Principle of Superposition

When two or more waves travel in the same medium, they are bound to interact with each other. They retain their wave nature after combining with each other, but usually, the resultant wave is different from both of the individual waves.

The superposition principle helps us describe the resulting wave or motion that is produced when two or more waves combine with each other. 

The figure below shows two waves that are producing some displacement in the particles of the given medium.

In the figure given above, two waves with individual displacements y₁ and y₂ are given. Notice that the resultant wave from the superposition of these two waves has a greater displacement than the two individual waves. 

The principles of superposition can be applied to any type of wave provided that: 

• The waves that are superimposed are of the same type.
• The medium in which the waves are propagating behaves linearly, this means that the particles of the medium which are displaced with twice the displacement experience twice the amount of restoring force on them.

In the case of waves, the figure above shows two waves that are travelling in opposite directions. These waves produce equal displacements in the rope.

In mathematical terms, the superposition principle can be described as given below. Let’s say y₁(x, t) and y₂(x, t) is the displacements produced by two waves in the medium. Let P be the point where these two ways come and meet. Now using the principle of superposition to find the resultant displacement (y). 

y = y₁(x, t) + y₂(x, t) 

If two or more waves are travelling and meeting at one point in a medium and the wave functions for the individual waves are given by, 

y = f₁(x – vt)

y = f₂(x – vt)

… 

y = f_n(x – vt)

The resultant wave after displacement is given by, 

y = f₁(x – vt) + f₂(x – vt) +  f₃(x – vt) + …. f_n(x – vt)

When two waves propagating in the same medium interfere with each other the amplitude of the resultant of the two waves is the vector sum of the amplitude of the two waves, this is called the Principle of Superposition of Waves.

Waves are disturbances that transfer energy between two points without there being actual contact between the two points. We are completely surrounded by waves and these are used for performing a variety of tasks in our daily life.

We encounter different types of such as Radio waves, Light waves, Microwaves and others on a regular basis. The superposition of waves is the process of adding different waves together and finding their results. 

In this article, we will learn about the Superposition of Waves and others in detail.