Mechanical waves are waves which propagate through a material medium (solid, liquid, or gas) at a wave speed which depends on the elastic and inertial properties of that medium. There are two basic types of wave motion for mechanical waves: longitudinal waves and transverse waves. This is a great link and shows the difference between longitudinal and transverse wave motion. if the direction of propagation is at 90 degrees to the direction of travel, the motion is transverse (water, some earthquakes, all electromagnetic) If the oscillation direction is the same as the propagation direction, the waves are longitudinal (acoustic waves). Slinky springs can be made to do both.
While you’re here, check out this site as well. There’s a lot here and we’ll return to some of it later.
Transverse waves: each particle executes SHM in the vertical plane, travel in the horizontal plane (oscillation perpendicular to propagation)
Longitudinal waves: each particle exercises SHM in the horizontal plane, in the same direction as travel.
With one important exception, all waves need a material medium to travel through – the exception being EM waves which can travel through free space.
Waves universally obey the wave equation
v or c = fλ
where v or c = velocity, f = frequency, and λ = wavelength