(d) Let intensity of sound be I and I’.
Loudness of sound initially
$\beta_{1} = 10\log\left( \frac{I}{I_{0}} \right)$
Later,
$\beta_{2} = 10\log\left( \frac{I^{'}}{I_{0}} \right)$
Given, $\beta_{2} - \beta_{1} = 20$
$\therefore 20 = \log\left( \frac{I^{'}}{I} \right)\ $
$I^{'} = 100I$