Question

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

• A. 10 log2
• B. 20 log 3
• C. 10 log 3
• D. 20 log 2

Answer 1

The correct option is B

20 log 3

$\frac{I_1}{I_2}=\frac{4}{1}$ or $\sqrt{\frac{I_1}{I_1}}=\frac{2}{1}$

$\therefore \frac{I_{max}}{I_{min}}={\left(\frac{\frac{\sqrt{I_1}}{I_2}+1}{\sqrt{\frac{I_1}{I_2}}-1}\right)}^2={\left(\frac{2+1}{2-1}\right)}^2=9$

$\therefore L_1-L_2=10log\frac{I_{max}}{I_0}-10log\frac{I_{min}}{I_0}$

$=10log\frac{I_{max}}{I_{min}}=10log\left(9\right)=20log3$