Snell’s Law of Refraction for Ultrasonic Waves

Snell’s Law is a cornerstone of wave physics, originally formulated for light but equally applicable to sound waves. In ultrasonic testing, it is indispensable for designing inspections where a straight-on approach is impossible. This is most common in weld inspection, where the weld cap prevents placing a transducer directly on top. Instead, an angle beam transducer is used, which consists of a piezoelectric element mounted on a plastic wedge.

The formula [latex]\frac{\sintheta_1}{c_1} = \frac{\sintheta_2}{c_2}[/latex] dictates the behavior, where [latex]\theta_1[/latex] is the angle of incidence in the first medium (the wedge), [latex]c_1[/latex] is the sound velocity in the wedge, [latex]\theta_2[/latex] is the angle of refraction in the second medium (the test piece, e.g., steel), and [latex]c_2[/latex] is the sound velocity in the test piece. By carefully choosing the wedge angle and material, inspectors can generate a shear wave or longitudinal wave at a precise, desired angle within the test part to interrogate the weld volume effectively.

A critical aspect of this is mode conversion. When a longitudinal wave hits an interface at an angle, it can generate both a refracted longitudinal wave and a refracted shear wave, each at a different angle as predicted by Snell’s Law (since shear and longitudinal waves have different velocities). Technicians often use the generated shear wave because its shorter wavelength provides better sensitivity to small defects.