String Tension $T$

$$T = (2fL)^2\mu = (2f)^2LM = \pi\rho_s(Lfd_1)^2$$

where

$$\begin{eqnarray*} f &=& \mbox{ note frequency } \in [A_2,C_5]=[27.5,4186] \mbox{ Hz}\\ \mu &=& \mbox{ linear mass density}\\ M &=& \mbox{ entire string mass}\\ \rho_s &=& \mbox{ density of steel core ($7860 \mbox{kg}/\mbox{m}^3$)}\\ \end{eqnarray*}$$

• Should strive for $Lfd_1=$ constant
• In practice, the tension is distributed linearly or parabolically
• Uniform tension is good for the frame.
• Treble tension is pretty uniform at 620 N