Question

The African cicada is the world's loudest insect, producing a sound intensity level of 107 dB at a distance of 0.50 m. What is the intensity of its sound (in W/m2) as heard by someone standing 3.1 m away? Express your answer in watts per meter squared.

Answer 1

Answer:$0.00130 W/m^2$

Explanation:

Given

$\beta =107 db$

$d_1=0.5 m$

$d_2=3.1 m$

$I_0=10^{-12}$

sound level

$\beta =10log_{10}\frac{I_1}{I_0}$

$107=10log_{10}\frac{I_1}{10^{-12}}$

$I_1=0.05 w/m^2$

$Intensity \propto \frac{1}{distance^2}$

$\frac{I_1}{I_2}=\frac{d_2^2}{d_1^2}$

$I_2=0.00130 W/m^2$