Chapter 20: Problem 24

Question:        You are standing a distance D away from an isotropic source of sound waves. You walk $\Delta D = 51.4\ {\rm m}$ toward the source and observe that the intensity of these waves has doubled. Calculate the distance D

Solution:         The intensity I at a distance r from the source is $I\ \propto\ {1\over r^2}$. Thus the ratio of intensity at two different distances is

$${I_1\over I_2} {r_2^2\over r_1^2}$$ =

$$\rightarrow\ \ {1\over 2} \left({D-\Delta D\over D}\right)^2$$ =

$$175.5\ {\rm m} \ \ \ .$$ D = (2)