The question asks us to identify the wave that does not belong to the same category as the others. The waves mentioned in the options are X-rays, microwaves, radio waves, and sound waves.

X-rays, microwaves, and radio waves are all types of electromagnetic waves. They have similar properties such as being able to travel through space, having a wide range of frequencies, and being able to carry energy and information. They differ mainly in their frequencies and wavelengths.

However, sound waves are not electromagnetic waves. They are mechanical waves that require a medium, such as air or water, to travel through. Sound waves are produced by vibrating objects, and they require a medium to transmit the vibrations from the source to our ears. Sound waves have properties like frequency, wavelength, amplitude, and speed.

Therefore, sound waves do not belong to the same category as X-rays, microwaves, and radio waves. They are different types of waves, with different properties and mechanisms of propagation.

In conclusion, option 4 - sound waves - does not belong to the category of the other three waves mentioned in the question.