Question

How do you add two waves together?

Answer 1

Explanation:

Principle of Superposition of waves:

1. When two or more waves move across the same medium, they must eventually interact. Even when they combine, they keep their wave characteristics, the resulting wave usually differs from the original two waves.
2. When two or more waves combine with one another, a wave of motion is created that can be better understood using the superposition concept. Two waves that are causing some particle displacement in the specified medium are depicted in the figure below.
3. The principle of superposition in this situation dictates that,
4. The vector sum of the individual displacements that each wave at each location produces determines the overall displacement of a number of waves in the medium at a certain point.
   
5. Two waves are shown in the aforementioned illustration, each with a distinct displacement$(y_{1}and{y}_2).$ The resultant wave that results from the superposition of these two waves has a larger displacement than the two-component waves, as you can see.
6. Any kind of wave can be subject to the superposition principles under the following conditions:
7. The stacked waves are of the same kind. Because the medium in which the waves are propagating behaves linearly, the restoring force on medium particles that have been moved twice as far feels two times as strong.

1. The illustration above depicts two waves that are moving in opposing directions in the case of waves. The rope is displaced equally by these waves. Keep in mind that in$figure\left(c\right)$, the resultant displacement is$0$when both waves overlap.
2. The superposition principle can be explained mathematically as follows. Let's imagine that the displacements caused by two waves in the medium are $y_1(x,t)and{y2}_{}(x,t).$ Let $P$represent the intersection of these two routes. Using the superposition technique, find the resulting displacement now $\left(y\right).$

$\Rightarrow y=y_1(x,t)+y_2(x,t)$

If two or more waves are moving through a medium and colliding at a single location, then the wave functions for each wave are given by,

$$\begin{gathered} \Rightarrow y=f_1(x–vt) \\ \Rightarrow y=f_2(x–vt) \\ \dots \\ \Rightarrow y=f_n(x–vt) \end{gathered}$$

The resultant wave after displacement is given by,

$\Rightarrow y=f_1(x–vt)+f_2(x–vt)+f_3(x–vt)+\dots .f_n(x–vt)$

Hence, two waves are added by the principle of superposition of waves.