Chapter 5.2, Problem 84E

Sound Intensity The relationship between the number of decibels $\beta$ and the intensity of a sound $I$ (in watts per square meter) is

$\beta =10\log \frac{I}{{10}^{-12}}.$

$\left(\text{a}\right)$ Determine the number of decibels of a sound with an intensity of $1$ watt per square meter.

$\left(\text{b}\right)$ Determine the number of decibels of a sound with an intensity of ${10}^{-2}$ watt per square meter.

$\left(\text{c}\right)$ The intensity of the sound in part $\left(\text{a}\right)$ is $100$ times as great as that in part $\left(\text{b}\right)$ . Is the number of decibels $100$ times as great? Explain.