Relationship between pitch and string length

[guilesar]

Is the relationship between the length of a guitar string and the frequency of the pitch it produces a linear relationship? e.g. If the frequency of the pitch of a string is 60 Hz and I halve the length, should it produce a pitch with a frequency of 120 Hz?

This is assuming all other variables, tickness, tension and material are all held constant.

 

[DrClaude]

If the frequency of the pitch of a string is 60 Hz and I halve the length, should it produce a pitch with a frequency of 120 Hz?

Yes. Imagine you excite only the second harmonic of the string: the frequency is doubled and the mid point of the string is a node. Putting your finger there and letting half the string vibrate gives the same result.