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Infrasonic, Ultrasonic and Audio waves

About how man...

Question

About how many times more intense will the normal ear perceive a sound of $10^{- 6}$ $W / m^{2}$ than one of $10^{- 9}$ $W / m^{2}$ ?

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Solution

Loudness of sound $L = 10 l o g_{10} \frac{I}{I_{o}}$
$⟹$ $Δ L = L_{2} - L_{1} = 10 l o g_{10} \frac{I_{2}}{I_{1}}$
Given : $I_{1} = 10^{- 9} W / m^{2}$ and $I_{2} = 10^{- 6} W / m^{2}$
$Δ L = 10 l o g_{10} \frac{10^{- 6}}{10^{- 9}}$
Or $Δ L = 10 l o g_{10} 10^{3}$
Or $Δ L = 10 \times 3 = 30$ Decibel

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