FYKOS Year 36 Series 3 Problem 5 — guitar · FYKOS 36 #36.3.5

Physics · mechanics · thermodynamics

Problem

Assume you have a guitar that is perfectly tuned at room temperature. By how many semitones (in tempered tuning) will the individual strings be out of tune if we move to a campfire, where it is cooler by 10 ∘\mathupC10\,\mathrm{^\circ\mskip-2mu\mathup{C}}? Will the guitar still sound in tune? The distance between the string attachment points is d=65 cmd = 65\,\mathrm{cm}. The strings have a density ρ=8 900 kg⋅m−3\rho = 8~900\,\mathrm{kg\cdot m^{-3}}, a Young's modulus of elasticity E=210 GPaE = 210\,\mathrm{GPa} and a thermal expansion coefficient α=17⋅10−6 K−1\alpha = 17\cdot 10^{-6}\,\mathrm{K^{-1}}.

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