[CAUT] pre-stretching new string?

[David Love]

http://www.1728.com/unknwn2.htm

 

Maybe this will help.  Are you trying to tell me that you can't solve for
how a resulting change in length on a given string will change tension and
thus the frequency at which the string will vibrate?  You are incorrect.    

 

David Love
davidlovepianos at comcast.net
www.davidlovepianos.com 

-----Original Message-----
From: caut-bounces at ptg.org [mailto:caut-bounces at ptg.org] On Behalf Of
Richard Brekne
Sent: Monday, June 11, 2007 2:39 AM
To: caut at ptg.org
Subject: [CAUT] pre-stretching new string?

 

David, 

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. 

The equation for solving for this accompanying change in tension has been
posted several times. I post it again for your edification.

http://www.pianostemmer.no/files/stringdeflection/brekne.doc

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.  

Cheers
RicB


Of course you can.  The pitch (frequency) at which a string vibrates is a
function of length, diameter and tension.  A change in length will result in
a change in tension which will result in a change in pitch.  It's a complex
equation but it's not trigonometry, it's algebra.  You can certainly rewrite
the formula to isolate pitch, or tension, or length, or diameter.  That's
the beauty of Algebra.  The miraculous is simply the unexplained.  

 

A strings vibration period (I assume you mean frequency) will not be altered
by the soundboard.  The string continues to vibrate at its given frequency
until it stops no matter what the soundboard does (though it does influence
how long it will vibrate for).    

 

David Love
davidlovepianos at comcast.net
www 

You can not solve for change in pitch directly by re-writting / re-arranging
the formula for string tension. You can not because any given change in
length automatically carries with it a change in tension i.e. you have two
unknowns.... tension and length.  Length change is easy to calculate with
the simple trig talked about. But that leaves you with an unknown change in
tension still. You could measure pitch of course and calculate the new
tension that the new length resulted in...... but aside from being the long
way around... we are solving for pitch.  Its easy enough to do... just
calculate the change in length, and then the resultant change in tension.
Then you have all the variables you need to calculate for resultant pitch.

Thats.... for a string whose vibration period is truly reflected by the
soundboard... and not altered significantly due to any stiffness issues...
which just came up and of course sheds a different perspective on everything
to the degree that thought ends up being significant itself.

Cheers
RicB




David Love
davidlovepianos at comcast.net 
www.davidlovepianos.com

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