Three kinds of waves

WAVE - a disturbance in a medium in which a) there is no gross migration of the medium; and b) energy is transported from point A to point B.
A novel example of a wave that fits this operational definition is a stadium wave wherein people stand and then sit on cue, causing the wave to move rapidly through the stands. The pulse moves through the crowd , but the people (the medium in this example) do not move laterally at all. A stadium wave is an example of a
transverse wave in which whatever movement of the medium that exists occurs at right angles to the direction of propagation. Water waves are transverse, so, too, are stadium waves and light waves.
A second kind of wave is a
longitudinal wave, in which the displacement of the medium is parallel to the pulse moving through the medium. A homely example of a longitudinal wave is a row of domino standing on end. Pushing over the first domino causes it to fall onto the second; the second falls on the third,and so-on. It should be noted that pushing the domino in some direction perpendicular to the direction of the line form does nothing to establish a longitudinal wave. You may have noticed a second longitudinal wave if you have ever been near a railroad yard when a train has pulled out; there you have noticed that the engine starts to move first, followed one-by-one by the other cars. There is a very audible pulse that runs through the length of the train. As we shall see, sound is another example of a longitudinal wave.

This APPLET shows the difference between longitudinal and transverse waves
http://www.cbu.edu/~jvarrian/applets/waves1/lontra_g.htm

Torsional waves round out the different kinds of waves; in this scenario, the displacement of the medium is at right angles to the direction of propagation as well as perpendicular to the displacement of the other two kinds of waves. We will not do much with them; they are mentioned here for the sake of completeness. The twisting action seen on the Tacoma Narrows bridge before it collapsed was due to torsional waves.

We need to establish the definition of some new terms.

Wavelength = [symbol: lambda] the straight line distance from any point on a wave to the corresponding point on the next succeeding wave [measured in distance units, usually meters or fractions thereof].

Frequency = [symbol: f ] the number of waves that pass some observation point in 1 second [ measured in units called Hertz 1 Hz = 1/sec].
Period = [symbol T ] the time it takes one wavelength to pass the observation point [usually measured in seconds or fractions thereof] [note that f = 1/T ]
Velocity = [symbol v] the speed of a wave in a given direction [measured in conventional units for velocity]
Displacement = the distance that the medium moves from equilibrium as the wave passes through.
Amplitude = maximum displacement
Phase = two wave sources are in phase if they produce identical waves at the same time. Differences in phase are usually expressed as a phase angle.

How waves combine

Superposition = the addition of two or more waves to produce a new wave. Superposition can take one two forms: constructive interference (waves combine to form a bigger wave) and destructive interference (waves combine to form a smaller wave)