Chapter 3.5, Problem 77E

Decibel levels. The decibel level of Professor Stout’s voice decreases with the distance from

the professor according to the formula

$L=10\log \left(\frac{4\times {10}^4}{r^2}\right),$

where $L$ is the decibel level and $r$ is the distance in feet from the professor to the listener.

a. Find the decibel levels at distances of $10,25,50$, and $100$ feet,

b. How far must a listener be from the professor so that the decibel level drops to $0$?

c. Express L in the form $L=a+b\log r$, for suitable constants a and b.

d. Express $r$

as a function of $L$.