https://youtu.be/MuEhsSUKQlY
PHYS 1101: Lecture Twenty-Five, Part Three
Okay, number one: motion of the red spot, a segment of the string. I’m going to bring the animation over. We’re going to reset it and play it. Let me emphasize for you, it’s this red segment you need to watch. As I play this animation and the wave is generated and it starts propagating along, focus on the motion of that red spot. What’s it doing?
My first quiz question for you asks if the red spot is moving purely up/down? Is the red spot moving right/left? Or is it going through a circular path? This is a tricky question. You have to watch it carefully. And therefore, I’m going to give you ten points if you get it right.
One way to help might be to lay a piece of paper onto the screen and lay it in this orientation, just the edge of the red dot and see if the red dot follows along this line. With that piece of paper there, you’ll be able to see if the red dot is going in and out or behind the paper and appearing? Is it doing this? Watch carefully; you might be able to tell if it’s doing this.
Lay a piece of paper on your screen, so the red dot, you see it just to the right. Choose A, B or C for question five.
Okay, the first thing to appreciate about the motion of this red spot as the wave travels along is that it is set by the motion of the source. It echoes the same behavior and time, as does the motion of the source. Think of it this way: certainly the segment that’s attached right to the source goes through the same motion as the source. And that’s true of its neighbor and the other neighbor.
Now, there’s a slight time delay in everybody’s motion. But when they do go through that motion, it’s the same as the plunger.
Okay. If this plunger is going up and down like a mass on a spring, if it’s undergoing simple oscillatory motion, simple harmonic motion–the same kind of motion that we studied intensively in the last chapter–if that statement’s true, it then logically follows that every spot on the string is undergoing that same simple oscillatory motion.
If I consider this red spot…one way to visualize it, then, is that this spot is like a mass attached to a spring. And it’s going up and down, just like a mass would oscillating on a spring because the source. I’m asserting, I’m defining, that the source is going up and down like a mass on a spring.
In other words, I’m attaching this spring to the same kind of mass. I’m sorry, this plunger. This plunger goes up and down like a mass on a spring, so does this point. That’s very useful, then, because now we can leverage all we learned last chapter about the physics of this motion for mass on a spring and assign it to the same characteristics we see for this red spot.
Question six: Where’s the speed, then, of the red spot a minimum? It is a minimum when this red spot is at the top of its motion, in the middle or at the bottom? Or is the speed a minimum when it’s at the top and at the bottom?
Question seven: Where’s this speed of this red spot going to be a maximum? Top, middle, bottom or both at the top and the bottom?
Okay. Scroll back to the movie. And I want you to watch it more carefully. Look at your watch or count to yourself in terms of seconds. And ask yourself, “What’s the period of this red spot’s motion?” Remember, the period for simple harmonic motion was the time that it takes the motion to repeat one cycle.
Focus on that red dot. Count to yourself. How long is it, roughly, for one cycle? You should be able to get close enough to determine if it’s closer to one second or five seconds or ten seconds.
After you do that, now go back and watch it and look at the plunger, look at the end of the plunger. And ask yourself, “How does it compare?” If you estimate it takes the plunger to go up and down through one cycle, is that period less than, equal to or greater than the period of the red spot?
Okay. Question ten is a numeric question. You’re going to have to type in a number into WebAssign. Now, I’m asking you about the maximum speed of the red spot. Let’s assume that the plunger is undergoing simple harmonic motion; therefore, so is the red spot. It’s going up and down like a mass on a spring.
The maximum y coordinate of the plunger is +10 centimeters. The minimum y coordinate of the plunger is +2 centimeters. So, the plunger oscillates up and down between a position of 2 and 10 centimeters. It goes down to 2, back up to 10. Down to 2, back up to 10.
With that information, with the information about the period of this motion being approximately one second, what’s the maximum speed of the red spot?
Question 11. Again, the red spot, it’s undergoing simple harmonic motion. You have enough information to figure out the amplitude of that motion, capital “A,” the angular frequency, Omega, for that motion. You needed to do that to calculate the maximum speed of the red spot.
Now, do the next step. What’s the maximum acceleration of the red spot?
Question 12: Where is the red spot’s acceleration a maximum? Does that happen at the very bottom of its motion, at a trough? Or is it in the middle? And then at that location or, rather, at the instant that the red spot is at the very bottom. It’s at a trough; it’s turning around now and heading back up. At that instant, what arrow best represents the acceleration vector for that red spot at that instant?
Okay. If we watch the movie again, answer this question. The main motion that your eye follows is something moving to the right as time goes on. How would you best describe the thing that is moving to the right? A, is it the red spot? B, the wave crest? Or, C, the string itself?