# A small speaker delivers 2W of audio output. At what distance from the speaker will one detect 120 DB intensity sound? [Given reference intensity of sound as $10^{-12}W/m^{2}]$ Option 1) 40 cm Option 2) 20 cm Option 3) 10 cm Option 4) 30 cm

S solutionqc

Sound level in decibels -

$\beta = \: \: 10 \log_{10}\left ( I/I_{0} \right ),\\for \: \: I=I_{0}\\ \beta =0$

- wherein

Where $I$ is the intensity of the sound and $I_{0}$  is a constant reference intensity = 10-12 W/m2

$I_{o}=10^{-12}w/m^{2}$

$dB=10\log \left ( \frac{I}{I_{o}} \right )= loudness$

$120=10\log \left ( \frac{I}{I_{o}} \right )$

$\frac{I}{I_{o}}=10^{12}$

$I=1 w/m^{2}$

And we know

$I=\frac{P}{A}=\frac{P}{4\pi r^{2}}=\frac{2}{4\pi r^{2}}$

so $r^{2}=\frac{2}{4\pi }$

$r= 40 cm$

Option 1)

40 cm

Option 2)

20 cm

Option 3)

10 cm

Option 4)

30 cm

Exams
Articles
Questions