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Physics in Action: Standing Waves on a Rope

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About this Lesson

  • Type: Video Tutorial
  • Length: 3:59
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 43 MB
  • Posted: 07/01/2009

This lesson is part of the following series:

Physics (147 lessons, $198.00)
Physics: Waves (19 lessons, $27.72)
Physics: Standing Waves (5 lessons, $5.94)

This lesson was selected from a broader, comprehensive course, Physics I. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/physics. The full course covers kinematics, dynamics, energy, momentum, the physics of extended objects, gravity, fluids, relativity, oscillatory motion, waves, and more. The course features two renowned professors: Steven Pollock, an associate professor of Physics at he University of Colorado at Boulder and Ephraim Fischbach, a professor of physics at Purdue University.

Steven Pollock earned a Bachelor of Science in physics from the Massachusetts Institute of Technology and a Ph.D. from Stanford University. Prof. Pollock wears two research hats: he studies theoretical nuclear physics, and does physics education research. Currently, his research activities focus on questions of replication and sustainability of reformed teaching techniques in (very) large introductory courses. He received an Alfred P. Sloan Research Fellowship in 1994 and a Boulder Faculty Assembly (CU campus-wide) Teaching Excellence Award in 1998. He is the author of two Teaching Company video courses: “Particle Physics for Non-Physicists: a Tour of the Microcosmos” and “The Great Ideas of Classical Physics”. Prof. Pollock regularly gives public presentations in which he brings physics alive at conferences, seminars, colloquia, and for community audiences.

Ephraim Fischbach earned a B.A. in physics from Columbia University and a Ph.D. from the University of Pennsylvania. In Thinkwell Physics I, he delivers the "Physics in Action" video lectures and demonstrates numerous laboratory techniques and real-world applications. As part of his mission to encourage an interest in physics wherever he goes, Prof. Fischbach coordinates Physics on the Road, an Outreach/Funfest program. He is the author or coauthor of more than 180 publications including a recent book, “The Search for Non-Newtonian Gravity”, and was made a Fellow of the American Physical Society in 2001. He also serves as a referee for a number of journals including “Physical Review” and “Physical Review Letters”.

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You've seen that we can set up standing waves on a rope. We're going to demonstrate that with this string. Recall, the standing wave arises when a wave starting at one end is reflected back from a post which doesn't move, and the combination or the interference between the wave going in this direction and the wave reflected back in that direction leads to a pattern called a standing wave. A standing wave can be characterized in different ways - by the number of nodes or points that don't move, and also by the number of harmonics. You can describe the standing wave pattern in different ways. We'll see that. Let's take a look at some examples.
Randy over here is going to start causing this string to vibrate. Let's watch this. This is called a fundamental mode or the first harmonic. Notice the only points, which do not move are the end points of the string. Otherwise, there are no other nodes in this pattern. Notice also that for this mode, the wavelength of this wave is twice the length of the string. If you imagine continuing this wave beyond Randy, you'd see the full wavelength.
Now, in order to go in to another mode or another pattern, you have to stop the string and start over again. Now, here we have another mode. Notice that in this mode we have a node, a point over here where the string is not moving. Correspondingly, there are also points where the string moves the maximum amount. Those are called antinodes. This is called the second harmonic. It's a pattern, which forms when one node is present in the middle. Let's watch that for a few seconds.
Randy is very talented. Let's see if he can get two nodes in this standing wave pattern. We see that in addition to the nodes, the point that began which we always expect is now one node over here and one node over here. Let's watch that for a few seconds. Notice that in-between the nodes, there are points where the string moves very, very far--over here--which are called antinodes. This pattern or mode on the string is called the third harmonic. Let's stop it now.
Let's go for one more node, if we can do it. Now in addition to the nodes at the end, you have one node over here in the middle, one node over here in the middle, a third node over here. Note that between every two nodes there is a region of maximum displacement that's called an antinode. This is called the fourth harmonic. Let's watch it for a few seconds.
So let's review. We can set up a standing wave on a rope or a string like this. When the wave leaving Randy's hand bounces back, it interferes with the next wave leaving Randy's hand and forms sort of a stationary-looking pattern. We can set up standing waves of different numbers of nodes, points which do not move. And depending on how fast Randy moved his arm up and down, this goes on and on, and we can form an almost endless series of patterns.
Waves
Standing Waves
Physics in Action: Standing Waves on a Rope Page [1 of 1]

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