String vibrations (was Re: Stuart)

[Phillip Ford]

>Consider:
>
>The Stuart bridge agraffes steer the string excursion in the vertical 
>direction for better tone and longer sustain.
>
>The Wapin bridge modification steers the string excursion in the 
>horizontal direction for better tone and longer sustain.
>
>Ron N


Exactly.... but how do they compare in that effort. Might be interesting to
have the same kind of data on the Stuart as is available for the Wapin.

--
Richard Brekne

-------------
I think that anybody that thinks he is 'steering' the string vibration one 
way or another is kidding himself.

Phil Ford

Just for kicks see:

http://ccrma-www.stanford.edu/~jos/waveguide/Horizontal_Vertical_Transverse_Waves.html

and:

Unusual motions of a nonlinear asymmetrical vibrating string
R J Hanson???, H K Macomber???, A C Morrison???
???Univ. of Northern Iowa, Physics, Cedar Falls, IA, United States; ???Northern 
Illinois Univ., Physics, DeKalb, IL, United States

A rich variety of unusual motions of a sinusoidally driven vibrating string 
results from nonlinearities due to varying tension and longitudinal motion 
not included in simple linear theory and to intrinsic asymmetries in the 
string. In a brass harpsichord string(wire) the asymmetries cause a small 
splitting of each natural frequency of free vibration into two closely 
spaced frequencies (relative separation ~ 0.2% to 2%.) The two frequency 
components are associated with transverse motion along two orthogonal 
"characteristic" wire axes. The absolute amount of splitting for a given 
wire is inversely dependent on the tension. Introduction of a twist in the 
wire can also affect the amount of splitting. These asymmetric properties 
have a profound effect on the nonlinear behavior. Detailed measurements of 
the resulting features of the motion of a driven string have been reported 
(Hanson et al., Proceedings of ISMA 2001, pp. 157-160.) Generation of 
higher harmonics and of motion perpendicular to the driving direction 
result in elaborate motions which can suddenly change from one state to 
another. Emphasis will be on some motion patterns of a point on the wire as 
exhibited on videotape (e.g., one appearing almost chaotic but with a 
pattern period of over 10 seconds.)