A longitudinal ultrasonic wave is transmitted from water into steel at an angle of 5 degrees from the normal. The refracted angle of the transverse wave is

• A. Less than the refracted angle of the longitudinal wave
• B. Greater than the refracted angle of the longitudinal wave
• C. Not present at all
• D. Equal to the refracted angle of the longitudinal wave

Answer: (A)

When a wave passes from a liquid into a solid, the refraction angles follow Snell’s law for the specific wave speeds in each medium. In steel, the longitudinal (P) wave travels much faster than the transverse (S) wave, while in water the speed is about 1480 m/s for the incident longitudinal wave. Using Snell’s law, sin of the refracted angle equals the speed in the second medium divided by the speed in the first medium, times sin of the incident angle. For the longitudinal wave in steel, sin theta_t ≈ (5900/1480) * sin(5°) ≈ 0.35, giving theta_t ≈ 20°. For the transverse wave in steel, sin theta_t ≈ (3200/1480) * sin(5°) ≈ 0.19, giving theta_t ≈ 11°. Since 11° is smaller than 20°, the refracted angle of the transverse wave is less than that of the longitudinal wave. This is why the correct choice states the transverse refracted angle is smaller.