Waves

The “particle” and “wave” are two forms in which universe is manifested at the basic level. Either we interact with particle or wave. Generally, we tend to associate the concept of particle with “mass and energy” and that of “wave” with energy. In the light of Einstein formulation of “mass – energy equivalence”, we can further refine these associations :

Particle : It is aggregation or concentration of energy localized in space

Wave : It is distribution of energy in space

What is wave?

It is a difficult question to answer. The best we can offer is interpretation which arises from explanation of various observations : Wave is distributed energy or distributed “disturbance (force)”.

Take half bucket of water. Give the bucket a jerk and watch the movement of water surface. The water mass near the surface moves from one side of the bucket to another in oscillatory fashion for some time before it comes to a standstill. The movement of water mass here replicates water waves which undergo frequent collisions with the wall of the bucket. It is easy to interpret this real time observation in terms of ideal situation. Had there been no friction (viscosity) and loss of energy during collision of water mass with the inner wall of the bucket, the disturbance (jerk) imparted would have caused a disturbance to the water body that would be sustained for all time to come.

Now, we drop a pebble on a calm surface of water. The water ripples move outward in concentric circles. The concentric ripples are result of multiple disturbances created at the point where pebble hits the water surface. This is real time situation. Let us again infer the observation in terms of an ideal situation. If it is a single impact of the pebble with the surface, then a single disturbance spreads around in concentric circles and move away to cover the expanse of water surface. If it had been an infinite surface, the disturbance would have reached the farthest. We interpret this ideal situation in many different ways including :

1: The disturbance (force) is transmitted from one point to another.

2: The energy is transmitted from one point to another.

If we place a small piece of paper on the water surface, then we find that paper piece moves up and down with slight side way oscillation. However, it remains where it is without any net displacement. We conclude :

3: The energy or disturbance passes in the form of wave without any net displacement of medium.

Let us now have a closer look at the motion of paper. In the ideal approximation, we see that paper is executing simple harmonic motion (SHM) in both longitudinal (side ways) and transverse (vertical) directions. The net result is that it is following an elliptical (or circular) trajectory. We infer that each water particle on the surface is executing a periodic motion. The displacement of adjacent water particles are different creating crest and trough. It appears that oscillatory motion (and hence its kinetic energy) has been passed to the next neighboring water particle and so on. Conclusion :