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Thermodynamic Processes

If the intens...

Question

If the intensity of sound is doubled, by how many decibels does the sound level increase ?

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Solution

We know that, $β = 10 l o g_{10} \frac{I}{I_{0}}$

According to the questions,

$β_{A} = 10 l o g_{10} \frac{I}{I_{0}}$

and $β_{B} = 10 l o g_{10} (\frac{2 I}{I_{0}})$

$\Rightarrow β_{B} - β_{A} = 10 l o g (\frac{2 I}{I})$

$= 10 \times 0.3010 = 3 d B$

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