A certain noise has an intensity I of $9.61 \times 10 ^ { - 5 }$. Given that decibel level D is related to intensity by $\mathrm { D } = 10 \log \left( \frac { \mathrm { I } } { \mathrm { I } } \right)$, where $\mathrm { I } _ { 0 }$ is $10 ^ { - 12 }$, determine the decibel level of the noise. Round your answer to the nearest decibel.
A) 184 decibels
B) 8 decibels
C) 70 decibels
D) 80 decibels

Question

Quizplus · Accepted Answer

The correct formula for calculating decibel level is $D = 10 \log \left( \frac{I}{I_0} \right)$, where $I_0 = 10^{-12}$. Substituting $I = 9.61 \times 10^{-5}$ into the formula gives $D = 10 \log \left( \frac{9.61 \times 10^{-5}}{10^{-12}} \right) = 10 \log \left( 9.61 \times 10^7 \right)$, which rounds to approximately 80 decibels.

A Certain Noise Has an Intensity I Of 9.61×10−59.61 \times 10 ^ { - 5 }9.61×10−5

A Certain Noise Has an Intensity I Of $9.61 \times 10 ^ { - 5 }$