Answer to Question #206899 in Classical Mechanics for Rae

Question

In a bath, a plane wave propagates from the shallow part towards the suddenly deep part. As it passes the interface from shallow to deep, it refracts. The angle of incidence is 22º, the angle of refraction 31º. a) In which part is the speed of sound greater and by how many percent? b) Calculate the wavelength in the shallow part if it is 5.5 cm in the deeper part!

If you could explain in detail itd be great!

Answer 1

a)

$n=\frac{\sin 31°}{\sin 22°}=1.375,$

in the deep part the speed of sound greater by $37.5\%;$

b)

$\lambda_1=n \lambda_2=1.375\cdot 5.5=7.6~cm.$