Question

A small speaker delivers $3W$ of audio output. The distance from the speaker where one can detect $120dB$ intensity sound is $\alpha$. Write the value of $100\alpha$.
[Given reference intensity of sound as $10^{-12}W{m}^{-2}($ in m) Take $\frac{3}{\pi }=0.96,\sqrt{0.96}=0.98$

Answer 1

Answer: 49

Given, audio output $=3W$
Intensity, $I=120dB$
$I_0=10^{-12}W/m^2$
From loudness relation,
$dB=10log\frac{I}{I_0}$
$\Rightarrow 120=10log\left(\frac{I}{{\left(10\right)}^{-12}}\right)$
$\Rightarrow 10I=10$
$\Rightarrow I=1W/m^2$
Final intensity $=\frac{P}{4\pi r^2}$
$\Rightarrow I=\frac{P}{4\pi r^2}$
$\Rightarrow r=\sqrt{\frac{3}{4\pi (1)}}=\frac{0.98}{2}=0.49m=\alpha$