Originally Posted by bassist14
well, according to http://baen.tamu.edu/users/rel/perso...ssStrings.html
its an easy calculation
(i discovered right now for the first time that you can click on the tabs at the bottom of the page (which is based on an excel-sheet, i think) on the "105cm" "110cm" and "string tension" tabs
("9.80665 m/s^2 = acceleration due to gravity" is my favourite
Since we're an international forum I thought I should use the SI appropriate value for gravitational acceleration
. Let's just call it g for now.
<NERD ALERT - Skip this if math makes you woozy>
Starting with the original equation
f = 0.5 * sqrt(T/(9.80665*p*l*a))
f = frequency [Hz]
T = tension [N]
p = effective mass density [kg/m^3]
l = scale length [m]
a = cross sectional area of the string [m^m] = (pi*d^2)/4
d = string diameter [m]
pi = 3.14159
g = 9.80665 m/s^2 = acceleration due to gravity
If you're not familiar with spreadsheet math, d^2 is d squared, / is division, sqrt() is square root, and * is multiplication. If you rearrange the equation so you're solving for tension you get
T = 4 * f^2 * g * p * l * a
and since area is pi*d^2 /4
T = pi * f^2 * g * p * l * d^2
so for a given frequency as the length or diameter increases, the tension increases. Note also that since tension is a function of the square of diameter and frequency, small changes in either of those parameters will result in big changes in tension.
The fly in all this ointment is that you need to know p, effective string density. A more dense string, e.g. steel core versus a less dense string, e.g. nylon core, will have more tension. If a string was a wire made of a pure material this would be known, but strings are complex little buggers! Wrappings, core composition and construction, etc. make this data that you need to determine empirically for each string. This is also why some gut E & A strings are wrapped, increasing the effective density while decreasing the diameter. This allows you to maintain a desired low tension and low frequency without having to accommodate a big-ass string.
In the tension chart, if a tension value was given for a string at known frequency, length, and diameter I back-calculated the effective string density. With that data point I could calculate tensions at different frequencies or scale lengths. Without some way to get p I agree with Jake and Phil, you can't estimate tension based on dimensions alone. It would be really useful to collect a table of effective string densities but I suspect we would be running into proprietary areas for the string companies.
And of course, none of this has anything to do with how the string will sound on your bass.
If you skipped down to here, just know that the above is nothing short of brilliant and probably deserves the Nobel Prize for string theory.
Plus, I agree with two of our venerable TBDB members so it must be right!