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Re: [Phys-l] standing wave experiment

Continuing an old thread (~ one year):

--------------------------
We were doing the standard standing-waves-on-a-string experiment with a physical science class yesterday. The students decided to have an extra long (>2 m) string. They found a fundamental mode (a single "loop") at 8 Hz. They doubled the frequency to 16 Hz and found a single loop, not 2. Increasing to 24 Hz produced 3 loops. Going to 32 Hz, back to 2 loops. 40 Hz produced 5 loops. 48 Hz produced 3 loops. It looks like a double fundamental.

My best guess (strictly a guess) is: 1) the string is a "bungee" string which has a fabric sheath around an elastic core, 2) the length increases the possibility of non-linear or co-linear effects. One component (the elastic core by itself?) has a fundamental, and the combined string has another, and the length allows the bifurcation. I haven't measured the mass/length of the components, but will do that.

Anybody else see this before? (A friend commented that J. Denker probably has a paper already written up about this. :) )

Thanks,
Bill N
________________________________


Since posting I've remembered that using a stretchy string has a musical analogue.

http://en.wikipedia.org/wiki/Bebung

And more interestingly:


"When this experiment was first tried out, one of the teaching assistants, who was the instructor in the lab course, noticed a rather odd behavior of this sawblade oscillator when it is being driven by an oscillating magnetic field. In this mode, the driving frequency may be gradually increased or decreased through the resonant frequency of the blade and so illustrate the classical bell-shaped curve of the resonant response. However, what the instructor (and the student) noticed was a peculiar deviation from this expected bell-shaped curve: When the driving frequency was gradually increased, the oscillation amplitude increased at first (as expected) but then remained large, and as the driving frequency was further increased, the oscillation amplitude suddenly decreased. Then, as the driving frequency was gradually decreased, the oscillation amplitude remained small, and then, at a lower frequency from that at which it had suddenly decreased, suddenly increased. This odd behavior was a kind of hysteresis, and as we discovered, arose because this particular mechanical oscillator becomes nonlinear when it is strongly driven."



http://digitalcollections.ucsc.edu/cdm4/document.php?CISOROOT=/p265101coll13&CISOPTR=3379&CISOSHOW=3378

Search the document for hacksaw: (do not use the library's search box)

bc

p.s. Now a std. demo. at UMD:





On 2009, Apr 09, , at 21:13, Bernard Cleyet wrote:

Yes, my thought is the unexpected is heuristic. And in this case a
very "teachable moment". Allowing the students to "come up" w/
Joel's solution, I think, is very PER.


bc contrary to the Strunk and White dictate likes neologisms.

p.s. rubber bands make easy hardening oscillators.


On 2009, Apr 09, , at 11:33, Rauber, Joel wrote:


Since (I believe) the problem here is that PASCO supplies (even
sells)
this
string with their wave motion vibrators, one might think this is good
stuff
with which to work. I bit and ordered a reel of the string when we
bought
the vibrators. That reel remains sealed! The big stretchy stuff is
fine
for showing standing waves (demo mode), but I prefer a 20ft long
coiled
spring for that. I actually have not seen the reported behavior, but
the
stretching of the string makes the traditional experiment impossible
since
knowing the mass/length of the string becomes a function of the
tension
on
the string. Too complicated. We have some 50 lb test fishing line

Actually, if you want your lab to be a little more involved in the
art of experimentation; its not that hard to take it into account.
We take a sample string and put under the same tension as what you
have on the vibrating apparatus, measure its mass and measure its
length to get the mass per unit length under the actual tension
used. It fairly easy to do and gets across the idea of doing
procedures that correct for possible systematic sources of error.
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_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l