Answer to Question #103005 in Physics for Nyx

Question

A rock group is playing in a bar. Sound
emerging from the door spreads uniformly in
all directions. The intensity level of the music
is 82.6 dB at a distance of 4.21 m from the
door.
At what distance is the music just barely
audible to a person with a normal threshold
of hearing? Disregard absorption.
Answer in units of m.

Answer 1

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

$$∆L = 10\log_{10}\frac{I_2}{I_1}$$

$$∆L = 10\log_{10}\frac{r_1^2}{r_2^2}=-20\log_{10}\frac{r_2}{r_1}$$

$$r_2=r_110^{-\frac{\Delta L}{20}}$$

$$r_2=(4.21)10^{\frac{82.6}{20}}=56791\ m$$