1. Parts of a Wave
Parts

3. Parts of a Wave
The very top of a wave is called the crest. They very bottom is the trough. From one crest to the next is the wavelength. The center of the wave is the medium, or rest position. From the medium to the crest is the amplitude. The wave has two parts i.e. Crest and Trough the frequency equals
f = 1/t

4. A node is a point along a standing wave where the wave has minimal amplitude. For instance, in a vibrating guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the effective length of the vibrating string and thereby the note played. The opposite of a node is an anti-node, a point where the amplitude of the standing wave is a maximum. These occur midway between the nodes.

5. Longitudinal Waves
In a longitudinal wave the particle displacement is parallel to the direction of wave propagation. The animation below shows a one-dimensional longitudinal plane wave propagating down a tube. The particles do not move down the tube with the wave; they simply oscillate back and forth about their individual equilibrium positions. Pick a single particle and watch its motion. The wave is seen as the motion of the compressed region (ie, it is a pressure wave), which moves from left to right.

6. Longitudinal and Transverse Waves

7. Transverse Waves
In a transverse wave the particle displacement is perpendicular to the direction of wave propagation. The animation below shows a one-dimensional transverse plane wave propagating from left to right. The particles do not move along with the wave; they simply oscillate up and down about their individual equilibrium positions as the wave passes by. Pick a single particle and watch its motion.
The S waves (Secondary waves) in an earthquake are examples of Transverse waves. S waves propagate with a velocity slower than P waves, arriving several seconds later.

8. Rayleigh surface waves
[The following animation was produced with a Mathematica notebook, Rayleigh-v8.nb, which I created to investigate the behavior of Rayleigh waves which occur in solids. This Mathematica notebook contains several other graphs which further analyzer the behavior of Rayleigh waves.] Another example of waves with both longitudinal and transverse motion may be found in solids as Rayleigh surface waves (named after John W. Strutt, 3rd Baron Rayleigh). The particles in a solid, through which a Rayleigh surface wave passes, move in elliptical paths, with the major axis of the ellipse perpendicular to the surface of the solid. As the depth into the solid increases the "width" of the elliptical path decreases. Rayleigh waves are different from water waves in one important way. In a water wave all particles travel in clockwise circles. However, in a Rayleigh surface wave, particles at the surface trace out a counter-clockwise ellipse, while particles at a depth of more than 1/5th of a wavelength trace out clockwise ellispes. The movie below shows a Rayleigh wave travelling from left to right along the surface of a solid. I have identified two particles in yellow to illustrate the counterclockwise-clockwise motion as a function of depth.