 # Wave Motion

What is Wave Motion?

The wave motion is defined as the propagation of a disturbance or perturbation in the medium and it is due to the repeated periodic movements of the particles of the medium about their mean positions.The wave motion is one of the important methods of transferring energy.The wave carries energy but there is no transport of matter.

For Example: when the stone is dropped in the still water, it creates disturbance which propagates outwards. In this propagation water molecules do not move outward with the wave. If there is any floating object, it will move up or down near its own location, indicating that the water molecule do not move along with the wave. The disturbance which is over the short time is called as Pulse.

### Some Important Properties of Wave Motion are:

• It is the disturbance produced in the medium by periodic motion of medium particle.
• It is the wave which comes forward. There is no bodily movement. They simply vibrate about their mean positions.
• In any medium the velocity of the wave is uniform.
• There is the regular phase difference between the particles of medium.

### Types of Waves:

There are various types of waves in nature having different forms and properties. Waves can be classified into following categories.

1. #### Waves are of two types:

• Transverse waves: Those waves in which the displacement of the particles is at the right angles to the direction of propagation of wave, the medium.

For Example; Light waves, ripples on the surface of water and waves on the string.

• Longitudinal Waves:Those waves in which the particles of the medium vibrate (or oscillate) about their mean position along the same line as that of the propagation of the wave.

For Example; sound waves in air, waves in a spring.

#### 2.  Another category of waves are:

• Traveling Waves (Progressive) Waves:  The waves are generated by the driving force (that is coupled to an open system) are called travelling waves, these waves travel away form the point where the driving force produces the disturbance.
• Stationary (Standing)Waves:  The waves are called stationary or standing waves in which the disturbance or energy does not move while there is movement of particles of the medium.
For example: If the rope is reduced to a violin string, fixed at the ends, the progressive waves travelling on the string would be reflected at both ends, the vibration of the string would then be the combination of stationary waves which is moving to and fro along the string.

Properties of Stationary Waves:

• Each particle expect at nodes, executes simple harmonic motion with same period but different amplitudes about their mean positions.
• There is no flow of energy in any direction.
• There is no advancement of the wave in any direction.
• There are points which are permanently at rest and are known as nodes.
• The points midway between nodes, having maximum displacement either side, are known as antinodes.
• The distance between two consecutive nodes and antinodes are equal to λ/2. The distance between node and antinode is equal to λ/4.
• All the particles pass through their mean positions or reach their outermost positions simultaneously twice in a periodic time.
• The particles between two consecutive nodes are in the same phase of vibration while the particles on the opposite sides of a node are in opposite phase of vibration.
• There is no flow of energy in either direction in a stationary wave. The reason is that the energy due to progressive wave travelling in opposite direction is equal that is the resultant flow of energy is zero.

### Distinction Between Progressive and Stationary Waves:

Progressive waves:

1. This is an advancing wave which moves in the medium continuously with a finite velocity.
2. Energy flows across every plane in the direction of propagation of the wave.
3. Each particle of the medium executes simple harmonic motion about its mean position with the same amplitude.
4. No particle of the wave is permanently at rest.
5. The phase of vibration varies continuously from point to point.
6. All the particles do not pass through their positions or reach their outermost positions simultaneously.

Stationary Waves:

1. There is no advancement of the wave in any direction.
2. There is no flow of energy across ant plane.
3. Expect nodes, all the particles of the medium execute simple harmonic motion with varying amplitudes.
4. Nodes are permanent at rest.
5. All the points between any pair of nodes vibrate in the same phase, but the phase suddenly reverses at each node.
6. All the particles pass through their mean positions or reach their outermost positions simultaneously twice in periodic motion.

3. On the basis of direction of propagation of wave along a line, in a plane, or in space, the wave may be one-dimensional, two-dimensional or three dimensional respectively. Waves set up on the string is one-dimensional wave, ripples are the example of two -dimensional wave and light emitted from the point source spreading in all directions is three-dimensional wave.

4. Spherical Waves: The waves in which the surfaces of common phase are spheres and the source of waves is a central point are called spherical waves. These waves become plane waves after travelling a short distance.

Velocities in Wave Motion:

There are three types if velocities in wave motion,

• The particle velocity is the simple harmonic velocity of the oscillator about its equilibrium position.
• The Wave or Phase Velocity with which the planes pf equal phase, crests or troughs, progress through the medium is called wave or phase velocity.
• The Group Velocity, a number of waves of different frequencies , wavelengths and velocities may be superposed to foam a group of waves. The velocity with which the group of waves advances in the medium is called the group velocity.

Phase and Phase Velocity:

The individual particles which constitute the medium do not progress through the medium with the wave, they only oscillate about their mean positions. It is their phase relationship which we observe as the waves. Thus the wave velocity is also called the phase velocity. It is the velocity with which plane waves of equal phase travel through the medium. It is given by,

V=νλ=2πν λ÷2π