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.

Vibration

Vibration:

A back and forth motion about an equilibrium position.

Vibration is occasionally "desirable". For example the motion of a tuning fork or the cone of a loudspeaker is desirable vibration, necessary for the correct functioning of the various devices.

More often, vibration is undesirable, wasting energy and creating unwanted sounds. For example, the vibration motions of engines or any mechanical device in operation are typically unwanted. Such vibrations can be caused by imbalances in the rotating parts, uneven friction, the meshing of gear teeth, etc. Careful designs usually minimize unwanted vibrations.

Types of vibration:

Free Vibration:

It occurs when a mechanical system is set off with an initial input and then allowed to vibrate freely.

Forced vibration:

It occurs when an alternating force or motion is applied to a mechanical system.