Which of the following waves is both transverse and mechanical?

The wave that is both transverse and mechanical is "water waves." Transverse waves are waves that vibrate perpendicular to the direction of the wave's motion. In the case of water waves, the water molecules move up and down, perpendicular to the direction of the wave's motion. Mechanical waves are waves that require a medium (such as air, water, or solids) to travel through. In the case of water waves, the medium is water. The water waves are created by a disturbance on the surface of the water, such as wind or a moving object. Therefore, water waves are both transverse and mechanical because they vibrate perpendicular to the direction of their motion and require a medium (water) to travel through. The other options listed are not both transverse and mechanical. Radio waves and X-rays are both examples of electromagnetic waves, which are not mechanical waves as they do not require a medium to travel through. Sound waves are mechanical waves, but they are not transverse waves as they vibrate parallel to the direction of their motion.