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 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 $L = 10\log\frac{I}{I_0}$, with $I = 10^{-7}$ and $I_0=10^{- 12}$. Substitute these values: $L = 10\log\frac{10^{-7}}{10^{-12}}$.

Step2: Simplify the fraction inside the log

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

Step3: Use the log - property $\log(a^b)=b\log(a)$

Since $\log(10^{5}) = 5\log(10)$ and $\log(10)=1$, then $L = 10\times5\times1$.

Step4: Calculate the value of L

$L=50$.

Answer:

50 Db