Chapter 1.1, Problem 22E

Reminder Round all answers to two decimal places unless otherwise indicated.

Note Some of the formulas below use the special number $e$, which was presented in the Prologue.

Sound Pressure and Decibels Sounds exerts a pressure $P$ on the human ear. This pressure increases as the loudness of the sound increases. If the loudness $D$ is measure in decibels and the pressure $P$ is measured in dynes per square centimeter, then the relationship is give by

$P=0.0002\times {1.122}^D$.

a. Ordinary conversation has a loudness of about $65$ decibels. What is the pressure exerted on the human ear by ordinary conversation?

b. A decibel level of $120$ causes pain to the ear and can result in damage. What is the corresponding pressure level on the ear?