Question

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

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

Answer 1

Answer: (C)

$dB=10{\log }_{10}\left[\frac{I}{I_0}\right]$
where $I_0=10^{-12}w{m}^{-2}$
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, $\frac{I_2}{I_1}=10^{-2}=\frac{r_1^2}{r_2^2}$
$\Rightarrow r_2^2=100r_1^2$
$\Rightarrow r_2=10m$