Question

A rock group is playing in a bar. Sound

Answer 1

Answer:

5292.64 m

Explanation:

$dB \rightarrow \textrm{sound level}\\ I \rightarrow \textrm{sound intensity}\\ I_0 \rightarrow \textrm{threshold sound intensity}\\ x \rightarrow \textrm{distance of corresponding to threshold intensity of hearing}$

Taking threshold intensity as $1\times 10^{-12} W/m^{2}$ and since it's a constant then sound intensity for 66.7 dB will be

$66.7\;\rm dB = 10\; log_{10}\;\left(\dfrac{I}{I_0} \right)\\ \dfrac{I}{10^{-12}} = 10^{6.67}\\ I = 4.67735\times 10^{-6}\;\rm W/m^2\\ \boxed{I \approx 4.7\times 10^{-6}\;\rm W/m^2}$

Also, since sound intensity is inversely proportional to the square of the distance of the source then the distance can be given by

$\dfrac{I_1}{I_2} = \dfrac{r^2_2}{r^2_1}\\ \dfrac{4.7\times 10^{-6}\;\rm W/m^2}{10^{-12}\;\rm W/m^2} = \dfrac{x^2\;\rm m}{(5.96\;\rm m)^2}\\ x =\sqrt{28012000}\\ \boxed{x \approx 5292.64;\rm m}$