A room contains air in which the speed of sound is 340 m s⁻¹. The walls of the room are made of concrete, in which the speed of sound is 1700 m s⁻¹. (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)
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Question

A room contains air in which the speed of sound is 340 m s⁻¹. The walls of the room are made of concrete, in which the speed of sound is 1700 m s⁻¹. (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)

Options

G1 Physics · Accepted Answer

Derived solution: Step 1: Apply Snell’s law n₁sin i = n₂sin r. For total internal reflection the ray must go from denser to rarer medium and sin C = n₂/n₁. Step 2: Substitute the values given in the question and apply the geometry/sign convention shown. Step 3: On simplification the result is C = sin⁻¹(1/5); sound must travel in concrete. Therefore the correct option is A.