Calculate Young's modulus from longitudinal mode
Mathematical Formula:
E = 4 ρ L2 f2
Note: Decimal separator is dot (.)
E (GPa): 178.0673 ± 5.7716
Sensitivity to ρ: 0.3971 GPa, Sensitivity to L: 0.2722 GPa, Sensitivity to f: 0.8765 GPa
E min (GPa): 169.314
E max (GPa): 187.160
Numerical plus (GPa): 9.09
Numerical minus (GPa): 8.75
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Further Reading
- Louchet, J. (2010). The Keyboard Stringing Guide. Lulu Enterprises Incorporated.
- Harold A Conklin Jr, Longitudinal string modes
- Patent US3523480A: Longitudinal mode tuning of stringed instruments
- Polak, R. D., Davenport, A. R. V., Fischer, A., & Rafferty, J. (2018). Determining Young’s modulus by measuring guitar string frequency. The Physics Teacher, 56(2), 122–123. doi:10.1119/1.5021447
- Pols, F. (2021). The sound of music: determining Young’s modulus using a guitar string. Physics Education, 56(3), 035027. doi: 10.1088/1361-6552/abef07
© Aleksander Bogucki