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

Answer 1

Answer: (C)

Loudness of sound is given by
$Db=10log\frac{I}{I_0}{(}_{Iisintensityofsound}^{I_{0}isreferenceintensityofsound})$
$\therefore$ $120=10log\left(\frac{I}{I_0}\right)$
$\Rightarrow I=1W/m^2$
Also $I=\frac{P}{4\pi r^2}=\frac{2}{4\pi r^2}$
$\therefore$ r = $\sqrt{\frac{2}{4\pi }}=\sqrt{\frac{1}{2\pi }}m=0.399m$ $\sim 40cm$