Question

A sound wave is travelling in a medium in which the velocity is $v$. It is incident in the second medium in which the velocity of the wave is $2v$. What should be the minimum angle of incidence in the first medium, so that the wave fails to cross the surface of separation of the two media?

• A. ${60}^{\circ }$
• B. ${45}^{\circ }$
• C. ${30}^{\circ }$
• D. ${15}^{\circ }$

Answer 1

The correct option is C ${30}^{\circ }$

Using Snell's law, we get$\frac{\sin i}{\sin r}=\frac{\text{velocity in medium 1}}{\text{velocity in medium 2}}=\frac{v}{2v}$
$\therefore$ $\frac{\sin i}{\sin r}=\frac{1}{2}$

Since the wave fail to cross the surface, thus $r={90}^o$
$\frac{\sin i}{\sin {90}^{\circ }}=\frac{1}{2}$

Or $sini=\frac{1}{2}$

$⟹i={30}^{\circ }$