Question

A room contains air in which the speed of sound is $340$ m/s. The walls of the room are made of concrete, in which the speed of sound is $1700$ m/s.

(a) Find the critical angle for total internal reflection of sound at the concrete-air boundary.

(b) In which medium must the sound be traveling to undergo total internal reflection?(Assume sound waves follow snell's law)

Answer 1

(a) $\frac{{\mu }_{wall}}{{\mu }_{air}}=\frac{C_{wall}}{C_{air}}⟹\frac{{\mu }_{wall}}{{\mu }_{air}}=\frac{1700}{340}=5$

$⟹{\mu }_{wall}=5$ (Since, ${\mu }_{air}=1$)

Apply Snell's law to find critical angle

$5sin{\theta }_c=1sin{90}^0⟹{\theta }_c=si{n}^{-1}\frac{1}{5}$

(b) Sound must travel through air to undergo total internal reflection.