# What is "Young's modulus", and how does it relate to guitar?

I've come across some posts that mention "Young's modulus" in relation to guitar.

Young's modulus is discussed on physics.SE (Young's Modulus and Vibrating String Harmonics), but I'm looking for a less technical explanation.

On this site, it's mentioned in a few posts in relation to guitar:

• This answer to "What types of plastic and manufacturing techniques are used to make guitar picks?"
• This answer to "vibrato on classical guitar is more of a “side to side” motion?"
• This answer to "How does string gauge affect intonation?"
• This answer to "Bridge intonation patterns on stringed instruments"
• And this answer, also to "Bridge intonation patterns on stringed instruments"

In lay terms, what is Young's modulus, how does it relate to guitar, and does it similarly relate to other stringed instruments?

• This question is answered in the last two paragraphs of music.stackexchange.com/questions/114451/… Commented May 15, 2021 at 16:19
• The last sentence is important - it may well relate to fretless instruments, the players of which maybe don't even realise they compensate without even considering moduli!
– Tim
Commented May 15, 2021 at 16:35
• The last sentence has some importance. It may have relevance to fretless instruments, the players thereof not even realising that they compensate for moduli while in mid-flow! We await, with bated breath, the findings of Jemenake!
– Tim
Commented May 15, 2021 at 16:39
• It describes if you need a lot or a little force on the area(stress) to make stuff bend like rubberband(strain).
– Emil
Commented May 15, 2021 at 17:04
• Well, it's an inherent property of all solid materials. So it does apply to fretless instruments too, but be prepared to do some interesting integrals if you want to actually calculate something with it.
– ojs
Commented May 15, 2021 at 18:04

The formula is `E = σ/ε`, where `E` is Young's modulus, `σ = F/A` is the tensile stress, or force `F` over the cross-sectional area `A` (e.g. string cross-section), and `ε = (l - L0)/L0` is relative change of length. The units of `E` are Pa (pascals); one could visualize it as pressure occurring in the material in response to deformation. https://en.wikipedia.org/wiki/Young%27s_modulus https://en.wikipedia.org/wiki/Stress_(mechanics) https://en.wikipedia.org/wiki/Deformation_(physics)
Young's modulus determines speed of sound in the material. E.g. for an elongated rod (like a string) it is `c² = E/ρ` where `c` is the speed of sound and `ρ` is the density. (https://en.wikipedia.org/wiki/Speed_of_sound#One-dimensional_solids) I presume this must be an important factor when choosing materials to make an instrument, especially larger parts with resonances significant for the instrument sound.