What is the Vibrating Length of a Guitar String?

Does the effort needed to bend a guitar string when it`s under tension depend on the full length of the string from where it`s anchored behind the bridge to where it`s anchored at the tuner on the headstock ? AS opposed to longitudinal tension which is a function of the tension on the string and it`s thickness ( ? hope I got that right !! ).Does the fact that the string passes over the nut and the bridge affect the force needed to bend the string, assuming the string is free to move through nut and bridge ?Hope this is clear - many thanks for any responses.
- graham smith (age 61)
west midlands UK

Dear Graham,

The accepted vibrating length of a guitar string is usually taken as the distance between the bridge and the nut.  The distances between the nut and the tuning peg as well as that between the bridge and anchor don't contribute to the transverse vibrating length.

Almost all guitar nuts have groves in them that prevent sideways motion of the string.  On my acoustic guitar the distance between the bridge and the anchor is very small.  The corresponding vertical force on the bridge is large and friction will prevent the string from slipping side to side.    On my electric guitar the bridge itself is grooved.   That being said, the frequency of the string will be

where T is the tension, L is the distance between nut and bridge and μ is the mass per unit length.

 

LeeH

(published on 12/12/2014)