A source of sound emits 200π W power which is uniformly distributed over

Discussion Forum : Sound

Question -

A source of sound emits $200 π$ W 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: Option D
:
D
Intensity,

I = \frac{P}{A} = \frac{200 π}{4 π \times (10)^{2}} = 0.5 W / m^{2}

Loudness =

10 l o g_{10} \frac{I}{I_{0}} = 10 l o g_{10} \frac{0.5}{10^{- 12}}

= 10 l o g_{10} (5 \times 10^{11})

= 10 l o g_{10} (\frac{10^{12}}{2})

= 117 dB

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