Question

A thin plane membrane separates hydrogen at 27${}^o$C from hydrogen at 127${}^o$C, both being at the same pressure. A plane sound wave enters from the cooler to the hotter side. If the angle of incidence on the membrane is 30${}^o$C, then the angle of refraction is

• A. ${\text{sin}}^{-1}\left(\frac{1}{\sqrt{3}}\right)$
• B. ${\text{sin}}^{-1}\left(\frac{2}{\sqrt{8}}\right)$
• C. ${\text{sin}}^{-1}\left(\frac{3}{\sqrt{8}}\right)$
• D. ${\text{sin}}^{-1}\left(\frac{2}{\sqrt{3}}\right)$

Answer 1

The correct option is A ${\text{sin}}^{-1}\left(\frac{1}{\sqrt{3}}\right)$

$\mu =\frac{\text{sin}i}{\text{sin}r}=\frac{v_{colder}}{v_{hotter}}$

$\Rightarrow \sqrt{\frac{T_1}{T_2}}=\sqrt{\frac{273+27}{273+127}}=\sqrt{\frac{3}{4}}$

$\therefore \text{sin}r=\sqrt{\frac{4}{3}}\times \text{sin}i=\sqrt{\frac{4}{3}}\text{sin}{30}^0=\frac{1}{\sqrt{3}}$