Waves Motion

Overview

A wave is a continuous transfer of disturbance from one part of a medium to another through successive vibrations of particles of the medium about their mean positions. This note provides us information on the types of waves.

Types of wave

A wave is a continuous transfer of disturbance from one part of a medium to another through successive vibrations of particles of the medium about their mean positions. In wave motion, energy and momentum are carried from one region to another region of the medium. If there is no transfer energy, it is not a wave but an oscillation as there is no transfer of energy.

Types of wave

1. Mechanical wave
2. Non-mechanical wave

Mechanical Wave

If the wave requires a material medium to carry energy from one point to another point then it is called a mechanical wave. For a mechanical wave, a medium has elastic nature.

Non-mechanical Wave

If the wave does not require material medium to carry energy from one point is called a non-mechanical wave. Example: X-ray, microwave, electromagnetic wave.

Crest

It is the maximum displacement of the vibrating particle above equilibrium line of mean position.

Trough

It is the maximum displacement of the vibrating particle below the equilibrium line of the mean position. The velocity of a wave is maximum at equilibrium line and minimum at an extreme point.

Wavelength

It is the distance travelled by the wave to complete one oscillation of vibrating particle on the medium. In other words, a distance between two nearest crests or trough is called wavelength. It is denoted by ‘λ’. It’s unit is a meter. Hence, wave velocity is equal to the product of wavelength and frequency.

Wave velocity

The distance travelled by a wave in one second is called wave velocity, denoted by v.

Phase

The angular displacement of the wave at any time‘t’ is called phase of the wave. Phase indicates where the wave reaches and in which direction is the wave.

Characteristics of Wave Motion

1. Wave motion is the disturbance travelling through a medium.
2. When a disturbance is produced in a medium, the disturbed particles vibrate about their mean positions.
3. Particles handover their energy to their neighbors through the disturbance but their net displacement over one period is zero.
4. The energy transfer in the medium takes place with a constant, v = λf which depends on the nature of the medium.
5. As the disturbance reaches to a particle, it starts to vibrate. As the disturbance is communicated to the next neighbor a little later, so there is a phase difference in the vibratory motion of the consecutive particles.
6. The wave motion is possible in a medium which possess the property of elasticity and inertia.
7. Particle velocity is a function of time, so it is different in different points of a displacement. But wave velocity is constant in a medium.
8. Vibrating particles of the medium possess both kinetic and potential energies.

Types of Wave

1. Transverse Wave
2. Longitudinal Wave

Transverse Wave

If the vibrating particle of the medium has oscillated perpendicularly to the direction of propagation of the wave is called a transverse wave. Example: wave in a surface of liquid and wave in solid.

Propagation of Transverse Wave

To understand the propagation of a transverse wave, suppose nine particles of a medium numbered as 1 to 9 lying at an equal distance at the mean position shown in the figure. When a wave travels from to right, the particles vibrate up and down about their mean positions and the disturbance travel from the 1^st particles to a 9^th particle.

1. At t= 0, all the particles are at their mean positions.
2. After t = T/8 seconds, the particle 1 travels vertically a certain distance upward and the disturbance reaches to particle 2.
3. After t= 2T/8 seconds, particle 1 has reached to the maximum position and the disturbance has reached to particle 3.
4. After t= 3T/8 seconds, particle 1 has completed 3/8^th of its vibration and the disturbance has reached to particle 4. The positions of particles 2 and 3 are also shown in a figure.
5. In this way after t/2 seconds, particle 1 has come back to its mean position and the particles 2, 3 and 4 are at the positions shown in the figure in a figure. The disturbance has reached to particle 5.

After T seconds, the particle 1, 5 and 9 are at their mean positions and the wave has reached to particle 9. Particle 1 and 9 are in the same phase. The wave travelled a distance between particles 1 and 9 in the time in which the particle 1 has completed oscillation.

The top point on the wave at the maximum distance from the mean position is called crest, and the point at the maximum distance below the mean position is called trough. Thus in a transverse wave, crests and trough are alternately produced.

Properties of Transverse Waves

1. The particles of the medium vibrate simple harmonically perpendicular to the direction of propagation of the wave.
2. All particles vibrate with the same amplitude, frequency and period.
3. There is a gradual phase difference between the successive particles.
4. All the particles vibrating in phase will be at a distance equal to nλ, where n = 1, 2, 3 …. Etc. it means minimum distance between two particles vibrating in phase is equal to one wavelength.
5. The velocity of each particle is the maximum at the mean position and is zero at extreme positions.
6. At any instant, different particles have different displacements.
7. When the particles move above the mean position, it is in the region of a crest and when the particles move below the mean position, it is in the region of a trough.
8. Due to the repeated periodic motion of the particles, crests and troughs are produced alternately.