In 1885, Lord Rayleigh derived the characteristic equation for surface waves propagating on elastic solids (Rayleigh, 1885). These waves, which bear his name, have a few distinguishing properties; three will be discussed here. First, rayleigh waves are guided waves; they follow the contour of the surface they propagate on. Second, rayleigh waves are known to experience low attenuation along their propagation path. This is expected, since along the surface, the acoustic wave is propagating in what is said to be “half space”—that is, the wave propagates along the boundary between two media without interacting with any other existing boundary, such as edges or back wall. In contrast, bulk waves, such as longitudinal and transverse waves, attenuate more severely because the wave is penetrating the part where it is surrounded by the highly damped medium. Likewise, rayleigh waves attenuate exponentially with depth as the oscillating particles (or atoms) depart away from the low-damping air interface. Third, while rayleigh waves are essentially guided waves, as they inherently follow (are guided by) the contour of the surface, they differ from all other guided waves in that they are nondispersive. This is generally a well-known characteristic of rayleigh waves. Dispersion can be recognized when a wave packet, or wave envelope, begins to spread in the time domain with the distance it has traveled. A sharp pulse early from the time it was generated becomes a widespread, complicated oscillating event later in time in a dispersive regime (Figure 1). Mathematically, dispersion is recognized when the wave equation, from which the solution for the velocity may be derived, contains a variable for frequency. In the absence of this variable, the velocity is constant for all frequencies and the wave is nondis-persive. Conversely, in the presence of the frequency variable, the wave is dispersive. The different frequency components can travel at different velocities in the medium.
Kenderian, Shant, 2010, “Phase and Dispersion of Cylin-drical Surface Waves,” Research in Nondestructive Evalua-tion, Vol. 21, No. 4, pp. 224–240.
Rayleigh, Lord, 1885, “On Waves Propagated Along the Plane Surface of an Elastic Solid,” Proceedings of the London Mathematical Society, Vol. 1–17, No. 1, pp. 4–11.
Viktorov, Igor Aleksandrovich, 1958, “Rayleigh-Type Waves on a Cylindrical Surface,” Soviet Physics Acoustics, Vol. 4, No. 4, pp. 131–136.
Viktorov, Igor Aleksandrovich, 1967, Rayleigh and Lamb Waves: Physical Theory and Applications, Plenum Press, New York, NY.
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