2 select the correct answer from the drop - down menu. the formula \\(\\beta = 10\\log(\\frac{i}{i_0})\\) is…

2 select the correct answer from the drop - down menu. the formula \\(\\beta = 10\\log(\\frac{i}{i_0})\\) 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). the sound level on a busy street is 70 db. what is the sound intensity on the street? the sound intensity on the busy street is watts/meter². the sound intensity on the busy street is 10^-1 10^-10 10^-5 reset next
Answer
Explanation:
Step1: Substitute given values into formula
We are given $\beta = 70$ and $I_0=10^{- 12}$, and the formula $\beta = 10\log\left(\frac{I}{I_0}\right)$. So, $70 = 10\log\left(\frac{I}{10^{-12}}\right)$.
Step2: Isolate the logarithm
Divide both sides of the equation by 10: $\frac{70}{10}=\log\left(\frac{I}{10^{-12}}\right)$, which simplifies to $7=\log\left(\frac{I}{10^{-12}}\right)$.
Step3: Convert from logarithmic to exponential form
Since $\log_{10}x = y$ is equivalent to $x = 10^y$, we have $\frac{I}{10^{-12}}=10^{7}$.
Step4: Solve for $I$
Multiply both sides by $10^{-12}$: $I = 10^{7}\times10^{-12}$. Using the rule $a^m\times a^n=a^{m + n}$, we get $I=10^{7+( - 12)}=10^{-5}$.
Answer:
$10^{-5}$