<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <meta content="text/html;charset=ISO-8859-1" http-equiv="Content-Type"> <title></title> </head> <body bgcolor="#ffffff" text="#000000"> Hi JD Since you havent responded to this I thought I would supply the answer you querried. 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 segement 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 tension (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 immediatly lowers tension by roughly 2,8283 lbs.  Using the formula =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 <blockquote> At 5:51 pm +0100 29/4/07, RicB wrote: >Unfortunatly, you can not calculate the change in frequency for >change in string deflection this way. Or so I am told by a few of >the worlds physisists.  Please see the following for what according >to these is a more correct way of doing this.Ê > ><a class="moz-txt-link-rfc2396E" href="http://www.pianostemmer.no/files/String%20deflection_files/brekne.doc"><http://www.pianostemmer.no/files/String%20deflection_files/brekne.doc></a> Your "world's physicist", in the file above, uses Pythagoras' theorem and no other principle, just as I did, to calculate the changes in length.  The only difference in his equations is that he takes into account a change in length behind the bridge, considered as a violin bridge and not a piano bridge.  Clearly some slight difference in the results will arise if that is added in, with corrections for the actual disposition of the string on a real bridge, just as the re-angling of the dogleg 1/2mm lower round the slanting front pin on a real piano bridge will make a difference, but I'm at a loss to understand why you consider your famous person's Pythagorean theorem so superior to mine and intrigued to see your worked example and results based on this document. If, for instance, you take C76 with a speaking length of 100mm, as I proposed, and take into account a back-length of 50mm, with an initial deflection of +1.5mm (i.e the soundboard bridge is 1.5mm above the straight line from hitch-plate bearing to top bridge), what exact results do you get, using your valued equations, when you force the string down 1/2mm into the wood of the bridge at the front pin? JD </blockquote> <div class="moz-signature"> </div> </body> </html>