eli5 How does destructive interference work?

Question

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

Answer 1

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.