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
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$\mathrm{dB} = 10 \log_{10} \left(\frac{I}{I_{o}}\right); \text{ where } I_{o} = 10^{-12} \mathrm{Wm}^{-2}$ Since $40 = 10 \log_{10} \left(\frac{I_{1}}{I_{o}}\right)$ $\Rightarrow \frac{I_{1}}{I_{o}} = 10^{4} \quad ... (i)$ Also $20 = 10 \log_{10} \left(\frac{I_{2}}{I_{o}}\right)$ $\Rightarrow \frac{I_{2}}{I_{o}} = 10^{2} \quad ....(ii)$ $\Rightarrow \frac{I_{2}}{I_{1}} = 10^{-2} = \frac{r_{1}^{2}}{r_{2}^{2}} \Rightarrow r_{2}^{2} = 100 r_{1}^{2} \Rightarrow r_{2} = 10 \mathrm{m}$ $\{ : r_{1} = 1 \mathrm{m} \}$
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