Waves

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Question 141 of 142

A small speaker delivers 2W2W of audio output. At what distance from the speaker will one detect 120dB120dB intensity sound? [Given reference intensity of sound as 10−12W/m2{10}^{-12}W/{m}^{2} ]

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Answer: (A) 40cm40cm

Let the intensity of sound hear by observer is II
120=10log⁡10⁡I10−12120=10{\log }_{10}⁡\dfrac{I}{{10}^{-12}}
12=log⁡⁡I−log⁡10⁡10−1212=\log ⁡I-{\log }_{10}⁡{10}^{-12}
=log⁡⁡I+12=\log ⁡I+12
log⁡⁡I=0⇒I=1wattm2\log ⁡I=0\Rightarrow I=1\dfrac{watt}{{m}^{2}}
I=P4πr2I=\dfrac{P}{4\pi {r}^{2}}
⇒1=24πr2⇒r=12π=0.4m=40cm\Rightarrow 1=\dfrac{2}{4\pi {r}^{2}}\Rightarrow r=\dfrac{1}{\sqrt{2\pi }}=0.4m=40cm

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