## Waves

### Waves

1) Particles of the medium vibrate simple harmonically about their mean position.
2) Particles do not leave their mean position and the medium is not transported along with the wave.

3) With the wave, energy and momentum are transferred to the neighboring particles of the medium.

4) In a homogeneous medium, velocity of waves in all times is same. However, as particles are in SHM, their velocities at different positions/times are different.
5) There is a continuous phase difference amongst successive particles of the medium.

### Classification of waves

1) On the basis of necessity of material medium
a) Mechanical waves or elastic waves like sound waves, waves on the surface of water, waves on strings. All these waves require a material medium for propagation.
b) Electronic waves like light waves, radio waves which require no medium for propagation.

2) On the basis of vibration of particles
a) Longitudinal waves: in which particle vibrates in the direction of propagation of waves.

b) Transverse waves : in which particle vibrates in a direction perpendicular to the direction of propagation of waves.
3) On the basis of energy propagation
a) Progressive wave- along which energy is propagated.

b) Stationary waves- in which energy is confined in a particular region.

4) On the basis of dimension
a) One dimensional wave- where energy is transmitted in one single direction.

b) Two dimensional waves- where energy is transmitted along two mutually perpendicular directions.

c) Three dimensional waves- where energy is transmitted in three dimensional spaces. Some of the other type of waves we come across are shock waves, matter waves etc.

### Longitudinal waves

Longitudinal waves travel through a medium in the form of compression and rarefaction involving changes in pressure and volume. The medium required must possess elasticity of volume. Sound waves in air are longitudinal.

### Transverse waves

Transverse waves travel through a medium in the form of crests and troughs involving changes in shape. The medium required must possess elasticity of shape. Sound waves through air cannot be transverse as air does not have elasticity of shape.

### Stationary waves

When two waves of same type heaving same amplitude, same frequency and same wavelength, travelling with same speed in opposite directions along a straight line superimpose each other, they give rise to a new kind of waves, called stationary waves. The stationary waves are two types: Longitudinal stationary waves as in resonance apparatus and Transverse stationary waves as in case of sonometer.

### Nodes and antinodes in webs

Nodes and antinodes are formed in stationary waves. Nodes are the point of the medium which are permanently at rest i.e. amplitude of vibration of the particle at nodes is zero. Antinodes are the points of the medium at which amplitude of vibration of a particle are maximum. In case of longitudinal stationary waves, the pressure and density vibration are maximum at nodes and minimum at antinodes. Distance between two consecutive nodes and two consecutive antinodes is λ/2. Distance between a node and adjoining antinodes is λ/4.