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Sound is your brain's interpretation of a certain frequency range of waves formed by oscillating media, be it a solid, liquid or gas. The waves propagate longitudinally in all three states of matter, meaning the vibrations of the medium are in the same direction as the wave is traveling, via cyclic changes of lower and higher pressure. These are called compression waves and are the only form of waves that can travel through a liquid or a gas.

As for solids, a transverse wave, meaning the vibrations of the medium are perpendicular to the direction the wave is traveling, can also occur. This is effectively done by the solid's base structures, whether they be atoms, molecules, or a crystal lattices, rubbing against each other in parallel to their surfaces. This is known as lateral displacement strain due to shear stress.

It should be said that mechanical waves in general, including those in the frequency range of sound, need a medium to travel through, unlike electromagnetic waves. This is why light can travel through a vacuum but sound can not.

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