The second statement is NOT true - they transfer matter. The energy of a mechanical wave can travel only through matter. The matter through which the wave travels is called the medium. When waves travel through a medium, they don't carry the medium with them.
The medium of a mechanical wave can be any state of matter, even a solid.
There are three types of mechanical waves: transverse, longitudinal, and surface waves. They differ in how particles of the medium move. You can see this in the side figure and in the animation at the following URL: http://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html.
In a transverse wave, particles of the medium vibrate up and down perpendicular to the direction of the wave.
In a longitudinal wave, particles of the medium vibrate back and forth parallel to the direction of the wave.
In a surface wave, particles of the medium vibrate both up and down and back and forth, so they end up moving in a circle.
Get the best free study tips and strategies that will help you to perform better on tests and achieve higher grades from TestTakingTips.com.