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Superposition and Interference/重ね合わせと干渉

Superposition and Interference/重ね合わせと干渉
One of the most important concepts you must grasp to understand quantum computing is the superposition and interference of waves. Since waves are moving through space, you can have more than one wave passing through one place at the same time. When that happens, the waves add up or superimpose on one another. Imagine, we have a wave like this and another wave of a slightly different frequency like this. It doesn’t matter if they are light waves or water waves, it’s the same. If we take the two waves and we add them up, we get a pattern like this.
You can see that on the left, the waves are almost lined up, which we call “being in phase,” and so their peaks add up. This is called “constructive interference.” On the right, one wave is positive where the other is negative, which we call “being out of phase,” and the two waves cancel out. This is called “destructive interference.” When we let the waves run longer, you can see that the interference grows and shrinks. This growing and shrinking pattern is called “beating.” The figures show the waves moving up and down, but in sound the air moves back and forth instead but the principle is exactly the same. Let’s see if we can hear that beating pattern in sound.
Welcome Shinnosuke Ozawa, one of my students, and a talented bass guitar player. I am happy to be here. Good. So with the bass guitar, you adjust the tension on the strings using these pins and that adjusts the sound or the frequency at which the strings vibrate. First, let’s hear your bass guitar in tune. Play one note for me.
Okay, that’s an A, right? Yes. I think that’s 360 hertz if I did the calculation right. Now, by placing his fingers on the fret, he can play the same note on two different strings. Let’s hear the two strings together.
very nice. Now, we take one of those strings and put it just slightly out of tune with the other, if we are lucky, we will be able to hear the interference between the two types of waves. Let’s try that. Put one string a little bit out of tune here and see what happens.
Yeah, that’s fantastic. Did you hear that? As the frequency of the two strings got closer and closer together the beating got longer and slower until finally it stopped and they were in tune together. Thanks. You’re welcome The amount of interference we get depends on both the amplitude, how strong the wave is and the phase, whether it’s near the beginning, middle or end of its cycle. When waves are propagating through space, the distance they have to travel depends on the angle and the phase in turn depends on that distance. If we have one source, we can see the waves radiating out in every direction.
If we have two sources, we can see the waves radiating out in every direction and in some places those waves reinforce and in others they cancel giving us constructive and destructive interference. In the applications and animations in the article accompanying this video, you can explore interference in detail.





  1. 波の強め合い(建設的干渉)
  2. 波の弱め合い(相殺的干渉)
  3. 異なる周波数の波による波のうなり(ビート)




2-D wave propagation and interference of two sources, no decay






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