In longitudinal wave, the vibration of particles will be parallel to direction of propagation of wave.
in transverse wave, the vibration of particles will be perpendicular to direction of propagation of wave.

Longitudinal Wave:
A longitudinal wave is a type of mechanical wave that propagates in the same direction as the disturbance it carries. In other words, the particles of the medium through which the wave travels oscillate parallel to the direction of the wave's propagation. This creates areas of compression and rarefaction as the wave passes through the medium.

Transverse Wave:
A transverse wave is also a type of mechanical wave, but it propagates perpendicular to the direction of the disturbance it carries. In a transverse wave, the particles of the medium oscillate perpendicular to the direction of the wave's propagation. This creates crests and troughs as the wave passes through the medium.

Key Differences:
1. Particle Motion:
- Longitudinal Wave: Particles of the medium move parallel to the direction of the wave's propagation.
- Transverse Wave: Particles of the medium move perpendicular to the direction of the wave's propagation.

2. Wave Shape:
- Longitudinal Wave: It consists of compressions and rarefactions, creating regions of high and low pressure in the medium.
- Transverse Wave: It consists of crests and troughs, creating regions of maximum displacement and equilibrium in the medium.

3. Energy Transfer:
- Longitudinal Wave: Energy is transferred parallel to the direction of the wave's propagation.
- Transverse Wave: Energy is transferred perpendicular to the direction of the wave's propagation.

4. Examples:
- Longitudinal Wave: Sound waves are an example of longitudinal waves. In a sound wave, the compressions correspond to areas of higher air pressure, while the rarefactions correspond to areas of lower air pressure.
- Transverse Wave: Light waves and water waves are examples of transverse waves. In light waves, the crests represent areas of maximum intensity, while the troughs represent areas of minimum intensity.

5. Wave Polarization:
- Longitudinal Wave: They cannot be polarized due to the nature of their particle motion.
- Transverse Wave: They can be polarized, meaning their oscillations can be confined to a single plane.

Conclusion:
Longitudinal and transverse waves exhibit distinct characteristics in terms of particle motion, wave shape, energy transfer, examples, and polarization. Understanding these differences helps in comprehending the behavior and nature of different types of waves, which have significant applications in various fields of science and technology.