Chapter 6.2, Problem 63E

Sound Intensity The level of sound $\beta$ (in decibels) with an intensity of I is $\beta (I)=10{\log }_{10}(I/I_0)$, where $I_0$ is an intensity of ${10}^{-16}$ watt per square centimeter, corresponding roughly to the faintest sound that can be heard. Determine $\beta (I)$ for the following.

(a) $I={10}^{-14}$ watt per square centimeter (whisper)

(b) $I={10}^{-9}$ watt per square centimeter (busy street comer)

(c) $I={10}^{-4}$ watt per square centimeter (threshold of pain)