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In longitudinal waves, particles oscillate parallel to the direction of energy propagation, creating regions of compression and rarefaction. Sound waves are the primary example, and unlike transverse waves, longitudinal waves cannot be polarized.
From your study of wave motion, you know that a wave is a disturbance that transfers energy through a medium without transporting matter. What distinguishes longitudinal waves from transverse ones is the geometry of the disturbance. In a transverse wave — like a wave on a string — particles move perpendicular to the direction of energy flow. In a longitudinal wave, particles move back and forth along the same direction the wave is traveling. Picture a Slinky toy stretched horizontally: if you push and pull one end back and forth horizontally, you create a longitudinal wave traveling down the Slinky's length, with the coils bunching and spreading in the same axis as wave travel.
This back-and-forth motion produces two alternating regions. A compression is where particles are crowded together — local pressure is higher than the equilibrium pressure. A rarefaction is where particles are spread apart — local pressure is lower than equilibrium. These regions travel through the medium at the wave speed, carrying energy forward. The wavelength of a longitudinal wave is the distance from one compression to the next (or one rarefaction to the next), and the amplitude is the maximum displacement of a particle from its rest position. All the standard wave properties — frequency, period, wavelength, wave speed — apply to longitudinal waves exactly as they do to transverse waves.
Sound is the most important longitudinal wave. When a speaker vibrates, it alternately compresses and rarifies the air in front of it, and those pressure fluctuations travel outward in all directions as longitudinal waves. This is why sound can travel through gases, liquids, and solids — all of which can be compressed and expanded — but cannot travel through a vacuum (there are no particles to push). The speed of sound depends on the medium's elasticity (how readily it restores equilibrium) and density: denser media are harder to set in motion, while more elastic media spring back faster. Sound travels about 343 m/s in air, about 1480 m/s in water, and much faster in steel.
The inability of longitudinal waves to be polarized follows directly from their geometry. Polarization restricts the direction of particle oscillation — but for a longitudinal wave, particle motion is already locked to a single direction (along the wave travel). There is no perpendicular dimension to restrict. This distinguishes sound fundamentally from light: you can polarize light (select one plane of the transverse vibration), but no such operation exists for a longitudinal wave. This property has practical implications: optical polarizers and polarized sunglasses have no acoustic equivalent, and techniques like polarimetry that exploit transverse wave geometry do not apply to sound.