Question

A sound wave propagating along $x$-axis, in medium I of density ${\rho }_1=1.5kg/m^3$ is transmitted to a medium II of density ${\rho }_2=3kg/m^3$ 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)

$I=\frac{p^2}{\rho v}$
$\frac{I_2}{I_1}=\frac{p_2^2}{p_1^2}\times \frac{{\rho }_1}{{\rho }_2}\frac{v_1}{v_2}$
$=\frac{9}{16}\times \frac{1.5}{3}\times \frac{400}{1200}$
$=\frac{9}{16\times 3\times 2}=\frac{3}{32}$