What is principal of superposition??

Considering two waves, travelling simultaneously along the same stretched string in opposite directions as shown in the figure above. We can see images of <a href="https://byjus.com/physics/wave-theory-of-light/">waveforms</a> in the string at each instant of time. It is observed that the net displacement of any element of the string at a given time is the algebraic sum of the displacements due to each wave.

Let us say two waves are travelling alone and the displacements of any element of these two waves can be represented by y₁(x, t) and y₂(x, t). When these two waves overlap, the resultant displacement can be given as y(x,t).

Mathematically, y (x, t) = y₁(x, t) + y₂(x, t)

As per the principle of superposition, we can add the overlapped waves algebraically to produce a resultant wave. Let us say the wave functions of the moving waves are

y₁ = f1(x–vt),

y₂ = f2(x–vt) 

y_n = f_n (x–vt)

then the wave function describing the disturbance in the medium can be described as

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

or, y=∑ i=1 to n = fi (x−vt)