Longitudinal sound waves cannot propagate through

Answer: Vacuum

Longitudinal sound waves are mechanical waves, that is, they necessarily need a medium to propagate (unlike electromagnetic waves) therefore they cannot propagate in vacuum.

This is because in this type of longitudinal waves, the vibration is parallel to the propagation direction of the wave itself. These disturbances are due to the successive compressions of the medium, where the particles move back and forth in the same direction as the wave.