Waves are the propagation of particles with or without a medium. Fernando's wave is an example of a transverse wave, and x-rays, gamma rays, and UV rays are indeed examples of waves.
Transverse waves are the type of waves in which the particle oscillates in the perpendicular direction of the transmitted wave direction. The electromagnetic and the seismic waves are the type of transverse waves.
X rays, gamma rays, and ultraviolet rays are electromagnetic waves and have high energy radiations with frequency and wavelengths of their own. As electromagnetic waves are the type of waves hence they all are waves too.
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