Welcome to our second example video. Considering the basics of traveling waves and this video, we're going to return to the same function we had before. D of X T equals four centimeters multiplied by the sign of two per centimeter. Yes, per centimeter is three units for wave number. Times X minus four hurts times t plus pi over six. Um, let's then from this there on this equation from this formula draw. Ah, plot. Now, we can't do this very well because we have two independent variables here. So we need to do is set 1 to 0 or set it equal to a constant. At least I'm going to set t equal to zero seconds. So we have d of x zero, and we're going to plot this against X, so this term has disappeared. Um, first of all, we notice the amplitude is four centimeters and negative. Four centimeters. So those are vertical bounds. Um, we noticed that we have a phase change of pi over six. Sign of pi over six is 60.5. So we're gonna be starting at two centimeters and then we have, um our wave constant Here are wave number and we know that Lambda is equal to two pi over two times, one over centimeters. That's pi centimeters for the wavelength. So we expect to complete one wave every pie centimeters. So if I were to draw this and we could go on there, I'd say every wavelength I have gone Hi centimeters. So this would be a pie. Centimeters here, we'd have two pi centimeters, and here we'd have three pie centimeters. Okay, so we were able to take the information from the formula from the equation and write it out or draw it out in a plot. Now, if, on the other hand, we had said, What about we set X equal to zero? So in this case, we're going to have D of zero comma T. And of course, we plot against T. Now we're gonna have the same amplitude four centimeters and negative four centimeters, and in this case, we're gonna have the same phase constant. So we're still going to start here At T equals zero, But then we have to ask ourselves, what do we need? What we need. The period period is equal to two pi over omega, which is two pi over to hurts, which is gonna be equal to Oh, sorry. Four hurts here. So that's gonna be equal to Pi over two seconds. So every pi, over two seconds, we should see a full oscillation. So come up and down and up and down a few times, and we break it where We've made a full rotation. And I know that this will be at pi over two seconds. This will be at Pi seconds, and this will be at three Pi over two seconds. Okay, so now we've drawn our time plot. This is generally how we're going to proceed.

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## Video Transcript

Welcome to our second example video. Considering the basics of traveling waves and this video, we're going to return to the same function we had before. D of X T equals four centimeters multiplied by the sign of two per centimeter. Yes, per centimeter is three units for wave number. Times X minus four hurts times t plus pi over six. Um, let's then from this there on this equation from this formula draw. Ah, plot. Now, we can't do this very well because we have two independent variables here. So we need to do is set 1 to 0 or set it equal to a constant. At least I'm going to set t equal to zero seconds. So we have d of x zero, and we're going to plot this against X, so this term has disappeared. Um, first of all, we notice the amplitude is four centimeters and negative. Four centimeters. So those are vertical bounds. Um, we noticed that we have a phase change of pi over six. Sign of pi over six is 60.5. So we're gonna be starting at two centimeters and then we have, um our wave constant Here are wave number and we know that Lambda is equal to two pi over two times, one over centimeters. That's pi centimeters for the wavelength. So we expect to complete one wave every pie centimeters. So if I were to draw this and we could go on there, I'd say every wavelength I have gone Hi centimeters. So this would be a pie. Centimeters here, we'd have two pi centimeters, and here we'd have three pie centimeters. Okay, so we were able to take the information from the formula from the equation and write it out or draw it out in a plot. Now, if, on the other hand, we had said, What about we set X equal to zero? So in this case, we're going to have D of zero comma T. And of course, we plot against T. Now we're gonna have the same amplitude four centimeters and negative four centimeters, and in this case, we're gonna have the same phase constant. So we're still going to start here At T equals zero, But then we have to ask ourselves, what do we need? What we need. The period period is equal to two pi over omega, which is two pi over to hurts, which is gonna be equal to Oh, sorry. Four hurts here. So that's gonna be equal to Pi over two seconds. So every pi, over two seconds, we should see a full oscillation. So come up and down and up and down a few times, and we break it where We've made a full rotation. And I know that this will be at pi over two seconds. This will be at Pi seconds, and this will be at three Pi over two seconds. Okay, so now we've drawn our time plot. This is generally how we're going to proceed.

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