Wave

Wave:

A wave is a disturbance that propagates through space and time, usually with transference of energy. Waves travel and transfer energy from one point to another, often with little or no permanent displacement of the particles of the medium (that is, with little or no associated mass transport); instead there are oscillations around almost fixed locations.

All waves have common behavior under a number of standard situations. All waves can undergo the following:

Reflection — change in wave direction after it strikes a reflective surface, causing the angle the wave makes with the reflective surface in relation to a normal line to the surface to equal the angle the reflected wave makes with the same normal line.

Refraction — change in wave direction because of a change in the wave's speed from entering a new medium.

Diffraction — bending of waves as they interact with obstacles in their path, which is more pronounced for wavelengths on the order of the diffracting object size.

Interference — superposition of two waves that come into contact with each other (collide).

Dispersion — wave splitting up by frequency.

Rectilinear propagation — the movement of waves in a straight line, in the absence of any obstacles or change in media.

Absorption — the wave energy is converted into some other form of energy, such as heat.

Formula:

The general solution for the wave equation in one dimension was given by d’Alembert; it is known as d’Alembert’s formula:

u ( x , t ) = F ( x – vt ) + G ( x + vt )

This formula represents two shapes traveling through the medium in opposite directions; F in the positive x direction, and G in the negative x direction, of arbitrary functional shapes F and G.