String motions

[Jim]

Hi Robert and all:

back in the late 60's I had occasion to do strobe light studies of
string vibration modes.  We had a grand action model which could be
used to excite the single string of your monochord. With strings
terminated over a simulated V-Bar at each end of the speaking length,
the string exhibited an elliptical motion which rotated from side to
side in planes almost as steep as these:   /    \ .  It was not circular
but elliptical.  Although I did not do this experiment, I suspect that
if we had used a bridge pin type termination with the bridge pin slanting
upward to the left, the elliptical would have alternated between  |  \.
If I find time, I may try to duplicate this experiment.

For those of you not familiar with strobe lights, some can be varied in
speed to match a particular mode of vibration so that it appears that the
string is standing still or moving very slowly.

Jim Coleman, Sr.


On Sun, 13 Apr 1997, Robert Scott wrote:

> Jerry Anderson wrote:
> >
> >A number of years ago I witnessed Rick Baldassin, in a convention
> >class, demonstrate that a plucked string emits a different set of
> >frequencies according to whether it is plucked in a horizontal
> >(in the plane of the strings) or vertical (toward the soundboard)
> >direction.
> >
> >It  would seem that the vertical plucking would most approximate
> >the principal mode of a string struck by a hammer.
>
>
>   Again I must refer to that most excellent article in January 1979
> Scientific American, pg 118, by Gabriel Weinreich.  In that article
> he details his studies of string motions and their coupling to the
> soundboard and to each other.  He found by direct measurement
> that the initial vertical motion of the string precesses into a
> round-and-round motion with both vertical and horizontal components.
> This precession affects the decay too.  When plotting the decaying
> amplitude as a function of time, Weinreich observed that the inital
> rate of decay transformed into a somewhat slower rate of decay.  He
> found that this correlated with the vertical vs. round-and-round motion
> of the string.  When the string is initially struck, the motion is vertical.
> Vertical motion has maximum coupling of energy to the soundboard,
> so the amplitude decay rate is set by how fast energy is leaving the
> string and going into the soundboard.  But when the motion
> precesses to round-and-round, half of the energy is in vertical motion
> and half is in horizontal motion.  The horizontal motion does not
> couple to the soundboard nearly as well, so the energy stays in the
> string and the decay rate is not as great.
>
> This is only one of the interesting conclusions of Weinreich's article.
> If your library has back issues on microfilm or something, I strongly
> recommend taking a look at it.
>
> Bob Scott
> Ann Arbor, Michigan
>
>