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

Options

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

Answer

D

Explanation

Intensity,
`I=(P)/(A)=(200pi)/(4pixx(10)^2)=0.5(W)/(m^2)`
No. of decibels is given by
`10log_(10)=(I)/(I_0)=10log_(10)((0.5)/(10^-12))`
`=10log_(10)(5xx10^11)`
`10log_(10)((10^12)/(2))`
`=117dB`