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We know that ultraviolet light, X-rays and gamma rays have wavelengths shorter than visible light.
"shorter"
You mean as opposed to those late afternoon sunrises? Sunrises and sunsets are shifted towards the red end of the spectrum because the atmosphere scatters shorter wavelengths more effectively. Because of the angle, light at sunrise and sunset is going through a thicker "slice" of the atmosphere, and the shorter wavelengths get scattered out, while the longer reds and oranges make it through.
they get shorter
The wavelengths of incoming solar radiation are shorter than the wavelengths of reradiated heat.
X-rays have shorter wavelengths than radio, heat, infra-red, visible light, and ultra-violet.
Infrared rays have a shorter wavelength than microwaves and radio waves. All are examples of electromagnetic radiation.
Ultraviolet and up have shorter wavelengths.
This is the ultraviolet light.
Shorter wavelengths have more energy E= hc/w and this greater energy can do greater damage by ionizing atoms and changing chemical reactions and changing atoms even the Nucleus.
I'll answer your question for a variety of waves. For sound waves, higher pitch sounds have higher frequencies and shorter wavelengths. For water waves, the slowest moving waves have higher frequencies and shorter wavelengths. For seismic waves, S waves have higher frequencies and shorter wavelengths than P waves. For electromagnetic waves, X-rays and gamma rays have higher frequencies and shorter wavelengths than, say, visible light. For quantum mechanical, de Broglie waves, particles with classical analogues of momentum have higher frequencies and shorter wavelengths than individual particles.
The answer depends on "compared to what"? UV wavelengths are shorter than x-rays and longer than microwaves.