A room contains air in which the speed of sound is 343 m/s. The walls of the room are made of concrete in which the speed of sound is 1 850 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 initially traveling if it is to undergo total internal reflection? (c) ""A bare concrete wall is a highly efficient mirror for sound."" Give evidence for or against this statement.

n1 sinΘ1 = n2 sinΘ2 where n1 is the refractive index of air and n2 is the refractive index of the concrete, Θ1 is the incidence angle and Θ2 is the refracted angle also refractive index = velocity of light c / velocity of light in the medium.

(C/V1) sinΘ1 = (C/V2)sinΘ2

sinΘ1 / sinΘ2 = (C / V2) ÷ (C/V1) = (C/V2) × (V1/C) = V1 / V2

Θc is Θ1 while Θ2 must be 90o for total internal reflection to occur and sin 90 = 1

sin Θc = V1/V2 = 343 / 1850 = 0.1854

Θc = sin^-1 (0.1854) = 10.7o

b) It is must be air since air has area of low pressure and high pressure leading to pressure difference

c) A bare concrete wall is a highly efficient mirror for sound because sound wave is reflected by the wall leading to the phenomenon of echo although small part of the energy of the sound wave is absorbed by the concrete wall.