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<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>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. </span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'> </span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>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). </span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'> </span></font></p>
<p class=MsoNormal style='margin-right:0in;margin-bottom:12.0pt;margin-left:
.5in'><font size=2 color=black face="Times New Roman"><span style='font-size:
10.0pt'>David Love<br>
davidlovepianos@comcast.net<br>
www</span></font> </p>
<p class=MsoNormal style='margin-right:0in;margin-bottom:12.0pt;margin-left:
.5in'><font size=3 color=black face="Times New Roman"><span style='font-size:
12.0pt'>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.<br>
<br>
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.<br>
<br>
Cheers<br>
RicB<br>
<br>
</span></font></p>
<p class=MsoNormal style='margin-left:.5in'><font size=3 color=black
face="Times New Roman"><span style='font-size:12.0pt'><br>
David Love<br>
davidlovepianos at comcast.net <br>
<a href="http://www.davidlovepianos.com">www.davidlovepianos.com</a></span></font></p>
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