Skip distance is proportional to which trigonometric function of the refraction angle?

• A. sine of theta
• B. cosine of theta
• C. tangent of theta
• D. cotangent of theta

Answer: (C)

Skip distance in ultrasonics comes from the sideways shift caused by refraction as the wave travels to a reflector beneath the surface. If the reflector is at depth d and the refracted ray inside the material makes an angle θ with the normal, the horizontal displacement along the surface is x = d tan(θ). That means the skip distance is proportional to the tangent of the refraction angle. As the angle grows, tan(θ) grows, so the skip distance increases; when θ is small, skip distance is small, and it grows rapidly as the angle approaches grazing incidence. Sine would relate to the length of the ray path, not the lateral offset, and cosine would relate to the depth component along the ray, not the horizontal shift, so tan is the correct relationship.