Everyone, let's see if we can get some practice here so I can kind of visualize this whole phenomenon with wave interference. I have these two wave pulses, a and b, that are traveling towards each other. Imagine you and your friend grab the end of a rope, and you both flick it upwards, and the wave pulses travel towards each other. Now they each travel at a speed of 2 centimeters per second, and, basically, everything on the x and y axis is in centimeters, so we don't have to do any conversions. In other words, both of these things are moving towards each other with a speed of 2 centimeters per second. What we want to do is we want to sort of sketch out, not really calculate anything, what the wave is going to look like at different points throughout this sort of interaction. Alright?
We've actually got a couple of graphs to help us along with that. We're going to measure this, or we're going to draw this out when t equals 1 second and then 2 and then 3 and so on. So let's get started. Basically, what we're going to do here is we're going to take this sort of wave pulse, and we're actually given, you know, where the wave pulse starts and stops in terms of centimeters.
So let's take a look at what happens at t equals one second. Alright? From t equals 0 to 1, one second passes, and if these things move at 2 centimeters per second, then that means that they both are going to move towards each other by 2 centimeters. I'm initially starting here at 6, which means that the blue curve, that blue pulse, is going to travel to the right by 2 centimeters. So, you basically just line up the tip of this pulse, and now you're just going to shift it over by 2 centimeters after one second. The top of this little peak is actually going to happen now at 8, and the bottoms of these two triangles aren't going to be 4 and 8; they're all going to shift over by 2 centimeters to 6 and 10.
What does the red curve look like? Well, the red pulse is going to do the same but except it's actually going to move to the left. So what happens is this peak lines up with 14, but then it's going to move to the left by 2, so it's going to line up with 12. Notice at the top of this peak, it actually isn't 4; it's just 2. So, it's going to end up looking like this: the bottoms of these will look like that, and the rest of the wave pulse is flat.
What happens next? This pulse continues moving to the right. In other words, the top is going to be over at 10 on the x-axis. So the top is going to be at 10, and the bottom is going to be at 8, and this bottom over here is going to be at 12. And then, the rest will be flat. For the red, it will move the same again to the left. So, the tippy top will be over at 10 centimeters, and the bottoms are going to go from 10 to 8, and then 14 to 12. What happens at t equals 2 seconds, these waves will be on top of each other.
Now, remember what happens when waves interfere with each other. When you have waves that are stacked on top of each other, the resultant wave is just adding the two triangles together. So what ends up happening here is these wave pulses stack up, and they add on top of each other, and you'll end up with a strong wave pulse that goes all the way up to 6 centimeters, because it's going to add the 2 and the 4. So the real wave pulse is going to look something like this.
After they pass each other, the blue moves to the right, and the peak goes from 10 to 12. What about the red one? The red is going to move 2 centimeters to the left. So, the top is going to be here at 8. Because these things aren't on top of each other anymore, we don't have to do any addition; they have already passed each other, and the superposition has already happened. So this is what each of these stages look like throughout the motion of these two wave pulses. You can even try it at home if you have a string and create two little wave pulses. You're going to see this weird thing that happens when the pulses hit each other, and they'll add up like this. Anyway, folks, that's it for this one. Thanks for watching.
