Question

A point source emits sound waves with an average power output of $40\pi W$, find distance at which sound reduces to level of 30 dB. $(I_{min}={10}^{-12}W/m^2)$

• A. 10 km
• B. 1 km
• C. 15 km
• D. 100 km

Answer 1

The correct option is D 100 km

$\beta =10lo{g}_{10}\left(\frac{I}{I_{min}}\right)$
$30=10lo{g}_{10}\left(\frac{I}{I_{min}}\right)\frac{I}{I_{min}}={10}^3=1000I=1000\times {10}^{-12}={10}^{-9}W/m^2$

For point source :
$I=\frac{p}{4\pi r^2}=\frac{40\pi }{4\pi r^2}=\frac{10}{r^2}$

$r^2=\frac{10}{I}=\frac{10}{{10}^{-9}}={10}^{10}$

$r={10}^5=100\times {10}^{3}m=100km$