A small speaker delivers $2\, W$ of audio output. At what distance from the speaker will one detect $120\, dB$ intensity sound ... $cm$ ? [Given reference intensity of sound as $10^{-12}\,W/m^2$]
JEE MAIN 2019, Diffcult
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Loudness of sound is given by
$\mathrm{dB}=10 \log \frac{I}{\mathrm{I}_{0}}$ ($I$ is intensity of sound, $I_0$ is reference intensity of sound)
$120=10 \log \left(\frac{I}{I_{0}}\right)$
$\Rightarrow I=1 \mathrm{W} / \mathrm{m}^{2}$
Also, $\mathrm{I}=\frac{\mathrm{P}}{4 \pi \mathrm{r}^{2}}=\frac{2}{4 \pi \mathrm{r}^{2}}$
$\therefore r=\sqrt{\frac{2}{4 \pi}}=\sqrt{\frac{I}{2 \pi}} \mathrm{m}=0.399 \mathrm{m}$
$\approx 40 \mathrm{cm}$
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