When a longitudinal wave refracts and a transverse (shear) wave is produced in the second medium, the refracted angle of the transverse wave is:

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

Answer: (B)

When a longitudinal (P) wave hits a boundary and a shear (S) wave is produced in the second medium, each wave mode follows Snell’s law with its own velocity in the second medium. The transmitted P-wave angle follows sin(theta_p2) = (v_p2 / v_p1) sin(theta_i), while the transmitted S-wave angle follows sin(theta_s2) = (v_s2 / v_p1) sin(theta_i). Here v_p2 is the longitudinal (P) velocity in the second medium and v_s2 is the shear (S) velocity in the second medium. In most solids, the P-wave speed is greater than the S-wave speed, so v_p2 > v_s2. Because both angles start from the same incident angle, a larger multiplier for the P-wave and a smaller multiplier for the S-wave result in theta_s2 being smaller than theta_p2. Therefore, the refracted angle of the transverse wave is less than the refracted angle of the longitudinal wave, with the caveat that if the S-wave cannot propagate (sin(theta_s2) would exceed 1), it becomes evanescent.