Can transverse waves travel through vacuum?

No, transverse waves cannot travel through a vacuum. Transverse waves, such as those found in electromagnetic waves (like light), do indeed travel through a vacuum, but this is because electromagnetic waves are not mechanical waves—they don’t require a medium.

Mechanical transverse waves, like those found in waves on a string or surface water waves, need a medium (like solid material or water) to propagate. Since a vacuum lacks any medium, these mechanical transverse waves cannot travel through it.