inharmonicity

[Richard Brekne]

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While I was digging about the net on this one I ran into the
following:
The following is THE equation for EVERYTHING you desire (and then
some):

    n * sqrt(T/u)
f = ------------
        2L

f = the frequency of a streched string (or wire)
n = 1 for FUNDAMENTAL frequency (which is what we want)
T = Tension in wire
u = (actually a greek mu) mass per unit length of wire

Solve this for T and we get

T = 4 L^2 F^2 u

The mass per unit length (mu) is defined as

    R A
u = ---
     g

R = (rho in greek) = density of wire material
    steel = 0.283 lb/in^3    brass = 0.310 lb/in^3
A = cross-sectional area of the wire (pi * r^2) or (pi * (d/2)^2)

    r = wire radius or d = wire diameter
g = gravitational constant (32.2 ft/sec^2)

This reduces to

     pi * (d/2)^2 * R * F^2 * L^2
T = ------------------------------
           96.6                     (the 96.6 is (32.2 * 12
in/ft) / 4 )

so, for #8 steel wire (d = 0.020"), 16 in long, tuned to A (440
hz)
it will be under 45.6 lbs tension!

You will need to dig up a table of string #s to find the diameter

(#6 = 0.016" #8 = 0.020" #10 = 0.024" #12 = 0.029") and other
densities if you don't use steel or brass wire. ANY college
physics
book should also have these equations as well as the wire
diameter table
and the wire densities.



Just in case anybody is interested....grin


>  Djalma Carvalho - Brazil

--
Richard Brekne
RPT, N.P.T.F.
Bergen, Norway
mailto:Richard.Brekne@grieg.uib.no


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