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

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

Option: 1

4m


Option: 2

5m


Option: 3

10m


Option: 4

20m


Answers (1)

best_answer

dB = 10\log_{10} (\frac{I}{I_{0}})    where I_{0} = 10^{-12}W/m^{2}

Since 

        40 = 10 \log_{10} (\frac{I_{1}}{I_{0{}'}}) \implies \frac{I_{1}}{I_{0}} = 10^{4}

        20 = 10 \log_{10} (\frac{I_{2}}{I_{0}}) \implies \frac{I_{2}}{I_{0}} = 10^{2}

\therefore \frac{I_{2}}{I_{1}} = 10^{-2} = \frac{r_{1}^2}{r_{2}^2}

        {r_{2}^2} = 100 {r_{1}^2}

        {r_{2}} = 10 {r_{1}} \implies {r_{2}} = 10m

Posted by

Sayak

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