - 10 logarithm $\log(10^{5}) = 5$. So $L=10\times5$.

Step3: Find the final result

$L = 50$.

Answer:

D. 50 Db