JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Waves & Sound

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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

1 0^{- 12} W / m^{2}

]

(A)30 cm
(B)10 cm
(C)40 cm✓ Correct
(D)20 cm

Answer: (C)

Solution

From

β = 10 lo g_{10} \frac{I}{I _{0}}

with

β = 120

dB and

I_{0} = 1 0^{- 12}

W/m

^{2}

, the intensity is

I = 1

W/m

^{2}

. Treating the speaker as a point source spreading power over a sphere,

I = \frac{P}{4 π r ^{2}}

, so

1 = \frac{2}{4 π r ^{2}}

, giving

r^{2} = \frac{1}{2 π}

and

r \approx 0.40

m, about

40

cm.

JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Single correct option

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