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.

Interference of Waves

Interference of Waves:

In physics, interference is the addition (superposition) of two or more waves that result in a new wave pattern.

Interference usually refers to the interaction of waves which are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency.

Constructive Interference:

During the time when one wave passes through another we say that the waves interfere. It is really not correct to say that the waves collide or hit, although this is often how such an interaction is termed.

When the crest of one wave passes through, or is super positioned upon, the crest of another wave, we say that the waves constructively interfere. Constructive interference also occurs when the trough of one wave is super positioned upon the trough of another wave.

Destructive Interference:

During the time when one wave passes through another we say that the waves interfere. It is really not correct to say that the waves collide or hit, although this is often how such an interaction is termed.

When the crest of one wave passes through, or is super imposed upon, the trough of another wave, we say that the waves destructively interfere.

Superposition:

In physics and systems theory, the superposition principle, also known as superposition property, states that, for all linear systems.