Chapter 4.3, Problem 96PE

Sounds are produced when vibrating objects create pressure waves in some medium such as air. When these variations in pressure reach the human eardrum, it causes the eardrum to vibrate in a similar manner and the ear detects sound. The intensity of sound is measured as power per unit area. The threshold for hearing (minimum sound detectable by a young, healthy ear) is defined to be $I_0={10}^{-12}\text{W}/{\text{m}}^2$ (watts per square meter), The sound level L, or “loudness” of sound, is measured in decibels (dB) as $L=10\text{ log}\left(\frac{I}{I_0}\right)$, where I is the intensity of the given sound. Use this formula for Exercises 95–96.

a. Find the sound level of a motorcycle if its intensity is ${10}^{10}\text{ times }{I}_0$.

b. Find the sound level of a vacuum cleaner if its intensity is ${10}^7\text{ times }{I}_0$.

c. How many times more intense is the sound of a motoreycle than a vacuum cleaner?