Mechanical Waves
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There are only two fundamental mechanisms for transporting energy
and momentum: a streaming of particles and a flowing of waves.
And even these two seemingly opposite conceptions are subtly intertwined -
there are no waves without particles and no particles without waves.
(From the latter we only get a glimpse, when we talk about some specific properties of light.) In general a wave is a moving self-sustained disturbance of a medium, and that medium can be either a field (e.g. the gravitational field) or a substance (a solid or fluid). Here, the focus is on waves in a material media, and these are known as mechanical waves . First we need to consider
Harmonic Motion Consider an object - a bell, a rope, or even the earth. Each is a vast collection of atoms forming an essentially continous elastic medium. Within limits, if the atoms in a material are pushed together, they repel, and, if separated, they attract. Electrically interacting, the atoms behave as if they are connected to one another via springs. As a result of this, once displaced, the medium tries to return to its equilibrium state. Only the state of being displaced moves through the medium as wave. The disturbance of a medium under the influence of a restoring force (like the springs) is common to all mechanical waves. Thus we need to consider
Traveling WavesFor a summary on waves, watch Waves: Light, Sound, and the nature of Reality
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Ch. Elster