Question

A source of sound emits $200\pi$ W power which is uniformly distributed over a sphere of radius $10m$. What is the loudness of sound on the surface of the sphere?

• A. 70 dB
• B. 107 dB
• C. 80 dB
• D. 117 dB

Answer 1

The correct option is D 117 dB

Intensity,
$I=\frac{P}{A}=\frac{200\pi }{4\pi \times (10{)}^2}=0.5W/m^2$
Loudness = $10lo{g}_{10}\frac{I}{I_0}=10lo{g}_{10}\frac{0.5}{{10}^{-12}}$
$=10lo{g}_{10}(5\times {10}^{11})$
$=10lo{g}_{10}\left(\frac{{10}^{12}}{2}\right)$
= 117 dB