In a water immersion test on steel, an incident angle of 14 degrees yields a refracted shear angle of 31 degrees. What is the refracted angle?

• A. 45 degrees
• B. 23 degrees
• C. 31 degrees
• D. 13 degrees

Answer: (C)

The concept being tested is how a wave changes direction when crossing a boundary between two media with different speeds, described by Snell’s law for acoustic waves. When a wave goes from water into steel, the angle in steel (for the refracted shear wave) is found from sin(i)/v_water = sin(r)/v_steel_shear, where i is the incident angle in water and r is the refracted angle in steel.

Using typical speeds: v_water ≈ 1480 m/s and v_steel_shear ≈ 3200 m/s, with i = 14°, sin(14°) ≈ 0.2419. Solving for r gives sin(r) ≈ (3200/1480) × 0.2419 ≈ 0.52, so r ≈ 31°. Therefore, the refracted angle is about 31 degrees. This matches the given refracted shear angle, since that angle describes the direction of the shear wave inside the steel after refraction. The ray bends away from the normal because the wave speeds are greater in steel than in water for this mode.