Question

The ratio of intensities between two coherent sound sources is $4:1$. The difference of loudness in decibels between maximum and minimum intensities, when they interfere in space, is

• A. $10\log 2$
• B. $20\log 3$
• C. $10\log 3$
• D. $20\log 2$

Answer 1

Answer: (B)

Given $\frac{I_1}{I_2}=\frac{4}{1}$
We know
$I\propto a^2$
$\therefore \frac{a_1^2}{a_2^2}=\frac{I_1}{I_2}=\frac{4}{1}$
$\frac{a_1}{a_2}=\frac{2}{1}$
$\therefore \frac{I_{\max }}{I_{\min }}=\frac{{\left(a_1+a_2\right)}^2}{{\left(a_1-a_2\right)}^2}$
$={\left(\frac{2+1}{2-1}\right)}^2$
$={\left(\frac{3}{1}\right)}^2=\frac{9}{1}$
Therefore, difference of loudness is given by
$L_1-L_2=10\log \frac{I_{\max }}{I_{\min }}=10\log (9)$
$=10\log 3^2=20\log 3$