Q. A source of sound emits $400\pi W$ power which is uniformly distributed over a sphere of $10\ m$ radius. What is the loudness of sound on the surface of a sphere
A) $200\ dB$
B) $200\ \pi\ dB$
C) $120\ dB$
D) $120\ \pi\ dB$
Explanation
(c) $Intensity = \frac{power}{area} = \frac{400\pi}{4\pi \times 10^{2}} = 1\ Watt/m^{2}$
$Now\ L = 10\log_{10}{\frac{I}{I_{0}} = 10\log_{10}\left( \frac{1}{10^{- 12}} \right)}$
$= 10\log_{10}{10^{12} = 120\ dB}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.