Guitar string tension question

[Apex]

OK, any takers on this one?  It's not a music-related question, just simple physics or whatever.

> Given the exact same set of strings gauge-wise on two different guitar scale lengths, for example, short (24.00") and long (25.5"), both tuned to A=440, which set has the higher string tension?

I oughta know this one, I've played all sorts of guitars, but don't have a clue.

[Steve M]

I would have thought they would be equal when tuned to 440Hz but the longer neck would have more stress on it?

[patchz]

I agree with Steve, the longer neck should have more tension. But I'm much better at playing guitar than I am at physics.

[Apex]

Well, I needed a fun brain teaser.  Logically the long scale should have the higher tension, but we seem to not be sure about that. 

My ex-drummer, who is a math super-whiz and now plays guitar and knows a lot about guitar necks etc., did not know this one. 

[Groundbound1]

If you're getting the same notes out of both, the sting tension should be the same I'd think. Higher tension, results in higher pitch.

[Apex]

www.mcdonaldstrings.com/stringxxiii.html

Looks like given a constant pitch, the longer the scale, the higher the tension.

Some scale length stuff:
Gibson is typically 24.75", Les Pauls, SG's, etc.
Fender Jaguar = 24.00, Strats & Jazzmasters 25.5.
PRS = 25 1/8 I think, maybe some variations.

Your typical or standard classical guitar length scale is 650mm.

I once had an Ovation electric nylon string acoustic with a 670mm scale, the longest scale I've ever played.

[Steve M]

I would still argue that the tension of the string between the bridge and  the nut need to be equal because we measure string tuning tension in Hz. The footpounds (or kilograms) of tension only would incorporate the neck and bridge from the body to the tuning pegs. The bits under the strings. I am likely wrong again.  I do think a longer string will resonate for a longer time.   

[BigTruck]

I say forget the strings and go straight Peter Frampton with the voice thingy
8-)

[patchz]

I say forget the strings and go straight Peter Frampton with the voice thingy
8-)

It's not as easy as you might think, especially when trying to match it to the riff you are playing on the guitar, trust me.