select the correct answer from the drop - down menu. the sound level, β, in decibels (db), of a sound with…

select the correct answer from the drop - down menu. the sound level, β, in decibels (db), of a sound with an intensity of i is calculated in relation to the threshold of human hearing, i₀, by this equation. β = 10log(\\frac{i}{i₀}) the threshold of human hearing is 10⁻¹² watts/meter². the sound level of a jet plane is approximately 140 db. the intensity of the sound of a jet plane is approximately watts/meter².

select the correct answer from the drop - down menu. the sound level, β, in decibels (db), of a sound with an intensity of i is calculated in relation to the threshold of human hearing, i₀, by this equation. β = 10log(\\frac{i}{i₀}) the threshold of human hearing is 10⁻¹² watts/meter². the sound level of a jet plane is approximately 140 db. the intensity of the sound of a jet plane is approximately watts/meter².

Answer

Explanation:

Step1: Substitute given values into formula

Given $\beta = 140$ and $I_0=10^{- 12}$, so $140 = 10\log\left(\frac{I}{10^{-12}}\right)$.

Step2: Isolate the logarithm term

Divide both sides by 10: $\frac{140}{10}=\log\left(\frac{I}{10^{-12}}\right)$, which gives $14=\log\left(\frac{I}{10^{-12}}\right)$.

Step3: Convert from logarithmic to exponential form

Since $\log_{10}x = y$ is equivalent to $x = 10^y$, we have $\frac{I}{10^{-12}}=10^{14}$.

Step4: Solve for $I$

Multiply both sides by $10^{-12}$: $I = 10^{14}\times10^{-12}$. Using the rule $a^m\times a^n=a^{m + n}$, we get $I = 10^{14-12}=10^{2}=100$.

Answer:

100