Question

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 1850 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 in order to undergo total internal reflection?

air concrete    

(c) "A bare concrete wall is a highly efficient mirror for sound." Give evidence for or against this statement.

Answer 1

Solution a The given quantities are as follow- speed of sound speed of sound in air= Vair= 343m)s in concrete wall a Vwall = 1850m/s To find critical angle for total internal reflection of sound at the concrete-air boundary, let us use Shell's law of refraction. - Shell's law is given as sin i = 42 sin - 42 1 Where, i angle of inädence r= angle of refraction M2= refractive index of second medium M = refractive index of first medium. Here, we know that at a critical angle angle of refraction becomes go. So l = Oca critical angle r = go put these values in equation ④

- Sin Oc singo = but, M2 ll - N V2 = speed of sound in 1st medium speed of sound in and medium sinoc singo - vi but, singo =) sinaca Oc=sini (vi) Here, V = 343 m/s = speed of sound in air - V2 = 1850m)s = speed of sound in wall & Oc= sin [348] = sin [ 0.1856) - Oca 10.68°) 11850] & critical angle would be 10.680 6 sound must be travelling I in order to undergo total reflection. in air medium internal

ter Because sound should travel into taste medium for total internal reflection. The main condition for total internal reflection is sound should travel from a medium of high refractive index to the medium of low refractive index. Here, the refractive index of air is high because speed of sound in air is less than speed of sound in concrete wall. A bare concrete wall is a highly efficient mirror for sound. - As the concrete wall being rigid, stands in equillibrium, when pressure increases due to compression and compression is pushed back by the wall as a compression in the opposite direction. Thus, compression is reflected as a compression and rare faction is reflected back as a rarefaction. . so, when sound energy is Incident on rigid wall, it will get reflected.
Answer question