A certain noise has an intensity $I$ of $1.91 \times 10^{-5}$. Given that decibel level $D$ is related to intensity by $\mathrm{D}=10 \log \left(\frac{\mathrm{I}}{\mathrm{I}_{\mathrm{O}}}\right)$, where $\mathrm{I}_{\mathrm{O}}$ is $10^{-12}$, determine the decibel level of the noise. Round your answer to the nearest decibel.
A) 7 decibels
B) 63 decibels
C) 168 decibels
D) 73 decibels

Question

Quizplus · Accepted Answer

Using the given formula $D = 10 \log \left(\frac{I}{I_0}\right)$ with $I = 1.91 \times 10^{-5}$ and $I_0 = 10^{-12}$, we calculate $D = 10 \log \left(\frac{1.91 \times 10^{-5}}{10^{-12}}\right)$. This simplifies to $D = 10 \log (1.91 \times 10^7)$, which rounds to approximately 73 decibels.

A Certain Noise Has an Intensity III Of 1.91×10−51.91 \times 10^{-5}1.91×10−5 Given That Decibel Level

A Certain Noise Has an Intensity $I$ Of $1.91 \times 10^{-5}$ Given That Decibel Level