Question

The laws of refraction and reflection are the same for sound as for light. The speed of sound in air is 340 m/s and in water it is 1510 m/s. If a sound wave approaches a plane water surface at an angle of incidence of 12.0 °, what is the angle of refraction?

Answer 1

θ = 67.4242°

Step-by-step explanation:

The law of refraction, or Snell's law, states that:

`{\text{n1} \sin (\text{$\theta $1})}={\text{n2} \sin (\text{$\theta $2})}`

With n1 = v1/c n2 = v2/c

Therefore:

`\frac{\text{v1}}{\text{v2}}=\frac{\sin (\text{$\theta $1})}{\sin (\text{$\theta $2})}`

If 1 denotes the air-side:

v1 = 340 m/s

v2 = 1510 m/s

θ1 = 12°

`\theta2 =\sin ^(-1)\left(\frac{\text{v1} \sin (\text{$\theta $1})}{\text{v2}}\right)`

θ2= 67.4242°