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 = 10log i/i₀, where i₀ = 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? -58 db -50 db 9 db 50 db

the loudness, l, measured in decibels (db), of a sound intensity, i, measured in watts per square meter, is defined as l = 10log i/i₀, where i₀ = 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? -58 db -50 db 9 db 50 db

Answer

Explanation:

Step1: Substitute values into formula

Given $L = 10\log\frac{I}{I_0}$, $I = 10^{-7}$ 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 log - property

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

Step4: Calculate the final value

$L=50$.

Answer:

50 Db