$∆\beta ={\beta }_2-{\beta }_1=10\log \frac{I_2}{I_0}-10\log \frac{I_1}{I_0}$

$=10\log \frac{I_2}{I_1}$

Increasing the intensity by a factor $10$ changes the sound level by $10 \mathrm{dB}$, increasing by 100 changes $\beta$ by $20 \mathrm{dB}$.

Since, $32 = 2^5$
 $∆\beta =5\left(10\right)=50\mathrm{ }\mathrm{d}\mathrm{B}$