A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 d B intensity sound? [Given reference intensity of sound as 10 - 12 W / m 2 ]

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TestHub · Accepted Answer

Let the intensity of sound hear by observer is $I$
$120 = 10 \log_{10} \frac{I}{10^{- 12}}$
$12 = \log I - \log_{10} 10^{- 12}$
$= \log I + 12$
$\log I = 0 \Rightarrow I = 1 \frac{w a t t}{m^{2}}$
$I = \frac{P}{4 π r^{2}}$
$\Rightarrow 1 = \frac{2}{4 π r^{2}} \Rightarrow r = \frac{1}{\sqrt{2 π}} = 0.4 m = 40 c m$

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