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  4. A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB intensity sound ? [Given reference intensity of sound as 10-12W/m2

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Q. A small speaker delivers $2\, W$ of audio output. At what distance from the speaker will one detect $120\, dB$ intensity sound ? [Given reference intensity of sound as $10^{-12}W/m^2$

JEE MainJEE Main 2019Waves

Solution:

Loudness of sound is given by
$Db = 10 log \frac {I}{I_0} \, \bigg( _{I \, is \, intensity \, of \, sound}^{I_0 \, is \, reference \, intensity\, of \, sound}\bigg)$
$\therefore $ $120 = 10\, log \bigg( \frac{I}{I_0}\bigg)$
$\Rightarrow \, \, I \, = \, 1 \, W/m^2$
Also $I \, = \, \frac{P}{4 \pi r^2} \, = \, \frac{2}{4 \pi r^2}$
$\therefore \, $ r = $\sqrt{\frac{2}{4\pi}} = \sqrt{\frac{1}{2 \pi}} m = 0.399 m$ $\sim \, 40\, cm$