Yes, compressional waves are what sound is made of. Since there is no sound in a vacuum, it can be assumed that compressional waves only travel through matter.
You can also think of it like this: they're called compression waves because something is compressing. If there was no matter, there'd be nothing for them to compress.
Waves can transfer energy.
energy
False. EM Waves do not transfer matter, they transfer energy.
Electromagnetic waves transfer energy to matter by heating up matter and changing configuration of matter including fission, breaking matter up.
No waves do not transfer matter but it transfers only the energy
Yes, waves can and do transfer energy. When the particles vibrate, this means energy is then being transferred. However, they do not transfer matter.
radiation
No waves do not transfer matter but it transfers only the energy
light gas
Mechanical waves
radiation
compression waves the moving particles move backwards and forward in the same direction as the energy transfer.