Question

The intensity level of sound $A$ is $30dB$ greater than of $B$. How many times more intense is the sound $A$ than $B$?

• A. 10
• B. 100
• C. 1000
• D. 2

Answer 1

Answer: (C)

The intensity level in sound is given by
$L={\log }_{10}\frac{I}{I_0}$
where $I_0$ is initial intensity.
Given, $L_A=30+L_B$
$\therefore {\log }_{10}\frac{I_A}{I_0}=30+{\log }_{10}\frac{I_B}{I_0}$
$\Rightarrow {\log }_{10}\frac{I_A}{I_B}=3$
$\Rightarrow \frac{I_A}{I_B}=10^3$
$\Rightarrow I_A=1000I_B$
Hence, sound $A$ is $1000$ times more intense than sound $B$.