The velocity of surface waves is approximately what fraction of the velocity of shear waves in the same material?

The velocity of surface waves, also known as Rayleigh waves, is approximately a fraction of the velocity of shear waves (S-waves) in the same material. Specifically, it has been established through theoretical analysis and empirical data that the velocity of surface waves is about 90% of the velocity of shear waves, which translates to a fraction of nine-tenths.

This relationship can be attributed to the nature of wave propagation in elastic media. Shear waves travel faster because they move the particles of the material perpendicular to the direction of wave propagation, and they require the material to resist changes in shape or shear stress. In contrast, surface waves travel along the surface, and their motion involves both vertical and horizontal displacements of the material particles. This combination of motion and the constraints of the surface environment results in a velocity that is lower than that of shear waves but reasonably close, falling in the range of 0.9 times the shear wave velocity.

Understanding this relationship is crucial for interpreting wave behavior in various materials during nondestructive testing, particularly in applications such as evaluating the integrity of structures or materials, where both surface and shear wave velocities provide insights into material properties and potential flaws.