If the intensity is increased by a factor of 20, then how many decibels in the sound level will increase?…
If the intensity is increased by a factor of 20, then how many decibels in the sound level will increase? [AIIMS 2015]
18
13
9
7
Solution
Let the initial intensity be $I$ and corresponding decibels level be $\beta_1$. When intensity is increased to $20 I$, let the corresponding increase in decibels level be $\beta_2$. Thus,
$\beta_1 = 10 \log (I / I_0)$ and $\beta_2 = 10 \log \frac{20 I}{I_0}$
$\Rightarrow \beta_2 - \beta_1 = 10 \log \left(\frac{20 I}{I}\right) = 10 \log 20 = 13\text{ dB}$