Question

A sound wave propagating along $x$-axis, in medium I of density $\rho_{1}=1.5 \,kg / m ^{3}$ is transmitted to a medium II of density $\rho_{2}=3\, kg / m ^{3}$ as shown.

The equation of excess pressure developed by wave in medium I and that in medium II respectively are
$p_{1}=4 \times 10^{-2} \cos \omega\left(t-\frac{x}{400}\right) $ (in SI units)
$p_{2}=3 \times 10^{-2} \cos \omega\left(t-\frac{x}{1200}\right) $ (in SI units)
Then the ratio of intensity of transmitted wave $I_{2}$ (wave in medium II) to the intensity of incident wave $I_{1}$ (wave in medium I), that is, $\frac{I_{2}}{I_{1}}$ is

• A. $\frac{3}{4}$
• B. $\frac{9}{16}$
• C. $\frac{3}{32}$
• D. None of these

Answer 1

Answer: (C)

$I=\frac{p^{2}}{\rho v}$
$\frac{I_{2}}{I_{1}}=\frac{p_{2}^{2}}{p_{1}^{2}} \times \frac{\rho_{1}}{\rho_{2}} \frac{v_{1}}{v_{2}}$
$=\frac{9}{16} \times \frac{1.5}{3} \times \frac{400}{1200}$
$=\frac{9}{16 \times 3 \times 2}=\frac{3}{32}$