Calculate Longitudinal Mode Frequencies

Mathematical Formula:

f_n = n × (1/2L) × √(E/ρ)

Note: Decimal separator is dot (.)

Young's Modulus, E (GPa): ±δE (GPa):

String density, ρ (kg/m³): ±δρ (kg/m³):

String length, L (mm): ±δL (mm):

Maximum mode number, n_max:

Young's Modulus Calculator
Rod Density Calculator
String Frequency Calculator
String Tension Calculator
Humidity Calculator

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