Editing String instrument (section)

=== Linear density ===

The pitch of a string can also be varied by changing the [[linear density]] (mass per unit length) of the string. In practical applications, such as with [[double bass]] strings or bass [[piano]] strings, extra weight is added to strings by winding them with metal. A string with a heavier metal winding produces a lower pitch than a string of equal length without a metal winding. This can be seen on a 2016-era set of gut strings for double bass. The higher-pitched G string is often made of synthetic material, or sometimes animal intestine, with no metal wrapping. To enable the low E string to produce a much lower pitch with a string of the same length, it is wrapped with many wrappings of thin metal wire. This adds to its mass without making it too stiff. The frequency is inversely proportional to the square root of the linear density:

:<math>
f \propto {1 \over \sqrt{\mu}}
</math>

Given two strings of equal length and tension, the string with higher mass per unit length produces the lower pitch.