 So now let's talk about waves from a graphical viewpoint. This quick reminder, we have our general wave equation. This is for a traveling oscillating wave. Now in this particular case, my y is a function of both position and time. In other words, my vertical position depends on horizontal position and time. Well, it's often hard to draw out functions of two different variables at the same time. But if we set a specific time, then I could have a plot of x versus y. It's kind of like taking a snapshot of the wave. So let's actually do this. Now again, I'm going to be using my simulation from PHET. If you're not familiar with this, I have another video that introduces this type of simulator. So here's my simulator. And it's already been set up to run here as an oscillating wave. So my y position measured up and down changes depending on time and also where I am along in this x-coordinate. But if I freeze in time, then I have a snapshot of this particular wave at any particular position for that one specific time. Now to see this a little more clearly, I can actually set a timer here. And as I freeze, it's at a specific time. Play more, freeze, it's at a new specific time. So I can set specific times on this timer to let me know when exactly I'm looking at the wave. So let's think about this in terms of something I can do some labeling on here. So I've got a couple of different things that I can take a look at. One, I can look at the amplitude. And the amplitude is the measurement of how high is the tallest peak from that baseline. And it doesn't matter whether I use the first peak or the second peak. I'll get the same height there as long as I don't have any damping on my wave. And we haven't studied damping yet. Now also notice that I could use the distance from the middle down to the lowest peak as well. That also gives me the same value for the amplitude. Now another property I could measure off of these is what's called the wavelength. And wavelength is the distance horizontally from peak to peak. So this is a measurement in x going from one peak to the other. How far apart are the peaks? And I don't just have to use the peaks. I could also use how far apart are the bases. I could measure it here at the midline. But I have to make sure that I've gone through a complete cycle of up and down. If I just measure till it comes back to the same midpoint, I've actually only gone through half of the cycle. But I can measure it from the midpoint to measure out a full wavelength. So our wavelength and amplitude are something that I can measure graphically off of a plot of the wave if I've frozen it at a specific time. Let's go back to our simulation here. As I'm playing, I freeze it at some specific time. And then I can pull a ruler out here and measure from peak to peak exactly how far that is. And I don't have the greatest precision on this particular one, but it looks like that's about 4.2 centimeters from peak to peak. I could also grab my ruler here and measure that from the base up to the peak, I've got about 1 centimeter. Now, this is actually 1.05 centimeters. Again, I'm kind of estimating off of a graph that it went just a little bit higher than the one mark. So that shows you how you can measure the amplitude and the wavelength off of a graph of the wave. But remember, you have to freeze it at a specific moment in time to make those measurements. So that's an introduction to working with a graphical picture of waves and how you can measure properties off of those graphs.