How is the motion of particles in the medium different than the motion of the wave

The particles in a medium only vibrate about their equilibrium positions while the waves that they mediate travel through them, transferring vibration to more distant particles in the medium.

In transverse waves, like the waves on a string, the particles of the medium vibrate perpendicular to the direction of the waves. And in longitudinal waves, like sound waves, the particles vibrate in the direction of the wave's travel. What is important to stress about waves is that they do not transfer matter from one place to another, but only energy. The effect is analogous to that observed in a Newton's cradle: the ball manages to transfer energy to the other end without actually moving there.

the answer would be 32*f