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There's also the possibility that the cores of the wound strings could be of different diameters while the overall diameter stays the same.

Pat

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formerly known around here as burbank
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http://www.patfosterguitars.com

Trevor:
The only test of strings I did that would directly show the Young's modulus was when I looked at the longitudinal resonant pitches. This is what's sometimes called the 'zip' tone. Normally it's not considered something that can affect the sound of the guitar, but it does through an interesting coupling effect that could be considered non-linear. Anyway, it's easy to find the 'zip' tone pitch of a string: just rub along the length with a piece of rosin, or a rag that has been rubbed with rosin. In most cases it's somewhere between the 7th and 8th partial of the string. The pitch is determined by the density of the string material and the Young's modulus.

Although we think of the Young's modulus as a 'constant' that's pretty well defined for a given material, in fact it's not that simple. As Trevor points out, drawing metal into a wire tends to align the crystal structure, and raises the Young's modulus along the wire. It also usually hardens the metal, so that at some point you have to anneal it or it will be liable to break. That 'resets' the crystal structure.

Putting the string under tension also aligns the crystal structure. It's not as much of an effect as you'd see from drawing the wire, since it's (supposed to be) a reversible stress, but it's there. This is very pronounced on nylon strings, but it also shows up with steel. A plain steel G string will have a lower 'zip' pitch than the high E. Just another example of what my father in law used to call the 'innate perversity of inanimate objects'.

Thanks, Alan.

The "two tone test" I use for measuring string stiffness for intonation purposes (it's in the book) can also be used to back out a number for Young's modulus. There's quite a variation in E across the plain strings and across brands, depending, I guess, on each makers drawing schedule and exact alloy composition.

Exactly!

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au