Question

The sound level at a point is increased by 30 dB. By what factor is the pressure amplitude increased?

• A. 30
• B. In 30
• C. 32
• D. 3

Answer 1

The correct option is C

32

The sound level in dB is

$\beta =10lo{g}_{10}\left(\frac{I}{I_0}\right)$

If ${\beta }_1$ and ${\beta }_2$ are the sound levels and $I_1$ and $I_2$ are the intensities in the two cases,

${\beta }_2-{\beta }_1=10\left[lo{g}_{10}\right(\frac{I_2}{I_0})-lo{g}_{10}(\frac{I_1}{I_0}\left)\right]$

or,$30=10lo{g}_{10}\left(\frac{I_2}{I_0}\right)$

or,$\frac{I_2}{I_1}={10}^3$

As the intensity is proportional to the square of the pressure amplitude,we have $\frac{p_2}{p_1}=\sqrt{\frac{I_2}{I_1}}=\sqrt{1000}\stackrel{\sim }{\sim }32$