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Graphs Of Mathematical Representation of Wave

Patrick Ford
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Hey, guys, let's do a quick example. Draw the displacement versus position and the displacement versus time graphs of a trans verse wave given by the following representation. And then they give us the mathematical representation of that way. Okay, I'm gonna draw the wave over a single period because there's no way to draw all of the waves. These waves go on from negative infinity to positive infinity. They go on forever. So I'm just gonna draw a single period. You might be asked to draw two periods of the way over three periods or four periods or whatever. But if you're told just to draw the wave, draw a full cycle doesn't really matter how much you draw. So here my graphs. Here's displacement versus time. Here's displacement versus position. In order to graft them, we need to know three things We're gonna need to know the amplitude. Okay, We're gonna need to know the period, and we're gonna need to know the wavelength. Okay. Amplitude is easy, right? 1.5 centimeters. Amplitude done. So on both of these graphs, I'm gonna write 15 centimeters and negative 1.5 centimeters. And these were gonna mark the boundaries that the leaves air going to oscillate in between the waves. You're gonna stay between the amplitude. Now, remember, this number right here represents the wave number, and this number right here represents the angular frequency. Don't forget that. So our wave number is in verse. Centimeters and that's two pi over Lambda. So Lambda is two pi over which is about 30 centimeters. Okay, Now the angular frequency, as we can see, is two pi over 0.1 seconds. And the angular frequency related to the period is two pi. Sorry, little technical difficulty. Two pi over the period. So relating these two equations together, we can see that the period is simply 20. seconds. Okay, so now we have enough information to draw. Ah, full period or a full cycle of each of these waves. We know that during the cycle, the wave is going to take 0. seconds. So if I draw 0.1 seconds right here on my displacement versus time graph, I can just draw my sine wave. Right? This is a sine wave. If this was CO sign we would start at a amplitude, drop down to the negative amplitude and go back up to the amplitude. Okay. For displacement versus position, we know that a cycle takes three centimeters, so I'm gonna mark three centimeters and I'm gonna draw the same Yeah, sine wave. Okay. And this is exactly the position. Sorry. The displacement versus time and the displacement versus position graphs for this function. All right, guys, Thanks for watching.