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. A jackhammer puts out 1 watt per square meter. How many decibels is that?
A) 12
B) 10
C) 120
D) 1200

Question

Quizplus · Accepted Answer

The formula for calculating the level of sound in decibels is $D = 10 \cdot \log \left( I \times 10 ^ { 12 } \right)$. Substituting $I = 1$ watt per square meter into the formula gives $D = 10 \cdot \log \left( 1 \times 10^{12} \right) = 10 \cdot \log \left( 10^{12} \right)$. Since $\log \left( 10^{12} \right) = 12$, the calculation is $D = 10 \cdot 12 = 120$ 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 $D = 10 \cdot \log \left( I \times 10 ^ { 12 } \right)$