Question

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

• A. $10\log \left(2\right)$
• B. $20\log \left(3\right)$
• C. $10\log \left(3\right)$
• D. $20\log \left(2\right)$

Answer 1

Answer: (B)

$20\log \left(3\right)$

WKT,$a\propto I^2$

So, $\frac{I_1}{I_2}=\frac{4}{1}$

So, $\frac{a_1}{a_2}=\frac{2}{1}$

So, $\frac{a_{max}}{a_{min}}=\frac{2+1}{2-1}=\frac{3}{1}$

$\therefore \frac{I_{max}}{I_{min}}=\frac{9}{1}$

Now, loudness,$L=10\log \left(\frac{I}{I_o}\right)$

So, difference of Loudness $=L_1-L_2=$ $10\log \left(\frac{9I}{I}\right)=10\log 9$

$=20\log 3$ .