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Question

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

Moderate

Solution

We know that $β = 10 \log_{10} \frac{I}{I_{0}}$
According to the problems $β_{A} = 10 \log_{10} \frac{I}{I_{0}}$
$\begin{array}{l} β_{B} = 10 \log_{10} (\frac{2 I}{I_{0}}) \\ β_{B} - β_{A} = 10 \log (\frac{2 I}{I}) = 10 \times 0 .3010 = 3.01 dB \end{array}$

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