[CAUT] Wire Stretch

[RicB]

Found a typo in 4th sentence and changed it...  ... "the change in 
tension" should have read "the change in frequency".  It is corrected below.
Cheers
RicB

Hi JD

Since you havent responded to this I thought I would supply the answer 
you queried. This answer takes into consideration only the tension and 
frequency change brought about by the deflection change you sketch out 
below.  It doesnt take into consideration that the strings offset angle 
through the bridge pins will also change by such a 0.5 mm sink into the 
bridge... and hence its length for this segment changes significantly 
altering the pitch and tension further and in the same direction. 
But...for the simple case of the deflection alone... the change in 
frequency (with a starting tension of  157 lbs and frequency of 2105 hz, 
lengths as per yours below) for a 0.5 mm drop in deflection is about 19 
hz. The strings length will shorten by about 0,018752 mm which 
immediately lowers tension by roughly 2,8283 lbs.  Using the formula  
F=SQRT((T*398*10^6)/(length in mm *string diameter in mm )^2) for 
frequency then... you get about 19 hz change.  Works out the same using 
your formula for F and a value of 18036 for K.

Quite a big difference from your 0.026 hz I'd say.  You can actually  
measure this on a monochord if you like... very easy to construct 
something to do this I would think.

If anyone wants a copy of the basic spreadsheet worked out to calculate 
this stuff using the formulas supplied by Galembo I'd be glad to share 
it with you and welcome comments.

Cheers
RicB