How many times more intense is a $60 d B$ sound than a $30 d B$ sound?

1000

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2

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100

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4

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Solution

The correct option is D $1000$
Loudness of two sounds are given as $L_{2} = 60 d B$ and $L_{1} = 30 d B$
Loudness of sound $L = 10 {log}_{10} \frac{I}{I_{o}}$
$⟹$ $L_{2} - L_{1} = 10 {log}_{10} \frac{I_{2}}{I_{1}}$
Or $60 - 30 = 10 {log}_{10} \frac{I_{2}}{I_{1}}$
Or ${log}_{10} \frac{I_{2}}{I_{1}} = 3$
Or $\frac{I_{2}}{I_{1}} = 10^{3} = 1000$
Thus $60 d B$ sound is $1000$ times more intense than $30 d B$ sound.

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