Chapter 1.8, Problem 75ES

The perceived loudness $\beta$ of a sound in decibels $\left(\text{dB}\right)$ is related to its intensity $I$ in watts per square meter $\left({\text{W/m}}^{\text{2}}\right)$ by the equation

$\beta =10\log \left(I/I_0\right)$

Where $I_0={10}^{-12}{\text{ W/m}}^2$ . Damage to the average ear occurs at $90\text{ dB}$ or greater. Find the decibel level of each of the following sounds and state whether it will cause ear damage.