A steel string guitar is strung so that there is negligible tension in the strin

Question

A steel string guitar is strung so that there is negligible tension in the strings at a temperature of 24.9 °C. The guitar is taken to an outdoor winter concert where the temperature of the strings decreases to –15.1 °C. The cross-sectional area of a particular string is 5.5 × 10–6 m2. The distance between the points where the string is attached does not change. For steel, Young's modulus is 2.0 × 1011 N/m2; and the coefficient of linear expansion is 1.2 × 10–5/C°. Use your knowledge of linear thermal expansion and stress to calculate the tension in the string at the concert.

Explanation / Answer

Let the length of string is L ,

Now,

change in temperature , del T = 24.9 - (-15.1) C

del T = 40 C

change in length , l = L*thermal coefficient * del T

l = L*1.2 *10^-5 * 40

l = 4.8 *10^-4 *L

let T be the tension in the string

stress = Young modulus * strain

T/(5.5 *10^-6) = 2 *10^11 * (4.8 *10^-4 L)/L

T = 528 N

the tension in the string is 528 N

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