Date: Thu Sep 6 14:27:21 2007

Author: Martin Simon

Subject: Re: Quantitative Chladni Plates experiments?

Post:
We have a couple versions. The bow driven version is connected at the
center to a table clamp. It does take some practice but it is not too hard
to get three different patterns by bowing at the right position and holding
the plate edge with fingers as shown in the drawings. This plate is
21.5 x 26 cm and is quite stiff. We use a violin or cello bow with rosin.
I have made a heavy duty bow from a D-shaped brush saw, replacing
the blade with plastic tubing. I saw something like that at the
Exploratorium years ago. However, it is heavy and doesn't work as
well.

The video shows the Pasco Chladni plate kit driven at the center
by their wave driver. It is 24 cm x 24 cm and made of thinner
material. The Pasco part is WA 9607. The wave driver is SF 9324
and it is powered by their function generator.

Marty

At 07:00 AM 9/6/2007, you wrote:

>Hi Marty,
>
>That's a nice web page you've got there.
>
>Do you mean to say that the video shown there is of your own Chladni
>plates, driven with a violin bow?
>
>And if so, is it reproducible by other faculty members of the Dept.
>with the same degree of success?
>
>It's quite impressive.
>
>What are the dimensions of that Chladni plate, if you don't mind my
>asking?
>
>Thanks for sharing.
>
>-- Steve W.
>
>
>
>On Wed, 5 Sep 2007, Martin Simon wrote:
>
> > Date: Wed, 05 Sep 2007 22:50:40 -0700
> > From: Martin Simon
> > Reply-To: tap-l@lists.ncsu.edu
> > To: tap-l@lists.ncsu.edu
> > Subject: Re: [tap-l] Quantitative Chladni Plates experiments?
> >
> > Tyndal made the Chladni patterns in the middle of the page below
> > by hand with a bow. They are very beautiful.
> >
>
> >
> > I just learned that the Hermann grid illusion was discovered when
> > Hermann was looking at these patterns. The grid illusion is when
> > black dots appear at the intersections. For an enhanced version
> > of the illusion, see
> > http://web.physics.ucla.edu/marty/illusions/dotillusion.jpg
> >
> > Martin Simon
> >
> > Urs Lauterburg wrote:
> > > Richard,
> > >
> > > Thank you so much for venturing into the subject for me and for
> > > providing me lot's of substantial information about the subject. Thank
> > > you also for providing the geometric dimensions of the plates. The plate
> > > I always use in my setup makes all types of different patterns at
> > > various frequencies. It is a thin, maybe about 1mm thick black anodized
> > > aluminum plate. Most of the possible patterns are two fold symmetric and
> > > a few are even four folded. One very fine and visually attractive
> > > pattern I get at a fairly high excitation frequency a bit above 5kHz. It
> > > always surprises our students that the plate shows a complicated fine
> > > but still very distinct oscillation pattern. Yes and the patterns are
> > > very predictable in the sense that if you hit the given excitation
> > > frequencies, you always get the very same Chladni figures.
> > >
> > > In my case the excitation is applied with a mechanical transducer from
> > > Bruel&Kijaer a device much like the PASCO Mechanical Wave Driver but
> > > with a higher bandwidth at the very center of the square plate. I drive
> > > the transducer with the 100V output of a special audio amplifier which
> > > amplifies a sine signal generated by a Stanford Research digital
> > > synthesizer DS345. The SR-DS345 is controlled through GPIB by means of a
> > > GPIB-ENET converter. This gives me the possibility to control the exact
> > > frequencies and amplitudes needed for various nice pattern combinations
> > > creating an interesting effect along with the audible sound.
> > >
> > > I guess I will have to experiment a bit more with different geometries
> > > and plate thicknesses to get the very repetitious and symmetrical
> > > patterns I would like to get. Do you think your type of exiting
> > > mechanism will be superior to the one I use? I am not quite sure if I
> > > understand the mechanism of your system. Is the nickel tube just pushed
> > > up and down by applying a B-field with a coil?
> > >
> > > Very interesting is your mentioning of the mathematician Sophie Marie
> > > Germain. I will definitely have to do some reading on her work before
> > > refining my Chladni plate demonstrations.
> > >
> > > Once again thank you for generously sharing your expertise.
> > >
> > > Kind regards
> > >
> > > Urs
> > >
> > > Urs Lauterburg
> > > Physics demonstrator
> > > Physikalisches Institut
> > > University of Bern
> > > Switzerland
> > >
> > >
> > >> Urs,
> > >>
> > >> Thank you for your message regarding Chladni plates. I believe that I
> > >> can answer most of your questions.
> > >>
> > >> The plates are 1/8 inch standard aluminum, black anodized so that the
> > >> sand is visible. The square (12"x12"), circular (12" diam) and
> > >> tie-shaped plates were made from sketches, with verbal instructions to
> > >> do the best reasonable job in keeping the plates symmetric. This
> > >> would mean about +or- 0.003 inch. You can't do much better than that
> > >> in drilling and tapping the center thread that couples the vibrating
> > >> nickel tube to the "exact" geometrical center of the plate. The
> > >> oscillation originated from magnetostriction in a thin-walled,
> > >> annealed nickel tube; ours is 0.5 inch diameter and 0.015" wall
> > >> thickness. A 1/4"x20 thread is brazed onto the end of the tube and
> > >> screwed into the plate to couple the vibrations to the center of the
> > >> plate. Last time I looked, they had apparently discontinued
> > >> fabrication of this material. However, we have some that we will
> > >> probably never use that I would be willing to part with. You only
> > >> need one for several plates; just screw it into the plate being used.
> > >>
> > >> The magnetic field is supplied by a 25 foot length of #18 enameled
> > >> copper wire: about 88 turns with a resistance of about 0.167 ohm. Coil
> > >> ID 0.65" and OD 1.6": I don't believe this is critical. It is driven
> > >> by a large audio amplifier connected to a reasonably stable but very
> > >> old oscillator, seen in the photograph of the demo:
> > >>
> > >> http://www.physics.umd.edu/lecdem/services/demos/demosg4/g4-22.htm
> > >>
> > >> I "borrowed" the idea of the magnetostriction Chladni plate from E. R.
> > >> Pinkston, now retired from the U.S. Naval Academy, with his permission
> > >> and assistance. (He is author of some of the papers in our reference
> > >> list.)
> > >>
> > >> A sideline story that goes nicely with the use of the Chladni plate
> > >> demo involves one of the most prominent early female mathematicians,
> > >> Sophie Marie Germain, French mathematician (1776-1831) according to
> > >> ask.com. She apparently wrote some nice mathematical material under a
> > >> phony male name to get the attention of Lagrange, who recognized her
> > >> genius and helped her. Her main contribution was to explain Chladni
> > >> plate patterns using the principles of mathematics and calculus, for
> > >> which she received (on her third attempt) the Napolean award for the
> > >> best mathematical application of the year (1815). Chladni had earlier
> > >> demonstrated his plates to Napolean, who apparently then developed
> > >> some fondness for them.
> > >>
> > >> Here are some web sites that I found searching Google on "chladni
> > >> early female mathematician":
> > >>
> > >> http://womenshistory.about.com/library/bio/blbio_sophie_germain.htm
> > >>
> > >> and on "sophie germain":
> > >>
> > >> http://www.agnesscott.edu/lriddle/women/germain.htm
> > >> http://en.wikipedia.org/wiki/Sophie_Germain
> > >> http://www.sdsc.edu/ScienceWomen/germain.html
> > >>
> > >> I hope that this is more than you really wanted to know.
> > >>
> > >> Best wishes,
> > >>
> > >> Dick
> > >>
> > >> ***********************************************************************
> > >> Dr. Richard E. Berg, Professor of the Practice
> > >> Director, Physics Lecture-Demonstration Facility
> > >> U.S. mail address:
> > >> Department of Physics
> > >> University of Maryland
> > >> College Park, MD 20742-4111
> > >> Phone: (301) 405-5994
> > >> FAX: (301) 314-9525
> > >> e-mail reberg@umd.edu
> > >> www.physics.umd.edu/lecdem
> > >> ***********************************************************************
> > >
> > >
> > >
> > >
> >




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