Guitar string tension and deflection formulas - FAQ

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String equations

There's no need to be a mathematician to enjoy playing guitar, but a little look "behind the curtain" can be quite interesting if you don't mind a bit of algebra...

Here's a well-known formula that relates string tension, scale length, pitch and string gauge...

String formula

Here, f is the frequency of the note in Hertz, L is the scale length in metres, T is the tension in Newtons (divide by 9.81 to get tension in Kilograms), and µ is the mass per unit length of the string.

What does it mean? As the string gets heavier, the pitch goes down. As the length goes up, the pitch goes down, and as the tension goes down, the pitch goes down.

Why don't we...

Why don't we just use slacker strings to play deep bass then?

Displacement formula

Those who have tried will know that slack strings slap, and are very quiet! In fact there's a formula that connects the tension and how floppy it feels...

t is the deflection force, d is the deflection, T is the string tension and L is its scale length. The formula is only sound for small deflections - larger ones affect the string tension and length.

Armed with this formula, you can see that a longer string needs to be tighter if it's not to feel too floppy. And that's exactly why bass instruments have thicker strings as well as longer ones. Tight strings are loud strings