The question asks which mediums can longitudinal waves propagate in, and the answer is D: all of the above, including solids, liquids, and gases. In this response, we will explain why each of these mediums can support the propagation of longitudinal waves.

Longitudinal Waves:
- Longitudinal waves are a type of mechanical wave where the particles of the medium vibrate parallel to the direction of wave propagation. This means that the particles move back and forth in the same direction that the wave is traveling.

Solids:
- Solids are one of the mediums in which longitudinal waves can propagate. This is because the particles in a solid are closely packed together and have strong intermolecular forces that hold them in place. As a result, when a disturbance is applied to one end of a solid, such as compressing or stretching it, the particles transmit the disturbance by vibrating back and forth parallel to the direction of the wave.

Liquids:
- Liquids are also capable of supporting the propagation of longitudinal waves. Although the particles in liquids are not as tightly packed as in solids, they still have enough intermolecular forces to transmit vibrations. When a longitudinal wave passes through a liquid, the particles also vibrate parallel to the direction of the wave.

Gases:
- Unlike solids and liquids, gases have particles that are widely spaced and have weak intermolecular forces. Despite this, gases can still transmit longitudinal waves. In a gas, the particles move about randomly until a wave passes through. When a longitudinal wave reaches a gas, the particles are compressed and rarefied, causing them to vibrate back and forth parallel to the direction of the wave.

Conclusion:
In summary, longitudinal waves can propagate in solids, liquids, and gases. In solids, the closely packed particles transmit the vibrations through strong intermolecular forces. In liquids, the particles are not as tightly packed but still have enough intermolecular forces to transmit vibrations. In gases, the widely spaced particles with weak intermolecular forces can still transmit longitudinal waves by compressing and rarefying as the wave passes through.