Angle beam sound path, surface distance and depth

Angle-beam weld inspection is done with shear waves. The wedge refracts a compression wave in perspex into a transverse wave in the steel at 45°, 60° or 70°, and the compression component is deliberately left outside the material by keeping the incident angle above the first critical angle. Steel shear velocity is 3240 m/s; the corresponding wavelength is roughly half that of a compression wave at the same frequency, which is why angle-beam probes resolve small planar flaws so well.

Everything that follows is one right-angled triangle. The instrument displays the sound path — the slant distance from the beam index point to the reflector. Projecting that along the surface gives the surface distance, SD = SP × sin θ, and projecting it into the wall gives the depth, d = SP × cos θ. Any one of the three fixes the other two.

Two practical corrections turn the geometry into something you can chalk on the plate. The surface distance is measured from the beam index point, not from the case, so subtract the index-to-front dimension to get the projected distance from the front of the probe. And the actual refracted angle drifts as the wedge wears — verify it on a calibration block rather than trusting the label, because a 2° error at 70° moves the plotted depth of a 25 mm deep indication by about 2.4 mm.

The relationships above hold only for the first leg, before the beam reflects from the far surface. Past half skip the depth folds back and must be handled as a second-leg calculation.

SD = SP × sin θ
d  = SP × cos θ
SP = SD / sin θ = d / cos θ
projected distance from probe front = SD − x (index-to-front)