Question

A person speaking normally produces a sound intensity of $40 \,dB$ at a distance of $1 \,m$. If the threshold intensity for reasonable audibility is $20 \,dB$, the maximum distance at which he can be heard clearly is

• A. $4 \,m$
• B. $5 \,m$
• C. $10 \,m$
• D. $20 \,m$

Answer 1

Answer: (C)

$d B=10 \log _{10}\left[\frac{I}{I_0}\right]$
where $I_0=10^{-12} wm ^{-2}$
Since, $40=10 \log _{10}\left[\frac{I_1}{I_0}\right]$
$\Rightarrow \frac{I_1}{I_0}=10^4$
Also, $ 20=10 \log _{10}\left[\frac{I_2}{I_0}\right]$
$\Rightarrow \frac{I_2}{I_0}=10^2$
So, $\frac{I_2}{I_1}=10^{-2}=\frac{r_1^2}{r_2^2}$
$\Rightarrow r_2^2=100 r_1^2 $
$\Rightarrow r_2=10 \,m$