Chapter 6.2, Problem 63E

Sound IntensityThe level of sound β (in decibels) with an intensity of I is

$\beta (I)=10{\log }_{10}\left(\frac{I}{I_0}\right)$

where I₀ is an intensity of 10–¹⁶ watt per square centimeter, corresponding roughly to the faintest sound that can be heard. Determine β(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–^6.5 watt per square centimeter (air hammer)

(d) I = 10–⁴ watt per square centimeter (threshold of pain)