From: [EMAIL PROTECTED]
Subject: Re: re gut strings
Date: February 9, 2007 8:33:58 AM EST
To: [email protected]
The technical aspects aspects of this thread have wandered fairly far
from reality.
First, there is a small language problem: despite their literary
incestuousness in common usage, "stress" and "strain" mean different
things.
Stress is force / area, in this case the tension on the string
divided by its cross sectional area.
Strain is the percentage deformation of an object under stress:
change in length / length. Strain isn't particularly relevant here.
A given *material* has a breaking stress. When you break something,
you have to break atomic or molecular bonds to pull the pieces apart.
This requires a specific amount of force for a given material. If I
have two strings made out the same material, one thicker than the
other, I'll have to pull harder on the thicker one to break it
because I have to break more bonds.
This has an interesting consequence: when you write the equation for
the pitch (frequency ) of a string in terms of stress rather than
tension, the diameter of the string disappears. For a given length
and material, the pitch at which the string breaks doesn't depend on
the thickness.
True, at a given pitch the thicker string is yanking harder (greater
tension) on the bridge, but it's the stress not the tension that will
break it. If you're still unhappy with this, think of it this way -
the thicker string is under more tension, but that tension is being
handled by more molecular bonds.
Note that this has nothing to do with the length. The tension in a
string is the same everywhere along its length. If it weren't it
would immediately reconfigure itself so that it was. That it feels
like more tension when you pluck near the bridge is mostly a matter
of geometry. (Trying to displace the string sideways by some amount
will have a bigger component of tension perpendicular to the string
when you're near the bridge. You're also trying to bend the string at
a sharper angle, so the stiffness of the string material will have a
greater effect near the bridge.)
As a practical matter, very thin strings are probably more fragile
because nicks and minor wear and tear take a bigger chunk (as a
percentage) out of the area of thinner strings. This can make the
stress at the point of the damage exceed the breaking stress.
Last point (for those whose eyes have not yet glazed over): Most
lutes have the same length for the fingerboard strings and have the
first several courses strung in the same material. This means that
only the chanterelle would ever be near the breaking pitch. Pity your
friends the baroque harp players who get different pitches by
keeping tension and diameter (and thus stress) roughly the same and
varying the length. They can have many strings near their breaking
pitch. They break lots more strings than we do.
Bob Clair
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