A wave that is both mechanical and longitudinal is sound waves.
Sound waves are created by the vibration of an object, such as a speaker, which causes the air particles around it to vibrate. These vibrations then travel through the air in the form of a wave.
Sound waves are classified as mechanical waves because they require a medium, such as air, water, or solid objects, to travel through. Without a medium, sound waves cannot propagate.
Furthermore, sound waves are classified as longitudinal waves because the particles in the medium vibrate parallel to the direction of the wave. This means that as the sound wave travels, the particles in the medium move back and forth in the same direction as the wave itself.
In contrast, water waves and seismic waves are mechanical waves, but they are not longitudinal. Water waves are categorized as transverse waves because the particles in the water move up and down at right angles to the direction of the wave. Seismic waves, which include earthquake waves, can be both transverse and longitudinal, but typically the primary seismic waves are classified as transverse waves.
Lastly, light waves are not mechanical waves but rather electromagnetic waves. They do not require a medium to travel through and can propagate in a vacuum, unlike sound waves.