Okay, "guess" was too weak a word. Don't be so picky. The string is stretchy, and stretchy = nonlinear, but why so close to a 2:1 ratio for the two "fundamentals." My first thought was a false fundamental at 8 Hz, but the presence of the 24 Hz and 40 Hz modes killed that. Then I thought maybe the driver (Pasco wave driver with the speaker diaphragm) might have a non-linearity, but the 2:1 ratio seems too convenient for a non-linear system. Was that serendipitous or expected? If the ratio of the fundamentals had been 1.83 : 1 or some other non-integer ratio or maybe a cylindrical Bessell zero point (2.4:1), it wouldn't have surprised me as greatly. Plus, we've done this with stretchy string for years without seeing it before. Does the longer string enhance the non-linear effects? That makes sense. But the 2:1 ratio, while nice, doesn't seem automatic.
Thanks for the advice on how to reduce nonlinear effects.
Bill N
John Denker jsd@av8n.com> 4/9/2009 11:31 am >>
Why are we guessing? It takes two seconds to find out whether the
string is stretchy. Pull on it and see what happens.
If the string is stretchy, the equation of motion will be nonlinear.
The kernmantel construction (if any) is irrelevant. The boing/twang
of a rubber band is grossly nonlinear, even though the material is
homogeneous.
If you suspect your string is too stretchy, you can take Henny
Youngman's advice: don't do it that way. Non-stretchy cordage
is easy to come by.
For any given string, you can reduce the effect of stretchiness
by dialing up the static tension and dialing down the wave amplitude.
Also make sure there is no compliance in endpoints.
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