Two pulses are moving in opposite directions at 1.0 cm/s on a tau...

Question

Two pulses are moving in opposite directions at 1.0 cm/s on a taut string, as shown in Fig. E15.34. Each square is 1.0 cm.

Sketch the shape of the string at the end of (a) 6.0 s.

Accepted Answer

Hey everyone in this problem, we're told that at T equals 02 waves are traveling toward each other with the speed of 0.4 centimeters per second on a tight wire. As shown below, if each square measures 0.5 centimeters, what is the most likely shape of the wire at T equals five seconds. All right, So we have our two waves. We can see them in the diagram here. This one on the left, the one on the right. Okay, moving towards each other. Now let's try to figure out how far they're gonna move At T equals five seconds. How far will they have gone? That's gonna help us figure out this shape. So T equals five seconds. What is their position? Well, we know that the distance and we can write that the distance is equal to the velocity times the time. Now their speed is 0.4 centimeters per second. So we have 0.4 centimeters per second times the time, Which is five seconds. And you'll notice that the unit of second divides out and we're left with just a unit of cm, which is what we want for distance. Okay? So if you get stuck and you don't remember whether you should be multiplying or dividing when you have your distance formula with your velocity and time, you can always check the units and that will tell you which way it needs to be. Okay. So this is going to give us two cm traveled. So these waves have traveled, two centimeters by the time we get to five seconds and we're told that each square is 50.5 centimeters. Okay, so two centimeters divided by 20.5 centimeters per square Is gonna give us four squares. Alright, so we know that each wave has traveled four squares. So let's go ahead and draw out what happens when they move four squares. So this wave on the left, if we move it over four squares. Okay, So we're gonna start from the bottom right corner 1234. It's gonna be And let me actually draw this in blue so you can see it more easily, it's gonna be here. Okay. And then we're just gonna follow the shape of the wave. So it goes to to the left before it comes back down. So that is what that wave on the left is going to look like. What about the wave on the right? It's also going to move four squares. So from this bottom off corner 1, 2, 34. So it's gonna look something like this and it goes across three before coming back down. All right, now, when we're looking at the resultant wave, the resultant wave is gonna have the amplitude added together. Okay, so we have two waves that are kind of overlapping or interfering here. The result in amplitude is going to be the sum of those two amplitudes. So if we were to add these together. Okay, we have one box here from this smaller or shorter wave. Three boxes from this larger wave. Okay, so our resulting wave is actually going to go all the way up. 24 and it's gonna do that for these two boxes. And then down here we have just the one wave, the other wave has ended, so it doesn't interact. And so we're going to just have the one wave. So the one amplitude. Okay, so the resulting wave is going to look something like this. Okay, we've shifted those two waves the distance that they traveled in the time we were interested in. Okay. And then the resulting wave is going to be the sum of those amplitudes of those two waves. Alright, So if we look at our answer choices and we see that in answer choice A. Okay, this is just one big rectangle which isn't what we have in answer choice B. The waves are still apart, there's still two separate waves and answer choice C. They're two separate waves but they've kind of crossed paths. You can see that the shorter one is on the left. Now we don't have that situation either. Answer choice. D Well this looks like the wave we've drawn. Okay, the waves have overlapped and interfered a little bit and they're so kind of on top of each other. So we get a larger amplitude on the left and the smaller amplitude on the right with the tail of that shorter wave. And so what we have here is answer choice. D Thanks everyone for watching. I hope this video helped see you in the next one.

Struggling with Physics?

Two pulses are moving in opposite directions at 1.0 cm/s on a taut string, as shown in Fig. E15.34. Each square is 1.0 cm.
Sketch the shape of the string at the end of (a) 6.0 s.

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