If the sound level within a room is raised from 50 dB to 60 dB , by...

The sound level in decibels is given by \beta = 10 \log_{10} \left(\dfrac{I}{I_0} \right)

The difference in sound level is $\Delta \beta = 60 - 50 = 10 \text{ dB}$

$\beta_2 - \beta_1 = 10 \log_{10} \left( \dfrac{I_2}{I_1} \right)$

10 = 10 \log_{10} \left(\dfrac{I_2}{I_1} \right)

\dfrac{I_2}{I_1} =$10$

The intensity of a sound wave is directly proportional to the square of its pressure amplitude, $I \propto P_0^2$

\left( \dfrac{P_{02}}{P_{01}} \right)^2 =\dfrac{I_2}{I_1} =$10$

\dfrac{P_{02}}{P_{01}} = \sqrt{10}