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Loudness

A source of s...

Question

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

70dB

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107dB

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80dB

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112dB

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Solution

The correct option is B 112dB
Intensity is given by:
$I = \frac{W}{4 π r^{2}}$
$I = \frac{200}{4 π \times 100} = 0.159 W / m^{2}$
In terms of decibels, $I = 10 {log}_{10} I + 120 d B$
$I = 112 d B$

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