# How does a temperature change affect the pitch of the fundamental frequency produced by vibrating string? [duplicate]

The vibrating string is tightened using tuning keys of the guitar. Assuming the amount of tightening is constant, what will change in string (mass? tension? linear density?) when a temperature change causes expansion in the string? If an increase of 10K in temperature, will the change in fundamental frequency be significant to hear a difference in pitch?

• I would dispute the change in tension is negligible. Metal strings have a thermal expansion coefficient of the order of $10^{-5}/\text{K}$, so an $10\text{K}$ change in temperature gives a thermal strain of order $10^{-4}$. Compare that with the strain at the elastic limit, of the order of $2\times 10^{-3}$, and the relative change in strain, and therefore in tension, is about $5\%$ which would cause a pitch shift of the order of a semitone - unless the thermal expansion of the body of the instrument (which is usually a different material) happens to cancel out that effect exactly. Nov 13, 2018 at 15:29