# Principle of Superposition

Independence of waves, which we learned about last time, means that after two waves collide, they pass through each other unaided without affecting each other.

So what happens not after the waves collide, but at the moment of collision? That is the theme of this lecture.

## Associated wave

As it turns out, at the moment of collision, the two waves overlap and become one wave.
The wave created by the superposition is called an associated wave.

Now, how does the wave form of the associated wave relate to that of the original wave?

In fact, it is known to be a very simple relationship.

Thus, the displacement of the associated wave adds up to the displacement of the original wave!

This is called the principle of superposition.

The principle of superposition is simple and can be applied in many ways.
For example, if a wave of height 1 cm is hit by a wave of height -1 cm, an associate wave of height 1 + (-1) = 0 is generated.
This is utilized by the noise canceling function of the headphones.

The headphones read the waveform of the surrounding noise and hit it with a wave in the anti-phase to eliminate the noise.
It is quite a clever feature, don’t you think?

## Associated wave drawing

Now let’s use the principle of superposition to draw an associated wave!

Since we want to use the principle of superposition, we first read the heights of the two waves at each vertical line and then add them!
When you have added, mark the value.

When you have finished marking all the locations, connect the dots.

This completes the associated wave.

When associating sine waves, the associated wave is a curve, so the points should be connected by a smooth curve.

## Next Time

Next lecture will be on wave reflections!

https://www.yukimura-physics.com/entry/wave-f12

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