3\ntype the correct answer in the box. use numerals instead of words.\nthe formula $\beta =…

3\ntype the correct answer in the box. use numerals instead of words.\nthe formula $\beta = 10logleft(\frac{i}{i_0}\right)$ is used to find the sound - level, $\beta$, in decibels (db), of a sound with an intensity of $i$. in the formula, $i_0$ represents the smallest sound intensity that can be heard by the human ear (approximately $10^{-12}$ watts/meter²).\nwhat is the sound intensity of a noise that is 130 db?\nthe sound intensity is $square$ watts/meter².

3\ntype the correct answer in the box. use numerals instead of words.\nthe formula $\beta = 10logleft(\frac{i}{i_0}\right)$ is used to find the sound - level, $\beta$, in decibels (db), of a sound with an intensity of $i$. in the formula, $i_0$ represents the smallest sound intensity that can be heard by the human ear (approximately $10^{-12}$ watts/meter²).\nwhat is the sound intensity of a noise that is 130 db?\nthe sound intensity is $square$ watts/meter².

Answer

Explanation:

Step1: Substitute given values into formula

Given $\beta = 130$ and $I_0=10^{- 12}$, so $130 = 10\log\left(\frac{I}{10^{-12}}\right)$.

Step2: Isolate the logarithm

Divide both sides by 10: $\frac{130}{10}=\log\left(\frac{I}{10^{-12}}\right)$, which simplifies to $13=\log\left(\frac{I}{10^{-12}}\right)$.

Step3: Convert from logarithmic to exponential form

Since $\log$ is base - 10, we have $10^{13}=\frac{I}{10^{-12}}$.

Step4: Solve for $I$

Multiply both sides by $10^{-12}$: $I = 10^{13}\times10^{-12}$. Using the rule $a^m\times a^n=a^{m + n}$, we get $I = 10^{13+( - 12)}=10^1 = 10$.

Answer:

$10$