Four String Tension Equations

Here is a complete set of four string tension equations, where
each equation gives dimensionally consistent results.

T = tension, in Newtons

F = frequency, in Hertz, or cycles per second

L = length, in meters

D = diameter, in meters

r = radius, in meters

rho = mass density of the stringing material, in kg/m^3

M/u.l. = mass per unit length = Pi * r^2 * rho, in kg/m

M = total mass, in kg

When the string diameter is given:

((1)) T = F^2 * L^2 * D^2 * Pi * rho

((2)) T = 4 * F^2 * L^2 * Pi * r^2 * rho

When the string diameter is not known, one must determine the
mass per unit length ( M/u.l. ) by weighing one unit length (one
meter) of the string on a scale:

((3)) T = 4 * F^2 * L^2 * M/u.l.

When the string diameter is not known, one must determine the
total mass ( M ) by weighing the vibrating string length ( L ) on a
scale:

((4)) T = 4 * F^2 * L * M

Cris Forster, Music Director
www.Chrysalis-Foundation.org