Question

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

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

Answer 1

Answer: (C)

$40cm$

Loudness of sound is given by
$dB=10\log \frac{I}{I_0}$ (I is intensity of sound $I_0$ is reference intensity of sound)
$\therefore 120=10\log \left(\frac{I}{I_0}\right)$
$\Rightarrow I=1W/m^2$
Also $I=\frac{P}{4\pi r^2}=\frac{2}{4\pi r^2}$

$\therefore r=\sqrt{\frac{2}{4\pi }}=\sqrt{\frac{1}{2\pi }}m=0.399m\approx 40cm$