It probably isn't fair for me to answer either Jason but I'll give it a shot.
I'm guessing that in these pictures we are seeing a vibrating handbell being rotated in 90°increments as seen using a holographic interferometer -- after being colored in photoshop :). The interferometer uses lasers -- and black magic -- to how the bell's surface is actually moving. The concentration of lines is like a topographical map of the surface of the bell so the peaks, called nodes, are visible as the circles about 1/3 up the side of the bell and the valleys, call anti-nodes, are the bright lines that you see.
Bells vibrate in many different modes which correspond to the harmonic series the bell is tuned to -- read note, as in G#. In each vibrational mode a standing wave -- a wave that appears to simply change in amplitude without traversing through the medium in which it is propagating -- is set up in the bell. It appears stationary because the anti-nodes do not move around the bell's surface when the bell is excited -- like on it's birthday.
Each mode has two orthogonal components which differ sightly in frequency so my guess is that the top picture shows one and the bottom picture show the other. The difference between these modes is that the nodes and the anit-nodes trade places -- the valleys become peaks and vice versa. Normally each of these two patterns that are found in the same mode appear the same. In this case they do not. This is interesting. Really. Believe me. I'm serious.
This could vary well be a result of the driver placement. The diver coil is visible on the right and it uses induction to vibrate the bell at a highly controllable frequency. If the diver is placed over a node it works very well and if it is positioned over an anti-node it does not. Think of it as the difference between jumping onto a trampoline as opposed to concrete. When the driver coil applies a force to the surface of the bell the nodes can move freely and the anti-nodes cannot.
So, when one of the anti-nodes happens to line up with the driver as the bell is turned in a particular way the resulting pattern will be less intense because the driver is essentially beating its head against a wall.
Alternatively it could be something entirely different than driver placement. It could have something to do with imperfections in the bell. It's hard to say because when driving the bell in its fundamental mode, the one pictured, it can behave oddly.
Well, now you've got me all curious Danny. What was it that makes these pictures postworthy?
The answer is the bottom one, and I'll tell you why. First an explaination as to what the pictures are. They show a series of photographs taken as the bell is rotated 60° around its center, in 20° increments. The upper one shows what a bell normally looks like, i.e. the mode is "locked" to the bell no matter where you look from. It moves as you rotate it, just like the continents on a globe move as you rotate the globe. The second one shows what happens if you put a few (neodymium - they're cool) magnets of just the right mass, in just the right place: the two orthogonal degenerates, nearly identical modes which are seperated by only a few hertz, shift in frequency so as to overlap almost exactly, meaning that the greatest factor in the location of the mode is no longer the imperfections on the bell, but instead the driving mechanism (there must be an antinode at the driver); thus, the mode always appears to be in the same place. Yes, the A and B modes are mixed. How well? In a rotation around half of the bell, the nodal line that you see shifts maybe 3-5° instead of 180°. We like to call it "re-establishing pseudo-degeneracy."
Confused?
Movies (actually .gif animations) do a better job of showing the effect. See them at www.goshen.edu/~danielak/bellanims
John Ross, Sungdo, and I wrote a paper on this that we hope will be published in the Journal of the Acoustical Society of America. Maybe it will pay for grad school.
4 Comments:
Is anyone else having trouble finding Neo in this matrix code? I must be rusty. :P
It probably isn't fair for me to answer either Jason but I'll give it a shot.
I'm guessing that in these pictures we are seeing a vibrating handbell being rotated in 90°increments as seen using a holographic interferometer -- after being colored in photoshop :). The interferometer uses lasers -- and black magic -- to how the bell's surface is actually moving. The concentration of lines is like a topographical map of the surface of the bell so the peaks, called nodes, are visible as the circles about 1/3 up the side of the bell and the valleys, call anti-nodes, are the bright lines that you see.
Bells vibrate in many different modes which correspond to the harmonic series the bell is tuned to -- read note, as in G#. In each vibrational mode a standing wave -- a wave that appears to simply change in amplitude without traversing through the medium in which it is propagating -- is set up in the bell. It appears stationary because the anti-nodes do not move around the bell's surface when the bell is excited -- like on it's birthday.
Each mode has two orthogonal components which differ sightly in frequency so my guess is that the top picture shows one and the bottom picture show the other. The difference between these modes is that the nodes and the anit-nodes trade places -- the valleys become peaks and vice versa. Normally each of these two patterns that are found in the same mode appear the same. In this case they do not. This is interesting. Really. Believe me. I'm serious.
This could vary well be a result of the driver placement. The diver coil is visible on the right and it uses induction to vibrate the bell at a highly controllable frequency. If the diver is placed over a node it works very well and if it is positioned over an anti-node it does not. Think of it as the difference between jumping onto a trampoline as opposed to concrete. When the driver coil applies a force to the surface of the bell the nodes can move freely and the anti-nodes cannot.
So, when one of the anti-nodes happens to line up with the driver as the bell is turned in a particular way the resulting pattern will be less intense because the driver is essentially beating its head against a wall.
Alternatively it could be something entirely different than driver placement. It could have something to do with imperfections in the bell. It's hard to say because when driving the bell in its fundamental mode, the one pictured, it can behave oddly.
Well, now you've got me all curious Danny. What was it that makes these pictures postworthy?
oh snap!!! you got the A and B modes to combine!! w00t!!!11!!!
The answer is the bottom one, and I'll tell you why. First an explaination as to what the pictures are. They show a series of photographs taken as the bell is rotated 60° around its center, in 20° increments. The upper one shows what a bell normally looks like, i.e. the mode is "locked" to the bell no matter where you look from. It moves as you rotate it, just like the continents on a globe move as you rotate the globe. The second one shows what happens if you put a few (neodymium - they're cool) magnets of just the right mass, in just the right place: the two orthogonal degenerates, nearly identical modes which are seperated by only a few hertz, shift in frequency so as to overlap almost exactly, meaning that the greatest factor in the location of the mode is no longer the imperfections on the bell, but instead the driving mechanism (there must be an antinode at the driver); thus, the mode always appears to be in the same place. Yes, the A and B modes are mixed. How well? In a rotation around half of the bell, the nodal line that you see shifts maybe 3-5° instead of 180°. We like to call it "re-establishing pseudo-degeneracy."
Confused?
Movies (actually .gif animations) do a better job of showing the effect. See them at www.goshen.edu/~danielak/bellanims
John Ross, Sungdo, and I wrote a paper on this that we hope will be published in the Journal of the Acoustical Society of America. Maybe it will pay for grad school.
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