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 is ${10}^{-12}W/m^2$)

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

Answer 1

The correct option is A

$40cm$

Step 1. Given data:

Power of output audio, $P=2W$

Intensity of sound, $B=120dB$ with reference intensity $I_0={10}^{-12}W/m^2$.

Step 2. Finding distance from speaker:

$B=10{\log }_{10}\frac{I}{I_0}$

here,$I$ is the intensity

$120=10{\log }_{10}\frac{I}{{10}^{-12}}$
$12={\log }_{10}\frac{I}{{10}^{-12}}$

${10}^{12}=I\times {10}^{12}$

$\Rightarrow I=1$

Intensity equals power per unit area

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

$\Rightarrow r=\sqrt{\frac{P}{4\pi I}}=\sqrt{\frac{2}{4\times 3.14\times 1}}$

$\Rightarrow r=0.39m\approx 40cm$

Hence, option A is correct.