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JEE Main 201912 AprilEvening Shift

Exam: JEE Main
Year: 2019
Date: 12 April
Shift: Evening Shift
Subject: Physics
Chapter: Waves and Sound

JEE Main 2019 · 12 April · Evening Shift · Physics · Waves and Sound

A small speaker delivers 2W of audio output. At what distance from...

A small speaker delivers

2W

of audio output. At what distance from the speaker will one detect

120dB

intensity sound? [Given reference intensity of sound as

{10}^{- 12}W / {m}^{2}

]

Options

A $40cm$
B $20cm$
C $10cm$
D $30cm$

Correct answer

A. $40cm$

Step-by-step solution

Let the intensity of sound hear by observer is

I

120 = 10\log_{10} \dfrac{I}{{10}^{- 12}}

12 = log I - \log_{10} {10}^{- 12}

= log I + 12

log I = 0 ⇒ I = 1\dfrac{watt}{{m}^{2}}

I = \dfrac{P}{4\pi{r}^{2}}

⇒ 1 = \dfrac{2}{4\pi{r}^{2}} ⇒ r = \dfrac{1}{\sqrt{2\pi}} = 0.4m = 40cm

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