Jonathan Osbourne

**PhD., University of Maryland**

Published author

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

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**Wavelength** is the distance between two crests of a wave. It is related to frequency and period by the equations *wave speed = frequency x wavelength* and *wave speed = wavelength / period*.

Let's talk about wavelength of a periodic wave. The wavelength is the word used to describe the physical size of one whole assault of a periodic wave.

So that means that I got to go from one place where the periodic wave is doing something to another place where the periodic wave is doing the same thing, alright? So we can think of it as the distance between two consecutive peaks or two consecutive troughs. One easy way to think about this is that if you're sitting on a boat in the ocean and you're at a peak in an ocean wave, and you look down to where the next peak is, the distance to that is the wavelength. So if I've got a periodic wave here, the wavelength is the distance between two peaks or the distance between two troughs. But that's not the only way that I can do it. I can also say well, jeez. Here the wave's doing something. Wave's doing the same thing there. So that has to be the wavelength also. Alright.

Now, notice that it's not just where the wave mis in the same place because this distance is certainly not a wavelength. So it's got to be the in the same place doing the same thing. And then you get a wavelength.

Now, what's this weird symbol I'm using for wavelength? This is a Greek letter lambda and we write a lambda like this. It's real real real real simple. Back slash, forward slash. There you go, lambda.

So let's talk about some problems that I've seen on tests asking about wavelength. So suppose that we're given a wave, a periodic wave like this and we've got some points labeled, alright? And we're asked to find the wavelength given a bunch of different situations. Alright. So let's look at the first one, a to e is 6 meters, a to e. Alright. So what we've got to do is figure out how many wavelengths appear between a and e, alright? When I start at a, and here I go.

Well, that's a whole wave because I started off at a and c is doing the same thing. So that's a whole wave and then I got another whole wave. So if this is two waves and the distance is 6, then that means two lambda must equal 6. So lambda is 3 meters. Does that make sense? Not difficult at all. Alright. How about a to c? a to c is a wavelength. So that tells us the answer immediately, 5 meters.

Alright, what about this next one. a to b is 4 meters. Well, a to b right here looks like half a wave length because the piece here and the piece here are the same just inverted. Alright? So that means that one half of the wavelength will be four and that means that the wavelength will be 8 meters.

Alright, now this one's the most difficult one, still not that bad, but it is the most difficult. a to d is 8 meters. Alright. a to d. How much of a wavelength is that? Well, I've got a whole wave here from a to c and then I've got another half of a wave from c to d. So that means that I've got one and half or three halves wavelength and that's going to be given by 8 meters. So that means that the wave length in this case is 16 thirds of a meter. Now that's one, probably the only of these four that you probably really need to write down, alright? That you actually would have to write it down. And that's why wanted to do it because these are always so simple that you can just look and guess the answer.

Alright. Now, I just want to say a couple of words about what wavelength means. We said over there that wavelength is the characteristic size of a wave. But what does that mean? Why do I care? Well, if I'm on a ship, I care very much. Because let's say that the ocean wave looks like this, okay? There's my ocean wave. Now, what if my ship is much much much smaller than a wavelength? So my ship is right here. Great. I don't care about that wave. the wave's doing essentially the same thing, the whole time underneath me. So I don't really care. I'll just go up and down with the wave and I'm fine. Right? Alright. What if my ship is much much much bigger than the wave length? well, jeez.

Now, the wave is kind of just averaging out underneath my ship. Alright? So again, it doesn't really matter that much. But what if the wave and the ship are about the same size? Well, now I'm going to have one part of my ship here and the other part here, and now my ship is going to break. So that's the idea.

Wavelength is the physical size of the wave, the characteristic size and whenever we're doing problems involving waves, we want to be very very very careful when we're looking at the interaction between a wave and some physical object whose size is around the same as wavelength of that wave. Alright? And there's wavelength.