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David, <br>
<br>
No.. you can not calculate for a variable with two unknowns. If you
want to solve for pitch as you suggested in your earlier post.. you
first have to have all the other variables in any equation you use to
do so. Rewritting the tension formula still includes both tension and
length, and when you change length you change tension, resulting in two
unknowns, both of which must be known before you can solve for pitch. <br>
<br>
The equation for solving for this accompanying change in tension has
been posted several times. I post it again for your edification.<br>
<br>
<a class="moz-txt-link-freetext" href="http://www.pianostemmer.no/files/stringdeflection/brekne.doc">http://www.pianostemmer.no/files/stringdeflection/brekne.doc</a><br>
<br>
If you have a formula for arriving at change in pitch for change in
length directly without solving for the change in tension first...
please share it with us. <br>
<br>
Cheers<br>
RicB<br>
<br>
<blockquote><br>
Of course you can. The pitch (frequency) at which a string vibrates is
a<br>
function of length, diameter and tension. A change in length will
result in<br>
a change in tension which will result in a change in pitch. It's a
complex<br>
equation but it's not trigonometry, it's algebra. You can certainly
rewrite<br>
the formula to isolate pitch, or tension, or length, or diameter.
That's<br>
the beauty of Algebra. The miraculous is simply the unexplained. <br>
<br>
<br>
<br>
A strings vibration period (I assume you mean frequency) will not be
altered<br>
by the soundboard. The string continues to vibrate at its given
frequency<br>
until it stops no matter what the soundboard does (though it does
influence<br>
how long it will vibrate for). <br>
<br>
<br>
<br>
David Love<br>
davidlovepianos at comcast.net<br>
www <br>
<br>
You can not solve for change in pitch directly by re-writting /
re-arranging<br>
the formula for string tension. You can not because any given change in<br>
length automatically carries with it a change in tension i.e. you have
two<br>
unknowns.... tension and length. Length change is easy to calculate
with<br>
the simple trig talked about. But that leaves you with an unknown
change in<br>
tension still. You could measure pitch of course and calculate the new<br>
tension that the new length resulted in...... but aside from being the
long<br>
way around... we are solving for pitch. Its easy enough to do... just<br>
calculate the change in length, and then the resultant change in
tension.<br>
Then you have all the variables you need to calculate for resultant
pitch.<br>
<br>
Thats.... for a string whose vibration period is truly reflected by the<br>
soundboard... and not altered significantly due to any stiffness
issues...<br>
which just came up and of course sheds a different perspective on
everything<br>
to the degree that thought ends up being significant itself.<br>
<br>
Cheers<br>
RicB<br>
<br>
<br>
<br>
<br>
David Love<br>
davidlovepianos at comcast.net <br>
<a class="moz-txt-link-abbreviated" href="http://www.davidlovepianos.com">www.davidlovepianos.com</a><br>
<br>
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