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Wave Interference - Wave Pulse

Teacher/Instructor Jonathan Osbourne
Jonathan Osbourne

PhD., University of Maryland
Published author

Jonathan is a published author and recently completed a book on physics and applied mathematics.

Wave interference is the result of the interactions of multiple waves. Types of interference include constructive and destructive interferences. The difference between the two is the relative displacement of the waves. Wave interference often causes wave beats. Wave pulse is a short, non periodic, wave formed by a single input of energy rather than a continuous or repeated input of energy.

So let's talk about wave interference this is what happens when waves collide. Now it's really kind of a strange term to use for what actually happens because when waves actually are both affecting a medium at the same time they don't really interfere with each other although that's what we call it. What they really is they add together and then they move through each other and then once they've moved through each other, they go on as if nothing ever happened like 2 ships passing in the night. So suppose that I've got a wave here a little pulse coming with amplitude a and it's going to the right and I've got another pulse with amplitude b and he's going to the left. Alright when they reach the same point, the amplitude of the pulse that I get is a plus b. But notice that I don't have any arrows, that's because this guy consists of a part that's moving to the left and a part that's moving to the right, you can't say that this pulse right here is moving either to the left or to the right because it's really kind of doing both.

This property is called super position, when I add 2 waves together they are said to be super pose. It's almost like what you have when you super impose images but we just get rid of the im. Alright once the, this guy the super position is done they just kind of pass through each other and notice the smaller guy is now on the left and is still moving to the left. The bigger guy is on the right now and he's moving to the right so it's important to understand that these 2 waves have passed through each other they did not bounce off each other that's not the way it works because sometimes it kind of looks like that, like for example if both of these were the same height you wouldn't be able to tell the difference kind of why I made them different heights.

Alright this is called constructive interference, now constructive interference is what happens whenever the disturbances in both of the waves are in the same direction. And so when that happens when the 2 waves are overlapping the amplitudes add the 2 waves will add together and we get a larger wave. So the interference has constructed a larger wave. When the disturbances are in opposite directions we get destructive interference, in this case we subtract and now we get a smaller wave. Alright so let's look at what happens here when I've got a wave going to the right and another wave going to the left, this guy is disturbance down and this one is a disturbance up and they both have the same amplitude. And let's just see what happens when they super pose, alright here we go. As they come in they start to overlap, they're not fully overlapping but what I've done to try to illustrate what's happening is I've drawn the top guy in blue and the bottom guy in green. The sum is black, so see the sum comes over the green takes over but the blue is 0. The blue hasn't reached there yet so I get a little pulse down shorter and all down and he's still moving to the right.

Then here the blue and the green are both there, so when I add those together it's a minus a well that's 0. So this black line is just flat here, it looks like there's no wave there at all but really there's 2 waves there in cognito. Alright then over here the blue guy is there but the green guy is done, so that means that again I get this little black super position of the 2 waves which is thinner and all up this time. Alright moving on in time now the 2 waves are exactly on top of each other. The blue and the green are both there but what happens when I add them together? I get 0 everywhere so this is called totally destructive interference. I have 2 waves there but it doesn't look like I got anything going on, notice that I've got a arrow the blue guy is still moving to the left and the green guy is still moving to the right but I just can't see anything in the wave form. But I wait a little ebit longer and now the blue guy has passed through that region and the green guy has passed through on the other side. So now it looks just like it did over here except they're reversed. So it goes over I get little short pulse up then I get totally destructive interference flat then I get little short pulse down then no waves.

And then once they're done interfering, they pass through each other and they just go on as if nothing ever happened. It's really just that simple, you just have to do it exactly like that add them together when they're on top of each other, when they're not on top of each other anymore pretend that they're just moving separately because that's what they're doing. Alright now in a more complicated situation we've got sound waves so now let's imagine that we've got 2 sources of sound waves and they're both sending out waves. So let's see how this looks. Alright so we've got red source here, we've got green source here. The red circles represent places where I have a condensation of more sound waves from the red source. The green circles represent places where I've got a condensation from a green sound source. So let's see what happens when we watch these different waves fronts going out. Alright when I've got 2 condensations at the same place like here and here and here and here and here that's constructive interference. They're both condensations, they're both acting to push the molecules together and that means that I get a line of constructive interference right here.

On the other hand if I look along here I've got constructive for the greens and constructive for the reds but in different places. So in between I've got it the other way so the constructive, I'm sorry the condensation for the green takes place at the same point at the rarefaction for the red and so that adds together to give me nothing, so these are destructive interference and you can actually see this just by looking at it. Destructive, constructive, destructive, constructive, so I get these waves that come out of the center between the 2 sources that are associated with constructive and destructive interference. So this is called an interference pattern and these are very, very important when studying sound waves coming from 2 different sound sources and also it comes a lot when people are studying 2 different light sources. So that's interference.