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Re: standing waves on a string



At 12:07 PM 11/14/00 -0500, Ludwik Kowalski wrote:
Here is something new to me. Any comments?
...
1) The prong amplitude is not small in comparison
with the maximum [string] amplitudes (at antinodes) and the
first loop on my left side is less than complete;

Is this new or unexpected? What was the expected result?

What does this say about the Q of the standing wave?

the length changes with the amplitude of the prong.

I predict that the Q depends inversely on amplitude.

2) String oscillations are not confined to the vertical
plane

Is this new or unexpected?

as in the textbook model.

That rather depends on the textbook.

I can observe loops
from the side and I can observe them from above.
My string is black but it has white spots. White spots
near places where amplitudes are large move along
circles. The antinodes seen from above are about as
wide as when seen from a side. This confirms circular
trajectories.

I predict that Ludwik is using string "laid up" from twisted strands. I
say this because such a configuration would cause a huge matrix element
coupling the VP (vertically polarized) mode to the HP (horizontally
polarized) mode.

I further predict that switching to twist-free string, will result in
ellipses with greater eccentricity, OTBE, because there will be much less
coupling.

Really nice string with a woven "Kernmantel" design can be
found in a bait store -- check out the high-strength fishline.
Some high-strength kite string is equivalent.

3) Nodes seen from above are practically at rest

OK.

but "nodes" seen from the side are not at rest,

Ideal nodes would be at rest. But non-ideal nodes that are only
"relatively" free of motion are permitted by the definition
http://www.m-w.com/cgi-bin/dictionary?va=node
and permitted by the physics.

It is remotely possible that the VP mode has real nodes, just slightly
offset from the position of the nodes in the horizontally-polarized mode.
But it is more likely that Ludwik is making and reporting an accurate
observation that the VP mode has non-ideal nodes; this would be consistent
with the previous observation of 1/Q >> 0.

In general, a left-running wave of size 11 with a right-running wave of
size 10 is equivalent to a standing wave of size 20 plus a leftover
left-running wave of size 1 -- which would produce a node-amplitude of 1.

In other words points near the node do not
move along circles.

We have four phasor components in play: VP1, VP2, HP1, and HP2. They are
not all equal in magnitude. Is this surprising?

=====================

More food for thought: For your typical string, the HP mode is very very
nearly degenerate with the VP mode. How might you lift this degeneracy?