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

Option: 1
$4 \mathrm{~m}$

Option: 2
$5 \mathrm{~m}$

Option: 3
$10 \mathrm{~m}$

Option: 4
$20 \mathrm{~m}$

Answers (1)

best_answer

Sound level $(\operatorname{in} \mathrm{dB})$ $\mathrm{=10 \log 10\left(\frac{I}{I_0}\right)}$ , where

$\mathrm{I_0=10^{-12} \mathrm{w} / \mathrm{m}^2}$

Since, $\mathrm{40=10 \log 10\left(\frac{I_1}{I_0}\right) \Rightarrow \frac{I_1}{I_0}=10^{4}}$ _________(1)
Also, $\mathrm{20=10 \log 10\left(\frac{I_2}{I_0}\right) \Rightarrow \frac{I_2}{I_0}=10^2}$ ____________(2)

From equation (i) and (ii) we get -

$\mathrm{ \frac{I_2}{I_1}=10^{-2}=\frac{\gamma_1^2}{\gamma_2^2} }$

$\mathrm{ \gamma_2^2=100 \gamma_1^2 }$

$\mathrm{ \gamma_2=10 \gamma_1 \Rightarrow \gamma_2=10 \mathrm{~m} \quad\left(\because \gamma_1=1 . \mathrm{m}\right)}$

Hence option 3 is correct.

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