Wave Defination :-

A wave is a disturbance which propagates energy and momentum from one place to the other without the transport of matter.

Necessary properties of the medium for wave propagation :

These are the necessary properties for a wave to propagate in a medium

(i) Elasticity : So that particles can return to their mean position, after having been disturbed.
(ii) Inertia : So that particles can store energy and overshoot their mean position.
(iii) Minimum friction amongst the particles of the medium.
(iv) Uniform density of the medium.

Characteristics of wave motion :

(i) It is a sort of disturbance which travels through a medium.
(ii) Material medium is essential for the propagation of mechanical waves.
(iii) When a wave motion passes through a medium, particles of the medium only vibrate simple
harmonically about their mean position. They do leave their position and move with the disturbance.
(iv) There is a continuous phase difference amongst successive particles of the medium i.e., particle 2
starts vibrating slightly later than particle 1 and so on.
(v) The velocity of the particle during their vibration is different at different position.
(vi) The velocity of wave motion through a particular medium is constant. It depends only on the nature of medium not on the frequency, wavelength or intensity.
(vii) Energy is propagated along with the wave motion without any net transport of the medium.

Mechanical waves :

The waves which require medium for their propagation are called mechanical waves.

Example : Waves on string and spring, waves on water surface, sound waves, seismic waves.

Non-mechanical waves :

The waves which do not require medium for their propagation are called non- mechanical or electromagnetic waves.
Examples : Light, heat (Infrared), radio waves, Gamma- rays, X-rays etc.

Transverse waves :

Particles of the medium execute simple harmonic motion about their mean position in a direction perpendicular to the direction of propagation of wave motion.

(i) It travels in the form of crests and troughs.
(ii) A crest is a portion of the medium which is raised temporarily above the normal position of rest of the particles of the medium when a transverse wave passes through it.

(iii) A trough is a portion of the medium which is depressed temporarily below the normal position of rest of the particles of the medium, when transverse wave passes through it.
(iv) Examples of transverse wave motion : Movement of string of a sitar or violin, movement of the membrane of a Tabla or Dholak, movement of kink on a rope, waves set-up on the surface of water.
(v) Transverse waves can be transmitted through solids, they can be setup on the surface of liquids. But they can not be transmitted into liquids and gases.

Longitudinal waves :

If the particles of a medium vibrate in the direction of wave motion the wave is called longitudinal.
(i) It travels in the form of compression and rarefaction.
(ii) A compression (C) is a region of the medium in which particles are compressed.
(iii) A rarefaction (R) is a region of the medium in which particles are rarefied.
(iv) Examples sound waves travel through air in the form of longitudinal waves, Vibration of air column in organ pipes are longitudinal, Vibration of air column above the surface of water in the tube of resonance apparatus are longitudinal.
(v) These waves can be transmitted through solids, liquids and gases because for these waves propagation, volume elasticity is necessary.

One dimensional wave :

Energy is transferred in a single direction only.
Example : Wave propagating in a stretched string.

Two dimensional wave :

Energy is transferred in a plane in two mutually perpendicular directions.
Example : Wave propagating on the surface of water.

Three dimensional wave :

Energy in transferred in space in all direction.
Example : Light and sound waves propagating in space.