Rayleigh (surface) wave velocity

A Rayleigh wave travels along a free surface with an elliptical particle motion that dies away exponentially with depth. Its velocity is slightly below the shear velocity of the same material and depends only on Poisson's ratio, closely approximated by c_R ≈ c_S (0.87 + 1.12ν) / (1 + ν). For steel this gives about 0.92–0.93 of the shear velocity — roughly 2990 m/s.

Surface waves are generated just beyond the second critical angle, where the refracted shear wave has reached 90°. In practice a wedge angle a degree or two above the second critical angle is used. They follow gentle curvature, which makes them useful around fillet radii, bolt threads, turbine blade roots and shaft shoulders where a bulk beam cannot be aimed.

The energy is concentrated within about one wavelength of the surface, so the effective inspection depth is set by frequency alone. At 2 MHz in steel one Rayleigh wavelength is about 1.5 mm; at 5 MHz it is about 0.6 mm. That makes them very sensitive to surface-breaking cracks and equally sensitive to anything else on the surface — scale, weld spatter, a finger, or the couplant itself will all attenuate or reflect the wave, so the surface must be clean and dry ahead of the probe.

Because a Rayleigh wave reflects strongly from a surface-breaking crack and from any sharp edge, the technique needs a careful calibration on a notch of known depth and a clear understanding of where the component's edges are.

c_R ≈ c_S · (0.87 + 1.12·ν) / (1 + ν)
ν = (c_L² − 2c_S²) / [ 2 (c_L² − c_S²) ]  when not entered directly
λ_R = c_R / f
Effective depth ≈ 1 λ_R