eli5 How does destructive interference work?

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I understand that it’s basically opposite waves cancelling each other out. But I want to know why it works. Sorry in advance, if I’m not clear.

In: Mathematics
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Assume the top of the wave is +1, and the bottom of the wave is -1. When the waves are opposite the result is +1 + -1 = 0, and likewise -1 + 1 = 0.

The question of *why* waves cancel each other out comes down to something called the superposition principle. This says that the combined action of two processes is the sum of the two individual processes. For example, if I am in a boat, sailing East, but the current flows North, my boat will move Northeast. This direction is a sum of the two forces pushing the boat. The same thing happens with waves. The way waves combine is to simply add the amplitude of the wave at every point. [The Wikipedia article for the superposition principle has more info, including a section on wave interference. ](https://en.wikipedia.org/wiki/Superposition_principle)

This is beyond ELI5, but there is no fundamental reason why the superposition principle should hold for all systems. It is only a linear response. In practice, it is an extremely good approximation for most systems, but it does not always hold.

Constructive or destructive interference happens whenever two waves are added together. By adding, I mean literally that the output wave height is the sum of the two input wave heights.

Have you played Connect 4 before? The game board is a good simple way to visualize wave summing.

Suppose I decide to put a “waveform” into a Connect 4 board in the following way: I drop 3 chips in the first column, then 1 chip in the second column, then 3 chips in the third column, then 1, then 3, then 1, then 3.

Now you look at the Connect 4 board and you see a rhythmic up-down-up-down pattern. 3 1 3 1 3 1 3. The peak of the wave is 3 chips high and the trough is 1 chip high, so the amplitude of this wave is the distance between them, 2 chips high.

Now, you decide to add a waveform of your own to the board. This time you’re going to add 2 chips to some columns and 1 chip to others, so your waveform is gonna have an amplitude of 1 chip.

Now, are you gonna drop chips into columns like: 2 1 2 1 2 1 2 ? Or are you gonna do it like: 1 2 1 2 1 2 1 ?

In the first case, you’ll be producing constructive interference, where the peaks are aligned. The board will end up looking like: 5 2 5 2 5 2 5. The amplitude of this wave is 3 chips.

If you do it the other way, then you get destructive interference, and the resulting board will be: 4 3 4 3 4 3 4. The amplitude of this wave is only 1 chip. The second wave served to ‘fill in the gaps’ of the first wave instead of making it taller.

In the first case, the amplitude is 3 because that’s the result of adding a 1-chip wave to a 2-chip wave. In the second case, the amplitude is 1 because you subtract their amplitudes instead.

Imagine there is a big heavy box that you have to drag across the floor, so you call a buddy to help you out. If your friend is pushing from the same side as you, the mix of efforts results in a bigger push, but if he’s on the other side pushing againts you, then the efforts cancel each other out. That’s basically destructive interference.