Re: [Phys-l] standing wave experiment

[John Denker <jsd@av8n.com>]

On 04/09/2009 09:04 AM, Bill Nettles wrote:
> 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.

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.