A person speaking normally produces a sound intensity of 40 ,dB a… - Vidyadip

MCQ

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 ... $m$

A
$4$
B
$5$
✓
$10 $
D
$20$

✓

Answer

Correct option: C.

$10 $

c
(c) $dB = 10{\log _{10}}\left( {\frac{I}{{{I_0}}}} \right)$; where ${I_0} = {10^{ - 12}}W{m^{ - 2}}$

Since $40 = 10{\log _{10}}\left( {\frac{{{I_1}}}{{{I_0}}}} \right)$==> $\frac{{{I_1}}}{{{I_0}}} = {10^4}$ ....$(i) $

Also $20 = 10{\log _{10}}\left( {\frac{{{I_2}}}{{{I_0}}}} \right)$ ==>$\frac{{{I_2}}}{{{I_0}}} = {10^2}$ ....$(ii) $

==> $\frac{{{I_2}}}{{{I_1}}} = {10^{ - 2}} = \frac{{r_1^2}}{{r_2^2}}$

==> $r_2^2 = 100r_1^2$==> ${r_2} = 10m$ $\{\because {r_1} = 1m\} $

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