Q. The ratio of intensities between two coherent sound sources is $4\ :1$. The difference of loudness in decibels $(dB)$ between maximum and minimum intensities, on their interference in space is
A) $20\ \log 2$
B) $10\ \log 2$
C) $20\ \log 3$
D) $10\ log3$
Explanation
(c) $\frac{I_{1}}{I_{2}} = \frac{4}{1} = \frac{a^{2}}{b^{2}}\therefore\frac{a}{b} = \frac{2}{1}$
$\therefore\frac{I_{\max}}{I_{\min}} = \frac{(a + b)^{2}}{(a - b)^{2}} = \frac{(2 + 1)^{2}}{(2 - 1)^{2}} = 9$
Now, $L_{1} - L_{2} = 10\log\frac{I_{\max}}{I_{0}} - 10\log\frac{I_{mim}}{I_{0}}$
$= 10\log{\frac{I_{\max}}{I_{\min}} = 10\log 9}$
$L_{1} - L_{2} = 10\log{3^{2} = 20\log 3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.