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Introduction to Wave Motion

Two most important things in our daily life that is, sound and light, both travel as wave like disturbances, and the motion of all subatomic particles exhibits wave like properties. This is the reason why study of waves forms a topic of central importance in all engineering and physical science. In mathematics as well as in science, a wave is termed as some kind of disturbance which travels through time and space , which is usually accompanied by the transfer of energy. Waves travel through time and space and energy is transferred from one point to another by means of the wave motion. This energy transfer often happens with no permanent displacement of the particles of the medium that means, no associated mass transport or with little. They consist oscillations or vibrations around a location which is almost fixed. Say for example, a cork on rippling water will bob up and down, that is staying in about the same place but the wave generated itself moves onwards. Waves are of different types, among them one type of wave is called a mechanical wave, that propagates through a medium in which the substance of this very medium is get deformed. Sound waves propagate via air medium bumping into their neighbors that is nearer molecules. This results in transfer of some fraction of the energy to these neighbors, which will in turn cause a cascade of collisions between the neighbouring molecules. And when the air molecules collide with their neighboring molecules, they bounce away from them due to the restoring force. This mechanism keeps the molecules from continuing to travel in the direction of the wave. A different type of wave can travel through a vacuum, Electromagnetic radiation which includes infrared radiation, visible light, ultraviolet radiation, X-rays, radio waves, and gamma rays is another type of wave which can travel through vacuum. This type of wave is known as electromagnetic wave and this consists of periodic oscillations in electrical and magnetic fields .According to occurrence of disturbances waves can be of two types namely transverse waves and longitudinal waves. In transverse waves the disturbances occur in a direction perpendicular to the motion of the wave. Whereas in longitudinal waves, the disturbances travel in the same direction as that of wave. Waves can be described by a wave equation which actually sets or decides out how the disturbance proceeds over time. And depending upon the type of the wave the mathematical expression also varies.

The study of wave motion involves transfer of energy or disturbance from one center point to other point with the particles of medium oscillating about its mean position. The particles of medium do not travel along with the wave. Only disturbance is propagated.

Types of Wave

Transverse Wave: The particle of medium oscillates in perpendicular direction of wave. For example

a. Travelling wave on tight rope: If a rope is fixed rigidly with one end and other end is forced periodically by up and down, the disturbance propagates along with the length of the rope but particles of rope oscillate up and down. The disturbance travels in form of downward peaks known as troughs and upwards peaks known as crests.

Longitudinal Wave: Oscillation of particles and the propagation of wave are parallel

For example sound waves travelling in medium

Properties of Wave

a. Wave Speed (C) : Speed of wave is determined as the distance covered in one second

b. Wave Frequency : Frequency by which particles of medium oscillate

Frequency in transverse wave is determined as number of crests or toughs pass through a fixed point in one second.

Frequency in longitudinal wave is determined as the number of compressions pass through a fixed point in one second.

c. Time Period of Wave (T): Time period of oscillation of particles in medium

d. Amplitude (A): Amplitude of oscillating particles

e. Wavelength : It is determined as the distance b/w two consecutive crests or compressions



f. Phase: Particles move with same frequency but they reach corresponding position in from path in different time instant. It is mentioned by phase.

 

Topics under wave motion

1. Introduction to wave motion
2. Types of wave
3. Properties of wave
4. Equation of travelling wave
5. Equation of a simple harmonic plane wave
6. Energy of plane progressive wave
7. Transverse wave in stretched string
8. Superposition of waves
9. Interferences
10. Standing Waves
11. Reflection of waves
12. Stationary waves in string
13. Displacement waves and pressure wave
14. Sound waves in solid
15. Intensity of sound waves
16. Stationary waves in air column
17. Doppler effect

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