The level of a sound in decibels is calculated using the formula $D = 10 \cdot \log \left( I \times 10 ^ { 12 } \right)$ where I is the intensity of the sound waves in watts per square meter. The softest sound that a human can hear has an intensity of 10-12 watts per square meter. How many decibels is that?
A) 10
B) 24
C) -12
D) 0

Question

Quizplus · Accepted Answer

The formula for calculating the level of sound in decibels is $D = 10 \cdot \log \left( I \times 10 ^ { 12 } \right)$. For the softest sound a human can hear, $I = 10^{-12}$ watts per square meter. Substituting $I$ into the formula gives $D = 10 \cdot \log \left( 10^{-12} \times 10^{12} \right) = 10 \cdot \log(1)$. Since $\log(1) = 0$, the result is $D = 10 \cdot 0 = 0$ decibels.

The Level of a Sound in Decibels Is Calculated Using D=10⋅log⁡(I×1012)D = 10 \cdot \log \left( I \times 10 ^ { 12 } \right)D=10⋅log(I×1012)

The Level of a Sound in Decibels Is Calculated Using $D = 10 \cdot \log \left( I \times 10 ^ { 12 } \right)$