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

4 m

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5 m

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10 m

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20 m

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Solution

The correct option is D $10 m$
Loudness, $L = 10 l o g_{10} (\frac{I}{I_{o}})$ where $I = \frac{I_{o}}{r^{2}}$
$⟹ L = 10 l o g_{10} (\frac{1}{r^{2}})$

Thus $L_{2} - L_{1} = 10 l o g_{10} [\frac{r_{1}^{2}}{r_{2}^{2}}]$
$20 - 40 = 10 l o g_{10} [\frac{1^{2}}{r_{2}^{2}}]$
$- 2 = - 2 l o g_{10} r_{2}$
$⟹ r_{2} = 10 m$

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

The correct option is D 10mLoudness, L=10log10(IIo) where I=Ior2⟹L=10log10(1r2)Thus L2−L1=10log10[r21r22]20−40=10log10[12r22]−2=−2log10r2⟹r2=10m

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