Question

A small speaker delivers $2\text{W}$ of audio output. At what distance from the speaker, will one detect $120\text{dB}$ intensity sound ? [Given reference intensity of sound as ${10}^{12}{\text{W/m}}^2$]

• A. $30\text{cm}$
• B. $40\text{cm}$
• C. $10\text{cm}$
• D. $20\text{cm}$

Answer 1

The correct option is B $40\text{cm}$

Using, $\beta =10{\log }_{10}\left(\frac{I}{I_0}\right)$

$\Rightarrow 120=10{\log }_{10}\left(\frac{I}{{10}^{-12}}\right)$

$12=\log \left({10}^{12}\right)+\log \left(I\right)$

$12=12+\log \left(I\right)$

$\log I=0\Rightarrow I=1{\text{W/m}}^2$

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

$1=\frac{2}{4\pi r^2}$

$r^2=\frac{1}{2\pi }\Rightarrow r=\sqrt{\frac{1}{2\pi }}$

$\therefore r\approx 40\text{cm}$

Hence, $\left(A\right)$ is the correct answer.