JEE MAIN - Physics (2019 - 12th April Evening Slot - No. 2)
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/m2
]
20 cm
10 cm
40 cm
30 cm
Explanation
Sound level = 10$${\log _{10}}\left( {{I \over {{I_0}}}} \right)$$
$$ \Rightarrow $$ 120 = 10$${\log _{10}}\left( {{I \over {{{10}^{ - 12}}}}} \right)$$
$$ \Rightarrow $$ 12 = $${\log _{10}}\left( {{I \over {{{10}^{ - 12}}}}} \right)$$
$$ \Rightarrow $$ 1012 = $${{I \over {{{10}^{ - 12}}}}}$$
$$ \Rightarrow $$ I = 1 W/m2
Also we know,
I = $${P \over {4\pi {r^2}}}$$
$$ \Rightarrow $$ 1 = $${2 \over {4\pi {r^2}}}$$
$$ \Rightarrow $$ r = 40 cm
$$ \Rightarrow $$ 120 = 10$${\log _{10}}\left( {{I \over {{{10}^{ - 12}}}}} \right)$$
$$ \Rightarrow $$ 12 = $${\log _{10}}\left( {{I \over {{{10}^{ - 12}}}}} \right)$$
$$ \Rightarrow $$ 1012 = $${{I \over {{{10}^{ - 12}}}}}$$
$$ \Rightarrow $$ I = 1 W/m2
Also we know,
I = $${P \over {4\pi {r^2}}}$$
$$ \Rightarrow $$ 1 = $${2 \over {4\pi {r^2}}}$$
$$ \Rightarrow $$ r = 40 cm
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