Depends on the type of wave.
For example, sound makes air oscillate, but the air doesn't go anywhere
Electromagnetic waves ie. microwaves, visible light, x rays, radio waves, can travel through a vacuum but if they travel through for example the air, or glass, or water they don't move the material through which they move.
Mechanical waves are waves which involve the vibration (oscillation) of the particles of the material through which they move. The particles vibrate up and down, or backwards and forwards, but are not carried along with the wave. This is part of the definition of a wave, that a wave transmits (moves along) energy, not matter, the matter, if any is involved, just vibrates.
Both light and sound travel. Light travels the fastest.
Longitudinal waves move particles of the medium parallel to the direction in which the waves are traveling. This type of wave is characterized by compressions and rarefactions in the material through which it travels. An example of a longitudinal wave is sound waves.
Light energy travels in the form of electromagnetic waves, which do not require a medium to propagate. These waves consist of oscillating electric and magnetic fields that move through space at the speed of light.
A longitudinal wave that travels through the interior of the Earth is called a P-wave. P-waves move by compressing and expanding the material they pass through, making them the fastest seismic waves and the first to be detected during an earthquake.
Compressional Waves
Transverse waves move perpendicular to the direction of the wave's motion. As the wave travels, the particles in the medium oscillate up and down or side to side. Examples of transverse waves include light waves, water waves, and seismic S-waves.
Parallel to the direction the wave travels.
Water waves are transverse waves because they move perpendicular to the direction of the wave's energy transfer. This means that the particles of water move up and down as the wave travels horizontally.
longitudinal waves
its an easy question. you know sound needs material medium to propagate {or move} and the atoms in solids are bound more closely than air. and thus when sound travels its easy for its waves to propagate through solids as the atoms {material medium} are more close than in air and on the contrary the molecules {larger parts of atoms ,who serve as material medium } of air are losely bound and its a bit harder for the waves to travel from one point to another.
Sound travels in longitudinal waves, which means that the particles of the medium move in the same direction as the wave is propagating. This is in contrast to transverse waves where the particles move perpendicular to the wave's direction.
Transverse waves move by vibrating particles perpendicular to the direction of wave propagation. This motion creates crests and troughs as the wave travels. Examples of transverse waves include electromagnetic waves like light and water waves.