Question

The ratio of intensities between two coherent sound source is 4 : 1. The difference of loudness in decibels (dB) 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: (D)

20 log 2

Answer 2

$\frac{\nu_{1}}{\nu_{2}}$ = $\frac{\frac{1}{2\mathcal{l}}\sqrt{\frac{T_{1}}{\mu_{1}}}}{\frac{1}{2\mathcal{l}}\sqrt{\frac{T_{2}}{\mu_{2}}}}$ = $\sqrt{\frac{T_{1}}{T_{2}}\frac{\mu_{2}}{\mu_{1}}}$

= $\sqrt{\frac{T_{1}}{T_{2}}\frac{\rho_{2}A_{2}}{\rho_{1}A_{1}}}$ = $\sqrt{\frac{T_{1}}{T_{2}}\frac{\rho_{2}\pi{r_{2}}^{2}}{\rho_{1}\pi{r_{1}}^{2}}}$

= $\left( \frac{T_{1}}{T_{2}} \right)^{1/2}$ $\left( \frac{\rho_{2}}{\rho_{1}} \right)^{1/2}$ $\left( \frac{r_{2}}{r_{1}} \right)$